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

Percentage Accurate: 85.1% → 94.3%

Time: 14.2s

Alternatives: 21

Speedup: 1.2×

• 50.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot x\right) \cdot t, y \cdot 18, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, t\_1\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j)))
        (t_2
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_2 (- INFINITY))
     (fma (* (* z x) t) (* y 18.0) (fma c b (fma (fma i x (* a t)) -4.0 t_1)))
     (if (<= t_2 2e+292)
       t_2
       (fma
        (* -4.0 t)
        a
        (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(((z * x) * t), (y * 18.0), fma(c, b, fma(fma(i, x, (a * t)), -4.0, t_1)));
	} else if (t_2 <= 2e+292) {
		tmp = t_2;
	} else {
		tmp = fma((-4.0 * t), a, fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(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(-27.0 * Float64(k * j))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(Float64(z * x) * t), Float64(y * 18.0), fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, t_1)));
	elseif (t_2 <= 2e+292)
		tmp = t_2;
	else
		tmp = fma(Float64(-4.0 * t), a, fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(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[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision] * N[(y * 18.0), $MachinePrecision] + N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+292], t$95$2, N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 91.9%

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

   3. Applied rewrites 95.1%

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

   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)) < 2e292

   1. Initial program 99.4%

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

   if 2e292 < (-.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 61.7%

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

   3. Applied rewrites 83.8%

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

Alternative 2: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, t\_1\right)\right)\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot x\right) \cdot t, y \cdot 18, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j)))
        (t_2
         (fma
          (* -4.0 t)
          a
          (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b t_1)))))
   (if (<= x -5e-34)
     t_2
     (if (<= x 2.9e-91)
       (fma
        (* (* z x) t)
        (* y 18.0)
        (fma c b (fma (fma i x (* a t)) -4.0 t_1)))
       t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = fma((-4.0 * t), a, fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, t_1)));
	double tmp;
	if (x <= -5e-34) {
		tmp = t_2;
	} else if (x <= 2.9e-91) {
		tmp = fma(((z * x) * t), (y * 18.0), fma(c, b, fma(fma(i, x, (a * t)), -4.0, t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	t_2 = fma(Float64(-4.0 * t), a, fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, t_1)))
	tmp = 0.0
	if (x <= -5e-34)
		tmp = t_2;
	elseif (x <= 2.9e-91)
		tmp = fma(Float64(Float64(z * x) * t), Float64(y * 18.0), fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e-34], t$95$2, If[LessEqual[x, 2.9e-91], N[(N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision] * N[(y * 18.0), $MachinePrecision] + N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000003e-34 or 2.9000000000000001e-91 < x

   1. Initial program 78.7%

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

   3. Applied rewrites 93.0%

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

   if -5.0000000000000003e-34 < x < 2.9000000000000001e-91

   1. Initial program 94.6%

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

   3. Applied rewrites 96.1%

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

Alternative 3: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+238}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(b, c, \left(\left(x \cdot y\right) \cdot 18\right) \cdot \left(z \cdot t\right)\right) - \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -4.6e+238)
   (fma
    (* -27.0 j)
    k
    (- (fma b c (* (* (* x y) 18.0) (* z t))) (* (* a t) 4.0)))
   (fma
    (* -4.0 t)
    a
    (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b (* -27.0 (* k j)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -4.6e+238) {
		tmp = fma((-27.0 * j), k, (fma(b, c, (((x * y) * 18.0) * (z * t))) - ((a * t) * 4.0)));
	} else {
		tmp = fma((-4.0 * t), a, fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-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)
	tmp = 0.0
	if (y <= -4.6e+238)
		tmp = fma(Float64(-27.0 * j), k, Float64(fma(b, c, Float64(Float64(Float64(x * y) * 18.0) * Float64(z * t))) - Float64(Float64(a * t) * 4.0)));
	else
		tmp = fma(Float64(-4.0 * t), a, fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, 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_] := If[LessEqual[y, -4.6e+238], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(b * c + N[(N[(N[(x * y), $MachinePrecision] * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.60000000000000005e238

   1. Initial program 70.5%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 75.7%

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

   6. Applied rewrites 77.3%

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

   if -4.60000000000000005e238 < y

   1. Initial program 86.8%

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

   3. Applied rewrites 91.6%

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

Alternative 4: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+164}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq -10000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2000000:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, i, \left(\left(t \cdot y\right) \cdot z\right) \cdot 18\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -27.0 j)
          k
          (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b))))
        (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+164)
     (fma (* -4.0 t) a (fma (* i -4.0) x (fma c b (* -27.0 (* k j)))))
     (if (<= t_2 -10000000000000.0)
       t_1
       (if (<= t_2 2000000.0)
         (fma (* -4.0 t) a (fma c b (* (fma -4.0 i (* (* (* t y) z) 18.0)) x)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+164) {
		tmp = fma((-4.0 * t), a, fma((i * -4.0), x, fma(c, b, (-27.0 * (k * j)))));
	} else if (t_2 <= -10000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2000000.0) {
		tmp = fma((-4.0 * t), a, fma(c, b, (fma(-4.0, i, (((t * y) * z) * 18.0)) * x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+164)
		tmp = fma(Float64(-4.0 * t), a, fma(Float64(i * -4.0), x, fma(c, b, Float64(-27.0 * Float64(k * j)))));
	elseif (t_2 <= -10000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2000000.0)
		tmp = fma(Float64(-4.0 * t), a, fma(c, b, Float64(fma(-4.0, i, Float64(Float64(Float64(t * y) * z) * 18.0)) * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+164], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(i * -4.0), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -10000000000000.0], t$95$1, If[LessEqual[t$95$2, 2000000.0], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(c * b + N[(N[(-4.0 * i + N[(N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e164

   1. Initial program 79.1%

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

   3. Applied rewrites 86.6%

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

   4. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 84.1

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

   6. Applied rewrites 84.1%

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

   if -2e164 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e13 or 2e6 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.5%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 80.6%

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

   if -1e13 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e6

   1. Initial program 87.0%

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

   3. Applied rewrites 92.0%

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

   4. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.1

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

   6. Applied rewrites 76.1%

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

   7. Taylor expanded in b around inf

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

      1. lower-*.f64 73.8

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

   9. Applied rewrites 73.8%

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

   10. Taylor expanded in j around 0

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

       1. *-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lower-fma.f64 N/A

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

       6. *-commutative N/A

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

       7. associate-*r* N/A

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

       8. *-commutative N/A

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

       9. lift-*.f64 N/A

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

       10. lift-*.f64 N/A

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

       11. lower-*.f64 90.2

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

       12. lift-*.f64 N/A

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

       13. *-commutative N/A

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

       14. lower-*.f64 90.2

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

   12. Applied rewrites 90.2%

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

Alternative 5: 86.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -27.0 j)
          k
          (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))))
   (if (<= t -1.05e-13)
     t_1
     (if (<= t 3.6e+29)
       (fma (* -4.0 t) a (fma (* i -4.0) x (fma c b (* -27.0 (* k j)))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	double tmp;
	if (t <= -1.05e-13) {
		tmp = t_1;
	} else if (t <= 3.6e+29) {
		tmp = fma((-4.0 * t), a, fma((i * -4.0), x, fma(c, b, (-27.0 * (k * j)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)))
	tmp = 0.0
	if (t <= -1.05e-13)
		tmp = t_1;
	elseif (t <= 3.6e+29)
		tmp = fma(Float64(-4.0 * t), a, fma(Float64(i * -4.0), x, fma(c, b, Float64(-27.0 * Float64(k * j)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-13], t$95$1, If[LessEqual[t, 3.6e+29], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(i * -4.0), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999994e-13 or 3.59999999999999976e29 < t

   1. Initial program 83.4%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 86.3%

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

   if -1.04999999999999994e-13 < t < 3.59999999999999976e29

   1. Initial program 86.6%

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

   3. Applied rewrites 92.5%

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

   4. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 86.7

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

   6. Applied rewrites 86.7%

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

Alternative 6: 81.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right), t, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* y z) x) 18.0 (* a -4.0)) t (* (* j k) -27.0))))
   (if (<= t -4.5e+96)
     t_1
     (if (<= t 4.2e+30)
       (fma (* -4.0 t) a (fma (* i -4.0) x (fma c b (* -27.0 (* k j)))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(fma(((y * z) * x), 18.0, (a * -4.0)), t, ((j * k) * -27.0));
	double tmp;
	if (t <= -4.5e+96) {
		tmp = t_1;
	} else if (t <= 4.2e+30) {
		tmp = fma((-4.0 * t), a, fma((i * -4.0), x, fma(c, b, (-27.0 * (k * j)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)), t, Float64(Float64(j * k) * -27.0))
	tmp = 0.0
	if (t <= -4.5e+96)
		tmp = t_1;
	elseif (t <= 4.2e+30)
		tmp = fma(Float64(-4.0 * t), a, fma(Float64(i * -4.0), x, fma(c, b, Float64(-27.0 * Float64(k * j)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+96], t$95$1, If[LessEqual[t, 4.2e+30], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(i * -4.0), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999957e96 or 4.2e30 < t

   1. Initial program 82.2%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 77.1

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

   7. Applied rewrites 77.1%

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

   if -4.49999999999999957e96 < t < 4.2e30

   1. Initial program 86.9%

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

   3. Applied rewrites 92.5%

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

   4. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.1

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

   6. Applied rewrites 85.1%

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

Alternative 7: 81.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right), t, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* y z) x) 18.0 (* a -4.0)) t (* (* j k) -27.0))))
   (if (<= t -3.9e+96)
     t_1
     (if (<= t 4e+30)
       (- (fma (fma i x (* a t)) -4.0 (* c b)) (* (* j 27.0) k))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(fma(((y * z) * x), 18.0, (a * -4.0)), t, ((j * k) * -27.0));
	double tmp;
	if (t <= -3.9e+96) {
		tmp = t_1;
	} else if (t <= 4e+30) {
		tmp = fma(fma(i, x, (a * t)), -4.0, (c * b)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)), t, Float64(Float64(j * k) * -27.0))
	tmp = 0.0
	if (t <= -3.9e+96)
		tmp = t_1;
	elseif (t <= 4e+30)
		tmp = Float64(fma(fma(i, x, Float64(a * t)), -4.0, Float64(c * b)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+96], t$95$1, If[LessEqual[t, 4e+30], N[(N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e96 or 4.0000000000000001e30 < t

   1. Initial program 82.2%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 77.1

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

   7. Applied rewrites 77.1%

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

   if -3.9e96 < t < 4.0000000000000001e30

   1. Initial program 86.9%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. associate--r- N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

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

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

      9. metadata-eval N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

   4. Applied rewrites 84.0%

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

Alternative 8: 78.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+246}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \end{array} \]

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 (<= x -2.45e+148)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x 9.5e+246)
     (- (fma (fma i x (* a t)) -4.0 (* c b)) (* (* j 27.0) k))
     (* (fma -4.0 a (* (* (* z y) x) 18.0)) 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 (x <= -2.45e+148) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= 9.5e+246) {
		tmp = fma(fma(i, x, (a * t)), -4.0, (c * b)) - ((j * 27.0) * k);
	} else {
		tmp = fma(-4.0, a, (((z * y) * x) * 18.0)) * 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 (x <= -2.45e+148)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= 9.5e+246)
		tmp = Float64(fma(fma(i, x, Float64(a * t)), -4.0, Float64(c * b)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.45e+148], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 9.5e+246], N[(N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.45e148

   1. Initial program 68.3%

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

   2. Taylor expanded in x around inf

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

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

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

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

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

      5. distribute-lft-neg-out N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-neg-out N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

      11. distribute-rgt-neg-in N/A

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

      12. mul-1-neg N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

   4. Applied rewrites 76.6%

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

   if -2.45e148 < x < 9.50000000000000055e246

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. associate--r- N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

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

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

      9. metadata-eval N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

   4. Applied rewrites 80.4%

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

   if 9.50000000000000055e246 < x

   1. Initial program 66.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 56.9

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

   4. Applied rewrites 56.9%

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

Alternative 9: 73.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(i \cdot -4, x, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot z, 18, i \cdot -4\right) \cdot x\\ \end{array} \end{array} \]

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 -1.06e+141)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x -2.7e-62)
     (fma (* -4.0 t) a (fma (* i -4.0) x (* (* j k) -27.0)))
     (if (<= x 2.3e+98)
       (fma (* -4.0 t) a (fma (* k -27.0) j (* b c)))
       (* (fma (* (* y t) z) 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 <= -1.06e+141) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= -2.7e-62) {
		tmp = fma((-4.0 * t), a, fma((i * -4.0), x, ((j * k) * -27.0)));
	} else if (x <= 2.3e+98) {
		tmp = fma((-4.0 * t), a, fma((k * -27.0), j, (b * c)));
	} else {
		tmp = fma(((y * t) * z), 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 <= -1.06e+141)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= -2.7e-62)
		tmp = fma(Float64(-4.0 * t), a, fma(Float64(i * -4.0), x, Float64(Float64(j * k) * -27.0)));
	elseif (x <= 2.3e+98)
		tmp = fma(Float64(-4.0 * t), a, fma(Float64(k * -27.0), j, Float64(b * c)));
	else
		tmp = Float64(fma(Float64(Float64(y * t) * z), 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, -1.06e+141], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -2.7e-62], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(i * -4.0), $MachinePrecision] * x + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+98], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.05999999999999997e141

   1. Initial program 69.1%

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

   2. Taylor expanded in x around inf

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

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

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

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

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

      5. distribute-lft-neg-out N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-neg-out N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

      11. distribute-rgt-neg-in N/A

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

      12. mul-1-neg N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

   4. Applied rewrites 76.1%

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

   if -1.05999999999999997e141 < x < -2.70000000000000019e-62

   1. Initial program 86.5%

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

   3. Applied rewrites 92.7%

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

   4. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.6

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

   6. Applied rewrites 78.6%

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

   7. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 60.6

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

   9. Applied rewrites 60.6%

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

   if -2.70000000000000019e-62 < x < 2.30000000000000013e98

   1. Initial program 93.1%

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

   3. Applied rewrites 88.3%

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

   4. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 77.0

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

   6. Applied rewrites 77.0%

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

   if 2.30000000000000013e98 < x

   1. Initial program 71.3%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.4

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

   4. Applied rewrites 15.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 72.4

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

   7. Applied rewrites 72.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 72.9

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

   9. Applied rewrites 72.9%

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

Alternative 10: 72.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot z, 18, i \cdot -4\right) \cdot x\\ \end{array} \end{array} \]

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 -3.4e+131)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x 2.3e+98)
     (fma (* j k) -27.0 (fma (* a t) -4.0 (* b c)))
     (* (fma (* (* y t) z) 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 <= -3.4e+131) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= 2.3e+98) {
		tmp = fma((j * k), -27.0, fma((a * t), -4.0, (b * c)));
	} else {
		tmp = fma(((y * t) * z), 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 <= -3.4e+131)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= 2.3e+98)
		tmp = fma(Float64(j * k), -27.0, fma(Float64(a * t), -4.0, Float64(b * c)));
	else
		tmp = Float64(fma(Float64(Float64(y * t) * z), 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, -3.4e+131], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.3e+98], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.39999999999999986e131

   1. Initial program 69.8%

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

   2. Taylor expanded in x around inf

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

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

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

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

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

      5. distribute-lft-neg-out N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-neg-out N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

      11. distribute-rgt-neg-in N/A

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

      12. mul-1-neg N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

   4. Applied rewrites 75.6%

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

   if -3.39999999999999986e131 < x < 2.30000000000000013e98

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 27.3

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

   4. Applied rewrites 27.3%

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

   5. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 72.1

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

   7. Applied rewrites 72.1%

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

   if 2.30000000000000013e98 < x

   1. Initial program 71.3%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 15.4

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

   4. Applied rewrites 15.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 72.4

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

   7. Applied rewrites 72.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 72.9

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

   9. Applied rewrites 72.9%

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

Alternative 11: 72.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -7 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, \mathsf{fma}\left(x \cdot i, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -7e+44)
     t_1
     (if (<= t 4e+30) (fma (* j -27.0) k (fma (* x i) -4.0 (* b c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -7e+44) {
		tmp = t_1;
	} else if (t <= 4e+30) {
		tmp = fma((j * -27.0), k, fma((x * i), -4.0, (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -7e+44)
		tmp = t_1;
	elseif (t <= 4e+30)
		tmp = fma(Float64(j * -27.0), k, fma(Float64(x * i), -4.0, Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7e+44], t$95$1, If[LessEqual[t, 4e+30], N[(N[(j * -27.0), $MachinePrecision] * k + N[(N[(x * i), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999998e44 or 4.0000000000000001e30 < t

   1. Initial program 82.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 66.9

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

   4. Applied rewrites 66.9%

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

   if -6.9999999999999998e44 < t < 4.0000000000000001e30

   1. Initial program 86.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 28.4

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

   4. Applied rewrites 28.4%

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

   5. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 77.1

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

   7. Applied rewrites 77.1%

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

Alternative 12: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-209}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot z, 18, i \cdot -4\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -4.0 t) a (* b c))))
   (if (<= (* b c) -1e+22)
     t_1
     (if (<= (* b c) -2e-209)
       (fma (* -27.0 j) k (* (* a t) -4.0))
       (if (<= (* b c) 2e+63)
         (* (fma (* (* y t) z) 18.0 (* i -4.0)) x)
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * t), a, (b * c));
	double tmp;
	if ((b * c) <= -1e+22) {
		tmp = t_1;
	} else if ((b * c) <= -2e-209) {
		tmp = fma((-27.0 * j), k, ((a * t) * -4.0));
	} else if ((b * c) <= 2e+63) {
		tmp = fma(((y * t) * z), 18.0, (i * -4.0)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * t), a, Float64(b * c))
	tmp = 0.0
	if (Float64(b * c) <= -1e+22)
		tmp = t_1;
	elseif (Float64(b * c) <= -2e-209)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0));
	elseif (Float64(b * c) <= 2e+63)
		tmp = Float64(fma(Float64(Float64(y * t) * z), 18.0, Float64(i * -4.0)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2e-209], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+63], N[(N[(N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1e22 or 2.00000000000000012e63 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Applied rewrites 89.5%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 59.5

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

   6. Applied rewrites 59.5%

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

   if -1e22 < (*.f64 b c) < -2.0000000000000001e-209

   1. Initial program 86.3%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 74.5%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.3

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

   7. Applied rewrites 51.3%

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

   if -2.0000000000000001e-209 < (*.f64 b c) < 2.00000000000000012e63

   1. Initial program 86.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 4.6

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

   4. Applied rewrites 4.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 49.3

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

   7. Applied rewrites 49.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 50.6

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

   9. Applied rewrites 50.6%

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

Alternative 13: 54.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-209}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -4.0 t) a (* b c))))
   (if (<= (* b c) -1e+22)
     t_1
     (if (<= (* b c) -2e-209)
       (fma (* -27.0 j) k (* (* a t) -4.0))
       (if (<= (* b c) 2e+63)
         (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * t), a, (b * c));
	double tmp;
	if ((b * c) <= -1e+22) {
		tmp = t_1;
	} else if ((b * c) <= -2e-209) {
		tmp = fma((-27.0 * j), k, ((a * t) * -4.0));
	} else if ((b * c) <= 2e+63) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * t), a, Float64(b * c))
	tmp = 0.0
	if (Float64(b * c) <= -1e+22)
		tmp = t_1;
	elseif (Float64(b * c) <= -2e-209)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0));
	elseif (Float64(b * c) <= 2e+63)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2e-209], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+63], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1e22 or 2.00000000000000012e63 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Applied rewrites 89.5%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 59.5

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

   6. Applied rewrites 59.5%

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

   if -1e22 < (*.f64 b c) < -2.0000000000000001e-209

   1. Initial program 86.3%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 74.5%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.3

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

   7. Applied rewrites 51.3%

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

   if -2.0000000000000001e-209 < (*.f64 b c) < 2.00000000000000012e63

   1. Initial program 86.9%

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

   2. Taylor expanded in x around inf

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

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

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

      2. associate-*r* N/A

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

      3. metadata-eval N/A

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

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

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

      5. distribute-lft-neg-out N/A

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

      6. associate-*r* N/A

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

      7. distribute-lft-neg-out N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

      11. distribute-rgt-neg-in N/A

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

      12. mul-1-neg N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

   4. Applied rewrites 49.3%

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

Alternative 14: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)\\ t_2 := \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \cdot c \leq 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \left(x \cdot i\right) \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -4.0 t) a (* b c)))
        (t_2 (fma (* -27.0 j) k (* (* a t) -4.0))))
   (if (<= (* b c) -1e+22)
     t_1
     (if (<= (* b c) -5e-124)
       t_2
       (if (<= (* b c) 1e-13)
         (fma (* -4.0 t) a (* (* x i) -4.0))
         (if (<= (* b c) 5e+67) t_2 t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * t), a, (b * c));
	double t_2 = fma((-27.0 * j), k, ((a * t) * -4.0));
	double tmp;
	if ((b * c) <= -1e+22) {
		tmp = t_1;
	} else if ((b * c) <= -5e-124) {
		tmp = t_2;
	} else if ((b * c) <= 1e-13) {
		tmp = fma((-4.0 * t), a, ((x * i) * -4.0));
	} else if ((b * c) <= 5e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * t), a, Float64(b * c))
	t_2 = fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -1e+22)
		tmp = t_1;
	elseif (Float64(b * c) <= -5e-124)
		tmp = t_2;
	elseif (Float64(b * c) <= 1e-13)
		tmp = fma(Float64(-4.0 * t), a, Float64(Float64(x * i) * -4.0));
	elseif (Float64(b * c) <= 5e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5e-124], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1e-13], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+67], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1e22 or 4.99999999999999976e67 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Applied rewrites 89.5%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 59.8

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

   6. Applied rewrites 59.8%

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

   if -1e22 < (*.f64 b c) < -5.0000000000000003e-124 or 1e-13 < (*.f64 b c) < 4.99999999999999976e67

   1. Initial program 87.1%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 74.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 49.5

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

   7. Applied rewrites 49.5%

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

   if -5.0000000000000003e-124 < (*.f64 b c) < 1e-13

   1. Initial program 86.6%

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

   3. Applied rewrites 91.3%

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

   4. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 49.2

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

   6. Applied rewrites 49.2%

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

Alternative 15: 54.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -1.05e+44)
     t_1
     (if (<= t 1.65e-17) (fma (* -27.0 j) k (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -1.05e+44) {
		tmp = t_1;
	} else if (t <= 1.65e-17) {
		tmp = fma((-27.0 * j), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -1.05e+44)
		tmp = t_1;
	elseif (t <= 1.65e-17)
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.05e+44], t$95$1, If[LessEqual[t, 1.65e-17], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999993e44 or 1.65e-17 < t

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 64.6

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

   4. Applied rewrites 64.6%

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

   if -1.04999999999999993e44 < t < 1.65e-17

   1. Initial program 86.6%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in t around 0

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

      1. lower-*.f64 55.5

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

   7. Applied rewrites 55.5%

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

Alternative 16: 53.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -4.0 t) a (* b c))))
   (if (<= (* b c) -1e+22)
     t_1
     (if (<= (* b c) 5e+67) (fma (* -27.0 j) k (* (* a t) -4.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-4.0 * t), a, (b * c));
	double tmp;
	if ((b * c) <= -1e+22) {
		tmp = t_1;
	} else if ((b * c) <= 5e+67) {
		tmp = fma((-27.0 * j), k, ((a * t) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-4.0 * t), a, Float64(b * c))
	tmp = 0.0
	if (Float64(b * c) <= -1e+22)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e+67)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+22], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e+67], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1e22 or 4.99999999999999976e67 < (*.f64 b c)

   1. Initial program 82.8%

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

   3. Applied rewrites 89.5%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 59.8

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

   6. Applied rewrites 59.8%

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

   if -1e22 < (*.f64 b c) < 4.99999999999999976e67

   1. Initial program 86.7%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 73.3%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.7

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

   7. Applied rewrites 50.7%

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

Alternative 17: 53.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+216)
     (* -27.0 (* k j))
     (if (<= t_1 1e+71)
       (fma (* -4.0 t) a (* b c))
       (fma (* -27.0 j) k (* 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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+216) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 1e+71) {
		tmp = fma((-4.0 * t), a, (b * c));
	} else {
		tmp = fma((-27.0 * j), k, (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)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+216)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 1e+71)
		tmp = fma(Float64(-4.0 * t), a, Float64(b * c));
	else
		tmp = fma(Float64(-27.0 * j), k, 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_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+216], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+71], N[(N[(-4.0 * t), $MachinePrecision] * a + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999998e216

   1. Initial program 75.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.4

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

   4. Applied rewrites 70.4%

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

   if -4.9999999999999998e216 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e71

   1. Initial program 87.2%

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

   3. Applied rewrites 91.7%

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

   4. Taylor expanded in b around inf

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

      1. lower-*.f64 48.3

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

   6. Applied rewrites 48.3%

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

   if 1e71 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.3%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 83.5%

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

   5. Taylor expanded in t around 0

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

      1. lower-*.f64 63.2

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

   7. Applied rewrites 63.2%

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

Alternative 18: 45.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq 4.4 \cdot 10^{+211}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= i 4.4e+211) (fma (* -27.0 j) k (* b c)) (* (* -4.0 i) x)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (i <= 4.4e+211) {
		tmp = fma((-27.0 * j), k, (b * c));
	} else {
		tmp = (-4.0 * i) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= 4.4e+211)
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	else
		tmp = Float64(Float64(-4.0 * i) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[i, 4.4e+211], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 4.40000000000000009e211

   1. Initial program 85.4%

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

   2. Taylor expanded in i around 0

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

   4. Applied rewrites 78.4%

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

   5. Taylor expanded in t around 0

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

      1. lower-*.f64 45.5

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

   7. Applied rewrites 45.5%

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

   if 4.40000000000000009e211 < i

   1. Initial program 80.7%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 51.1

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

   4. Applied rewrites 51.1%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 37.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+135}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-209}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-13}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+67}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2e+135)
   (* c b)
   (if (<= (* b c) -2e-209)
     (* -4.0 (* a t))
     (if (<= (* b c) 1e-13)
       (* (* -4.0 i) x)
       (if (<= (* b c) 5e+67) (* -27.0 (* k j)) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+135) {
		tmp = c * b;
	} else if ((b * c) <= -2e-209) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 1e-13) {
		tmp = (-4.0 * i) * x;
	} else if ((b * c) <= 5e+67) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2d+135)) then
        tmp = c * b
    else if ((b * c) <= (-2d-209)) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 1d-13) then
        tmp = ((-4.0d0) * i) * x
    else if ((b * c) <= 5d+67) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+135) {
		tmp = c * b;
	} else if ((b * c) <= -2e-209) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 1e-13) {
		tmp = (-4.0 * i) * x;
	} else if ((b * c) <= 5e+67) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2e+135:
		tmp = c * b
	elif (b * c) <= -2e-209:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 1e-13:
		tmp = (-4.0 * i) * x
	elif (b * c) <= 5e+67:
		tmp = -27.0 * (k * j)
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+135)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -2e-209)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 1e-13)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (Float64(b * c) <= 5e+67)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2e+135)
		tmp = c * b;
	elseif ((b * c) <= -2e-209)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 1e-13)
		tmp = (-4.0 * i) * x;
	elseif ((b * c) <= 5e+67)
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+135], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-209], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-13], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+67], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999992e135 or 4.99999999999999976e67 < (*.f64 b c)

   1. Initial program 81.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 54.4

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

   4. Applied rewrites 54.4%

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

   if -1.99999999999999992e135 < (*.f64 b c) < -2.0000000000000001e-209

   1. Initial program 86.9%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 23.4

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

   4. Applied rewrites 23.4%

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

   if -2.0000000000000001e-209 < (*.f64 b c) < 1e-13

   1. Initial program 86.6%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 27.3

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

   4. Applied rewrites 27.3%

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

   if 1e-13 < (*.f64 b c) < 4.99999999999999976e67

   1. Initial program 88.8%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 27.5

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

   4. Applied rewrites 27.5%

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

Alternative 20: 35.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+22}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+67}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1e+22)
   (* c b)
   (if (<= (* b c) 5e+67) (* -27.0 (* k j)) (* c b))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e+22) {
		tmp = c * b;
	} else if ((b * c) <= 5e+67) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1d+22)) then
        tmp = c * b
    else if ((b * c) <= 5d+67) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e+22) {
		tmp = c * b;
	} else if ((b * c) <= 5e+67) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1e+22:
		tmp = c * b
	elif (b * c) <= 5e+67:
		tmp = -27.0 * (k * j)
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1e+22)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 5e+67)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1e+22)
		tmp = c * b;
	elseif ((b * c) <= 5e+67)
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1e+22], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+67], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1e22 or 4.99999999999999976e67 < (*.f64 b c)

   1. Initial program 82.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 47.8

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

   4. Applied rewrites 47.8%

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

   if -1e22 < (*.f64 b c) < 4.99999999999999976e67

   1. Initial program 86.7%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 29.0

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

   4. Applied rewrites 29.0%

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

Alternative 21: 23.5% accurate, 11.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Fortran

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

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

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(c * b)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = c * b;
end

Wolfram

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

Derivation

1. Initial program 85.1%

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

2. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 23.5

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

4. Applied rewrites 23.5%

   \[\leadsto \color{blue}{c \cdot b} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))