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

Percentage Accurate: 85.8% → 92.3%

Time: 12.6s

Alternatives: 18

Speedup: 0.5×

• 51.4% 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: 85.8% 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: 92.3% accurate, 0.5× speedup

Math

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   4. Applied rewrites 95.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   7. Applied rewrites 74.5%

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

4. Final simplification 93.1%

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

Alternative 2: 92.3% accurate, 0.5× speedup

Math

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. distribute-lft-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 95.6

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 95.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   7. Applied rewrites 74.5%

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

Alternative 3: 92.3% accurate, 0.5× speedup

Math

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   4. Applied rewrites 95.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   7. Applied rewrites 74.5%

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

Alternative 4: 80.2% accurate, 0.6× speedup

Math

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 20.3

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

   5. Applied rewrites 20.3%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

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

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

      4. metadata-eval N/A

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

      5. associate--r- N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   8. Applied rewrites 89.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   7. Applied rewrites 74.5%

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

Alternative 5: 37.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot a\right) \cdot t\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+60}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-130}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 a) t)))
   (if (<= (* b c) -5e+60)
     (* c b)
     (if (<= (* b c) -5e-302)
       (* (* k j) -27.0)
       (if (<= (* b c) 1e-297)
         t_1
         (if (<= (* b c) 1e-130)
           (* (* -4.0 x) i)
           (if (<= (* b c) 2e+116) t_1 (* c b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (k * j) * -27.0;
	} else if ((b * c) <= 1e-297) {
		tmp = t_1;
	} else if ((b * c) <= 1e-130) {
		tmp = (-4.0 * x) * i;
	} else if ((b * c) <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * a) * t
    if ((b * c) <= (-5d+60)) then
        tmp = c * b
    else if ((b * c) <= (-5d-302)) then
        tmp = (k * j) * (-27.0d0)
    else if ((b * c) <= 1d-297) then
        tmp = t_1
    else if ((b * c) <= 1d-130) then
        tmp = ((-4.0d0) * x) * i
    else if ((b * c) <= 2d+116) then
        tmp = t_1
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (k * j) * -27.0;
	} else if ((b * c) <= 1e-297) {
		tmp = t_1;
	} else if ((b * c) <= 1e-130) {
		tmp = (-4.0 * x) * i;
	} else if ((b * c) <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * a) * t
	tmp = 0
	if (b * c) <= -5e+60:
		tmp = c * b
	elif (b * c) <= -5e-302:
		tmp = (k * j) * -27.0
	elif (b * c) <= 1e-297:
		tmp = t_1
	elif (b * c) <= 1e-130:
		tmp = (-4.0 * x) * i
	elif (b * c) <= 2e+116:
		tmp = t_1
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * a) * t)
	tmp = 0.0
	if (Float64(b * c) <= -5e+60)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -5e-302)
		tmp = Float64(Float64(k * j) * -27.0);
	elseif (Float64(b * c) <= 1e-297)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-130)
		tmp = Float64(Float64(-4.0 * x) * i);
	elseif (Float64(b * c) <= 2e+116)
		tmp = t_1;
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * a) * t;
	tmp = 0.0;
	if ((b * c) <= -5e+60)
		tmp = c * b;
	elseif ((b * c) <= -5e-302)
		tmp = (k * j) * -27.0;
	elseif ((b * c) <= 1e-297)
		tmp = t_1;
	elseif ((b * c) <= 1e-130)
		tmp = (-4.0 * x) * i;
	elseif ((b * c) <= 2e+116)
		tmp = t_1;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+60], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-302], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-297], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-130], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+116], t$95$1, N[(c * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.99999999999999975e60 or 2.00000000000000003e116 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.1

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

      13. *-commutative N/A

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 60.3

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

   11. Applied rewrites 60.3%

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

   if -4.99999999999999975e60 < (*.f64 b c) < -5.00000000000000033e-302

   1. Initial program 84.4%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 37.4

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

   5. Applied rewrites 37.4%

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

   7. Applied rewrites 37.5%

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

   if -5.00000000000000033e-302 < (*.f64 b c) < 1.00000000000000004e-297 or 1.0000000000000001e-130 < (*.f64 b c) < 2.00000000000000003e116

   1. Initial program 84.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. distribute-lft-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 87.5

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 37.6

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

   7. Applied rewrites 37.6%

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

   9. Applied rewrites 37.6%

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

   if 1.00000000000000004e-297 < (*.f64 b c) < 1.0000000000000001e-130

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

Alternative 6: 37.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot a\right) \cdot t\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+60}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;b \cdot c \leq 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-130}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 a) t)))
   (if (<= (* b c) -5e+60)
     (* c b)
     (if (<= (* b c) -5e-302)
       (* (* k -27.0) j)
       (if (<= (* b c) 1e-297)
         t_1
         (if (<= (* b c) 1e-130)
           (* (* -4.0 x) i)
           (if (<= (* b c) 2e+116) t_1 (* c b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (k * -27.0) * j;
	} else if ((b * c) <= 1e-297) {
		tmp = t_1;
	} else if ((b * c) <= 1e-130) {
		tmp = (-4.0 * x) * i;
	} else if ((b * c) <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * a) * t
    if ((b * c) <= (-5d+60)) then
        tmp = c * b
    else if ((b * c) <= (-5d-302)) then
        tmp = (k * (-27.0d0)) * j
    else if ((b * c) <= 1d-297) then
        tmp = t_1
    else if ((b * c) <= 1d-130) then
        tmp = ((-4.0d0) * x) * i
    else if ((b * c) <= 2d+116) then
        tmp = t_1
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (k * -27.0) * j;
	} else if ((b * c) <= 1e-297) {
		tmp = t_1;
	} else if ((b * c) <= 1e-130) {
		tmp = (-4.0 * x) * i;
	} else if ((b * c) <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * a) * t
	tmp = 0
	if (b * c) <= -5e+60:
		tmp = c * b
	elif (b * c) <= -5e-302:
		tmp = (k * -27.0) * j
	elif (b * c) <= 1e-297:
		tmp = t_1
	elif (b * c) <= 1e-130:
		tmp = (-4.0 * x) * i
	elif (b * c) <= 2e+116:
		tmp = t_1
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * a) * t)
	tmp = 0.0
	if (Float64(b * c) <= -5e+60)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -5e-302)
		tmp = Float64(Float64(k * -27.0) * j);
	elseif (Float64(b * c) <= 1e-297)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-130)
		tmp = Float64(Float64(-4.0 * x) * i);
	elseif (Float64(b * c) <= 2e+116)
		tmp = t_1;
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * a) * t;
	tmp = 0.0;
	if ((b * c) <= -5e+60)
		tmp = c * b;
	elseif ((b * c) <= -5e-302)
		tmp = (k * -27.0) * j;
	elseif ((b * c) <= 1e-297)
		tmp = t_1;
	elseif ((b * c) <= 1e-130)
		tmp = (-4.0 * x) * i;
	elseif ((b * c) <= 2e+116)
		tmp = t_1;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+60], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-302], N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-297], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-130], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+116], t$95$1, N[(c * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.99999999999999975e60 or 2.00000000000000003e116 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.1

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

      13. *-commutative N/A

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 60.3

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

   11. Applied rewrites 60.3%

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

   if -4.99999999999999975e60 < (*.f64 b c) < -5.00000000000000033e-302

   1. Initial program 84.4%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 37.4

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

   5. Applied rewrites 37.4%

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

   7. Applied rewrites 37.4%

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

   if -5.00000000000000033e-302 < (*.f64 b c) < 1.00000000000000004e-297 or 1.0000000000000001e-130 < (*.f64 b c) < 2.00000000000000003e116

   1. Initial program 84.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. distribute-lft-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 87.5

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 37.6

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

   7. Applied rewrites 37.6%

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

   9. Applied rewrites 37.6%

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

   if 1.00000000000000004e-297 < (*.f64 b c) < 1.0000000000000001e-130

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

Alternative 7: 37.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot a\right) \cdot t\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+60}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-130}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 a) t)))
   (if (<= (* b c) -5e+60)
     (* c b)
     (if (<= (* b c) -5e-302)
       (* (* -27.0 j) k)
       (if (<= (* b c) 1e-297)
         t_1
         (if (<= (* b c) 1e-130)
           (* (* -4.0 x) i)
           (if (<= (* b c) 2e+116) t_1 (* c b))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 1e-297) {
		tmp = t_1;
	} else if ((b * c) <= 1e-130) {
		tmp = (-4.0 * x) * i;
	} else if ((b * c) <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * a) * t
    if ((b * c) <= (-5d+60)) then
        tmp = c * b
    else if ((b * c) <= (-5d-302)) then
        tmp = ((-27.0d0) * j) * k
    else if ((b * c) <= 1d-297) then
        tmp = t_1
    else if ((b * c) <= 1d-130) then
        tmp = ((-4.0d0) * x) * i
    else if ((b * c) <= 2d+116) then
        tmp = t_1
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 1e-297) {
		tmp = t_1;
	} else if ((b * c) <= 1e-130) {
		tmp = (-4.0 * x) * i;
	} else if ((b * c) <= 2e+116) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * a) * t
	tmp = 0
	if (b * c) <= -5e+60:
		tmp = c * b
	elif (b * c) <= -5e-302:
		tmp = (-27.0 * j) * k
	elif (b * c) <= 1e-297:
		tmp = t_1
	elif (b * c) <= 1e-130:
		tmp = (-4.0 * x) * i
	elif (b * c) <= 2e+116:
		tmp = t_1
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * a) * t)
	tmp = 0.0
	if (Float64(b * c) <= -5e+60)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -5e-302)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (Float64(b * c) <= 1e-297)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-130)
		tmp = Float64(Float64(-4.0 * x) * i);
	elseif (Float64(b * c) <= 2e+116)
		tmp = t_1;
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * a) * t;
	tmp = 0.0;
	if ((b * c) <= -5e+60)
		tmp = c * b;
	elseif ((b * c) <= -5e-302)
		tmp = (-27.0 * j) * k;
	elseif ((b * c) <= 1e-297)
		tmp = t_1;
	elseif ((b * c) <= 1e-130)
		tmp = (-4.0 * x) * i;
	elseif ((b * c) <= 2e+116)
		tmp = t_1;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+60], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-302], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-297], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-130], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+116], t$95$1, N[(c * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.99999999999999975e60 or 2.00000000000000003e116 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.1

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

      13. *-commutative N/A

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 60.3

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

   11. Applied rewrites 60.3%

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

   if -4.99999999999999975e60 < (*.f64 b c) < -5.00000000000000033e-302

   1. Initial program 84.4%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 37.4

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

   5. Applied rewrites 37.4%

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

   if -5.00000000000000033e-302 < (*.f64 b c) < 1.00000000000000004e-297 or 1.0000000000000001e-130 < (*.f64 b c) < 2.00000000000000003e116

   1. Initial program 84.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. distribute-lft-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 87.5

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 37.6

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

   7. Applied rewrites 37.6%

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

   9. Applied rewrites 37.6%

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

   if 1.00000000000000004e-297 < (*.f64 b c) < 1.0000000000000001e-130

   1. Initial program 83.3%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

Alternative 8: 82.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+250}:\\ \;\;\;\;t\_2 \cdot x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, x, c \cdot b\right) - t\_1\\ \end{array} \end{array} \]

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 (* (* j 27.0) k)) (t_2 (fma -4.0 i (* (* (* z y) t) 18.0))))
   (if (<= x -5.4e+250)
     (* t_2 x)
     (if (<= x 1.5e+70)
       (- (fma c b (* -4.0 (fma i x (* a t)))) t_1)
       (- (fma t_2 x (* c b)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = fma(-4.0, i, (((z * y) * t) * 18.0));
	double tmp;
	if (x <= -5.4e+250) {
		tmp = t_2 * x;
	} else if (x <= 1.5e+70) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - t_1;
	} else {
		tmp = fma(t_2, x, (c * b)) - 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(j * 27.0) * k)
	t_2 = fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0))
	tmp = 0.0
	if (x <= -5.4e+250)
		tmp = Float64(t_2 * x);
	elseif (x <= 1.5e+70)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - t_1);
	else
		tmp = Float64(fma(t_2, x, Float64(c * b)) - 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+250], N[(t$95$2 * x), $MachinePrecision], If[LessEqual[x, 1.5e+70], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t$95$2 * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4e250

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -5.4e250 < x < 1.49999999999999988e70

   1. Initial program 90.4%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 90.4

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

   5. Applied rewrites 90.4%

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

   if 1.49999999999999988e70 < x

   1. Initial program 65.1%

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

   3. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*l* N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 92.3%

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

Alternative 9: 82.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+250}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, -4 \cdot i\right), x, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -5.4e+250)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x 1.5e+70)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (fma (fma (* (* y z) t) 18.0 (* -4.0 i)) x (fma -27.0 (* k j) (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -5.4e+250) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= 1.5e+70) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma(fma(((y * z) * t), 18.0, (-4.0 * i)), x, fma(-27.0, (k * j), (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -5.4e+250)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= 1.5e+70)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(fma(Float64(Float64(y * z) * t), 18.0, Float64(-4.0 * i)), x, fma(-27.0, Float64(k * j), Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -5.4e+250], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.5e+70], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(-27.0 * N[(k * j), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4e250

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -5.4e250 < x < 1.49999999999999988e70

   1. Initial program 90.4%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 90.4

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

   5. Applied rewrites 90.4%

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

   if 1.49999999999999988e70 < x

   1. Initial program 65.1%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 16.6

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

   5. Applied rewrites 16.6%

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

   6. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   8. Applied rewrites 92.2%

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

Alternative 10: 68.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+196}:\\ \;\;\;\;\mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+263}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+196)
     (fma -27.0 (* k j) (* b c))
     (if (<= t_1 5e+263)
       (fma (fma i x (* a t)) -4.0 (* c b))
       (* (* -27.0 j) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = fma(-27.0, (k * j), (b * c));
	} else if (t_1 <= 5e+263) {
		tmp = fma(fma(i, x, (a * t)), -4.0, (c * b));
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+196)
		tmp = fma(-27.0, Float64(k * j), Float64(b * c));
	elseif (t_1 <= 5e+263)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, Float64(c * b));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -5e+196], N[(-27.0 * N[(k * j), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+263], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999998e196

   1. Initial program 75.7%

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

   3. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 79.5%

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

   if -4.9999999999999998e196 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000022e263

   1. Initial program 86.1%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 9.4

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

   5. Applied rewrites 9.4%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

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

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

      4. metadata-eval N/A

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

      5. associate--r- N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   8. Applied rewrites 83.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 59.0%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 74.6%

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

   if 5.00000000000000022e263 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 69.2%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 11: 70.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, x, a \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+15} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(t\_1, -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -4, -27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma i x (* a t))))
   (if (or (<= (* b c) -9e+15) (not (<= (* b c) 5e+26)))
     (fma t_1 -4.0 (* c b))
     (fma t_1 -4.0 (* -27.0 (* k j))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(i, x, (a * t));
	double tmp;
	if (((b * c) <= -9e+15) || !((b * c) <= 5e+26)) {
		tmp = fma(t_1, -4.0, (c * b));
	} else {
		tmp = fma(t_1, -4.0, (-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 = fma(i, x, Float64(a * t))
	tmp = 0.0
	if ((Float64(b * c) <= -9e+15) || !(Float64(b * c) <= 5e+26))
		tmp = fma(t_1, -4.0, Float64(c * b));
	else
		tmp = fma(t_1, -4.0, Float64(-27.0 * Float64(k * j)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(b * c), $MachinePrecision], -9e+15], N[Not[LessEqual[N[(b * c), $MachinePrecision], 5e+26]], $MachinePrecision]], N[(t$95$1 * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9e15 or 5.0000000000000001e26 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 12.8

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

   5. Applied rewrites 12.8%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

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

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

      4. metadata-eval N/A

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

      5. associate--r- N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 42.5%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 80.4%

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

   if -9e15 < (*.f64 b c) < 5.0000000000000001e26

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 27.2

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

   5. Applied rewrites 27.2%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

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

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

      4. metadata-eval N/A

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

      5. associate--r- N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   8. Applied rewrites 79.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 76.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9 \cdot 10^{+15} \lor \neg \left(b \cdot c \leq 5 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+250}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(t \cdot 18\right), i \cdot -4\right) \cdot x\\ \end{array} \end{array} \]

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
 (if (<= x -5.4e+250)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x 1.7e+88)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (* (fma y (* z (* t 18.0)) (* 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 tmp;
	if (x <= -5.4e+250) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= 1.7e+88) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma(y, (z * (t * 18.0)), (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)
	tmp = 0.0
	if (x <= -5.4e+250)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= 1.7e+88)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(y, Float64(z * Float64(t * 18.0)), 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_] := If[LessEqual[x, -5.4e+250], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.7e+88], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4e250

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -5.4e250 < x < 1.70000000000000002e88

   1. Initial program 90.1%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 90.1

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

   5. Applied rewrites 90.1%

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

   if 1.70000000000000002e88 < x

   1. Initial program 64.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

   7. Applied rewrites 83.7%

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

Alternative 13: 70.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+250}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-106}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \left(t \cdot 18\right), i \cdot -4\right) \cdot x\\ \end{array} \end{array} \]

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
 (if (<= x -4.4e+250)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x -1.7e-106)
     (fma (fma i x (* a t)) -4.0 (* c b))
     (if (<= x 5e+87)
       (fma (* t -4.0) a (fma (* k j) -27.0 (* c b)))
       (* (fma y (* z (* t 18.0)) (* 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 tmp;
	if (x <= -4.4e+250) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= -1.7e-106) {
		tmp = fma(fma(i, x, (a * t)), -4.0, (c * b));
	} else if (x <= 5e+87) {
		tmp = fma((t * -4.0), a, fma((k * j), -27.0, (c * b)));
	} else {
		tmp = fma(y, (z * (t * 18.0)), (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)
	tmp = 0.0
	if (x <= -4.4e+250)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= -1.7e-106)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, Float64(c * b));
	elseif (x <= 5e+87)
		tmp = fma(Float64(t * -4.0), a, fma(Float64(k * j), -27.0, Float64(c * b)));
	else
		tmp = Float64(fma(y, Float64(z * Float64(t * 18.0)), 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_] := If[LessEqual[x, -4.4e+250], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -1.7e-106], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+87], N[(N[(t * -4.0), $MachinePrecision] * a + N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.40000000000000029e250

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -4.40000000000000029e250 < x < -1.69999999999999991e-106

   1. Initial program 88.3%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 13.9

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

   5. Applied rewrites 13.9%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

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

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

      4. metadata-eval N/A

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

      5. associate--r- N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   8. Applied rewrites 87.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 67.0%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 81.2%

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

   if -1.69999999999999991e-106 < x < 4.9999999999999998e87

   1. Initial program 90.8%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 28.9

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

   5. Applied rewrites 28.9%

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

   6. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 81.8

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

   8. Applied rewrites 81.8%

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

   10. Applied rewrites 83.3%

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

   if 4.9999999999999998e87 < x

   1. Initial program 64.3%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

   7. Applied rewrites 83.7%

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

Alternative 14: 36.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+60}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+116}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+60)
   (* c b)
   (if (<= (* b c) -5e-302)
     (* (* -27.0 j) k)
     (if (<= (* b c) 2e+116) (* (* -4.0 a) t) (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 2e+116) {
		tmp = (-4.0 * a) * t;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-5d+60)) then
        tmp = c * b
    else if ((b * c) <= (-5d-302)) then
        tmp = ((-27.0d0) * j) * k
    else if ((b * c) <= 2d+116) then
        tmp = ((-4.0d0) * a) * t
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+60) {
		tmp = c * b;
	} else if ((b * c) <= -5e-302) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 2e+116) {
		tmp = (-4.0 * a) * t;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5e+60:
		tmp = c * b
	elif (b * c) <= -5e-302:
		tmp = (-27.0 * j) * k
	elif (b * c) <= 2e+116:
		tmp = (-4.0 * a) * t
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+60)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -5e-302)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (Float64(b * c) <= 2e+116)
		tmp = Float64(Float64(-4.0 * a) * t);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5e+60)
		tmp = c * b;
	elseif ((b * c) <= -5e-302)
		tmp = (-27.0 * j) * k;
	elseif ((b * c) <= 2e+116)
		tmp = (-4.0 * a) * t;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+60], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-302], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+116], N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.99999999999999975e60 or 2.00000000000000003e116 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.1

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-in N/A

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

      13. *-commutative N/A

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 60.3

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

   11. Applied rewrites 60.3%

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

   if -4.99999999999999975e60 < (*.f64 b c) < -5.00000000000000033e-302

   1. Initial program 84.4%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 37.4

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

   5. Applied rewrites 37.4%

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

   if -5.00000000000000033e-302 < (*.f64 b c) < 2.00000000000000003e116

   1. Initial program 83.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. distribute-lft-neg-in N/A

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 86.6

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 34.5

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

   7. Applied rewrites 34.5%

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

   9. Applied rewrites 34.5%

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

Alternative 15: 53.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{-9} \lor \neg \left(b \cdot c \leq 2000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \end{array} \end{array} \]

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 (or (<= (* b c) -5e-9) (not (<= (* b c) 2000000000000.0)))
   (fma -27.0 (* k j) (* b c))
   (* (fma i x (* a t)) -4.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5e-9) || !((b * c) <= 2000000000000.0)) {
		tmp = fma(-27.0, (k * j), (b * c));
	} else {
		tmp = fma(i, x, (a * t)) * -4.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -5e-9) || !(Float64(b * c) <= 2000000000000.0))
		tmp = fma(-27.0, Float64(k * j), Float64(b * c));
	else
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -5e-9], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2000000000000.0]], $MachinePrecision]], N[(-27.0 * N[(k * j), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.0000000000000001e-9 or 2e12 < (*.f64 b c)

   1. Initial program 83.8%

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

   3. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 64.1%

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

   if -5.0000000000000001e-9 < (*.f64 b c) < 2e12

   1. Initial program 84.3%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 23.5

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

   5. Applied rewrites 23.5%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

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

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

      4. metadata-eval N/A

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

      5. associate--r- N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. associate-+r+ N/A

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

   8. Applied rewrites 79.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 76.7%

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

   12. Taylor expanded in j around 0

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

   14. Applied rewrites 58.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{-9} \lor \neg \left(b \cdot c \leq 2000000000000\right):\\ \;\;\;\;\mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+153} \lor \neg \left(b \cdot c \leq 4 \cdot 10^{+139}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \end{array} \end{array} \]

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 (or (<= (* b c) -1e+153) (not (<= (* b c) 4e+139)))
   (* c b)
   (* (fma i x (* a t)) -4.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -1e+153) || !((b * c) <= 4e+139)) {
		tmp = c * b;
	} else {
		tmp = fma(i, x, (a * t)) * -4.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -1e+153) || !(Float64(b * c) <= 4e+139))
		tmp = Float64(c * b);
	else
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -1e+153], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4e+139]], $MachinePrecision]], N[(c * b), $MachinePrecision], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1e153 or 4.00000000000000013e139 < (*.f64 b c)

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      9. lower-*.f64 88.0

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. associate--l+ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-4 \cdot i\right) \cdot x} + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      12. distribute-rgt-in N/A

          \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   8. Applied rewrites 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, \mathsf{fma}\left(-27, k \cdot j, c \cdot b\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{c \cdot b} \]

       2. lower-*.f64 70.9

          \[\leadsto \color{blue}{c \cdot b} \]

   11. Applied rewrites 70.9%

       \[\leadsto \color{blue}{c \cdot b} \]

   if -1e153 < (*.f64 b c) < 4.00000000000000013e139

   1. Initial program 84.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      3. lower-*.f64 25.6

         \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

   5. Applied rewrites 25.6%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto b \cdot c - \color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) - \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)}\right) - 27 \cdot \left(j \cdot k\right) \]

      4. metadata-eval N/A

         \[\leadsto \left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) - \color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      5. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) + -4 \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(\color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right)} + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(\left(b \cdot c + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      9. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      10. +-commutative N/A

          \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)}\right) - 27 \cdot \left(j \cdot k\right) \]

      11. associate-+r+ N/A

          \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

   8. Applied rewrites 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, \mathsf{fma}\left(t, a, i \cdot x\right), \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 74.5%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), \color{blue}{-4}, -27 \cdot \left(k \cdot j\right)\right) \]

   12. Taylor expanded in j around 0

       \[\leadsto -4 \cdot \left(a \cdot t + \color{blue}{i \cdot x}\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 54.4%

       \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+153} \lor \neg \left(b \cdot c \leq 4 \cdot 10^{+139}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+131} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+116}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -5e+131) (not (<= (* b c) 2e+116)))
   (* c b)
   (* (* -4.0 a) t)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5e+131) || !((b * c) <= 2e+116)) {
		tmp = c * b;
	} else {
		tmp = (-4.0 * a) * t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-5d+131)) .or. (.not. ((b * c) <= 2d+116))) then
        tmp = c * b
    else
        tmp = ((-4.0d0) * a) * t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -5e+131) || !((b * c) <= 2e+116)) {
		tmp = c * b;
	} else {
		tmp = (-4.0 * a) * t;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -5e+131) or not ((b * c) <= 2e+116):
		tmp = c * b
	else:
		tmp = (-4.0 * a) * t
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -5e+131) || !(Float64(b * c) <= 2e+116))
		tmp = Float64(c * b);
	else
		tmp = Float64(Float64(-4.0 * a) * t);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -5e+131) || ~(((b * c) <= 2e+116)))
		tmp = c * b;
	else
		tmp = (-4.0 * a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -5e+131], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2e+116]], $MachinePrecision]], N[(c * b), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.99999999999999995e131 or 2.00000000000000003e116 < (*.f64 b c)

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. distribute-lft-out N/A

         \[\leadsto \left(b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{c \cdot b} + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      9. lower-*.f64 87.6

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 87.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. associate--l+ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      7. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-4 \cdot i\right) \cdot x} + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      12. distribute-rgt-in N/A

          \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   8. Applied rewrites 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, \mathsf{fma}\left(-27, k \cdot j, c \cdot b\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{c \cdot b} \]

       2. lower-*.f64 66.5

          \[\leadsto \color{blue}{c \cdot b} \]

   11. Applied rewrites 66.5%

       \[\leadsto \color{blue}{c \cdot b} \]

   if -4.99999999999999995e131 < (*.f64 b c) < 2.00000000000000003e116

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(x \cdot 4\right)\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot 4\right)\right) \cdot i + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(x \cdot 4\right), i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{x \cdot 4}\right), i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{4 \cdot x}\right), i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot x}, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot x}, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      10. metadata-eval 87.6

          \[\leadsto \mathsf{fma}\left(\color{blue}{-4} \cdot x, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      11. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c}\right) - \left(j \cdot 27\right) \cdot k \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      13. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right) \cdot t}\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      15. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot -4} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

      4. lower-*.f64 30.7

         \[\leadsto \color{blue}{\left(t \cdot a\right)} \cdot -4 \]

   7. Applied rewrites 30.7%

      \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot -4} \]
   8. Step-by-step derivation

   9. Applied rewrites 30.7%

      \[\leadsto \left(-4 \cdot a\right) \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+131} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+116}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.0% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = c * b
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(c * b)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = c * b;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 84.0%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
4. Step-by-step derivation

   1. distribute-lft-out N/A

      \[\leadsto \left(b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   2. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. *-commutative N/A

      \[\leadsto \left(\color{blue}{c \cdot b} + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) - \left(j \cdot 27\right) \cdot k \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   8. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   9. lower-*.f64 83.2

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right)\right) - \left(j \cdot 27\right) \cdot k \]

5. Applied rewrites 83.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

6. Taylor expanded in a around 0

   \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
7. Step-by-step derivation

   1. associate--r+ N/A

      \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   2. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

   3. metadata-eval N/A

      \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

   5. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

   6. associate--l+ N/A

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

   7. associate-*r* N/A

      \[\leadsto \left(\color{blue}{\left(-4 \cdot i\right) \cdot x} + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   8. associate-*r* N/A

      \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   10. associate-*r* N/A

       \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x}\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   11. associate-*r* N/A

       \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   12. distribute-rgt-in N/A

       \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   13. *-commutative N/A

       \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

8. Applied rewrites 72.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, \mathsf{fma}\left(-27, k \cdot j, c \cdot b\right)\right)} \]

9. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
10. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \color{blue}{c \cdot b} \]

    2. lower-*.f64 24.9

       \[\leadsto \color{blue}{c \cdot b} \]

11. Applied rewrites 24.9%

    \[\leadsto \color{blue}{c \cdot b} \]
12. Add Preprocessing

Developer Target 1: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024363 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))