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

Percentage Accurate: 85.3% → 90.8%

Time: 32.3s

Alternatives: 26

Speedup: 1.0×

• 50.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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: 85.3% 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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ t_2 := \left(18 \cdot x\right) \cdot y\\ \mathbf{if}\;\left(\left(c \cdot b + \left(t \cdot \left(t\_2 \cdot z\right) - \left(4 \cdot a\right) \cdot t\right)\right) - i \cdot \left(4 \cdot x\right)\right) - t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, t\_2, -4 \cdot a\right), t, c \cdot b\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)}{b} + c\right) \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))) (t_2 (* (* 18.0 x) y)))
   (if (<=
        (-
         (- (+ (* c b) (- (* t (* t_2 z)) (* (* 4.0 a) t))) (* i (* 4.0 x)))
         t_1)
        5e+299)
     (- (fma (* -4.0 x) i (fma (fma z t_2 (* -4.0 a)) t (* c b))) t_1)
     (*
      (+
       (/
        (fma
         (fma -4.0 i (* (* (* z y) t) 18.0))
         x
         (fma (* -27.0 k) j (* (* a t) -4.0)))
        b)
       c)
      b))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double t_2 = (18.0 * x) * y;
	double tmp;
	if (((((c * b) + ((t * (t_2 * z)) - ((4.0 * a) * t))) - (i * (4.0 * x))) - t_1) <= 5e+299) {
		tmp = fma((-4.0 * x), i, fma(fma(z, t_2, (-4.0 * a)), t, (c * b))) - t_1;
	} else {
		tmp = ((fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma((-27.0 * k), j, ((a * t) * -4.0))) / b) + 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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	t_2 = Float64(Float64(18.0 * x) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(t_2 * z)) - Float64(Float64(4.0 * a) * t))) - Float64(i * Float64(4.0 * x))) - t_1) <= 5e+299)
		tmp = Float64(fma(Float64(-4.0 * x), i, fma(fma(z, t_2, Float64(-4.0 * a)), t, Float64(c * b))) - t_1);
	else
		tmp = Float64(Float64(Float64(fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0))) / b) + c) * b);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(t$95$2 * z), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], 5e+299], N[(N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * t$95$2 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + c), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < 5.0000000000000003e299

   1. Initial program 95.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 95.6

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

      12. lift-+.f64 N/A

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

   4. Applied rewrites 95.6%

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

   if 5.0000000000000003e299 < (-.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 69.4%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 95.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(c \cdot b + \left(t \cdot \left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) - \left(4 \cdot a\right) \cdot t\right)\right) - i \cdot \left(4 \cdot x\right)\right) - k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(18 \cdot x\right) \cdot y, -4 \cdot a\right), t, c \cdot b\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)}{b} + c\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	t_2 = Float64(Float64(18.0 * x) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(t_2 * z)) - Float64(Float64(4.0 * a) * t))) - Float64(i * Float64(4.0 * x))) - t_1) <= Inf)
		tmp = Float64(fma(Float64(t_2 * t), z, fma(Float64(a * t), -4.0, fma(c, b, Float64(Float64(i * x) * -4.0)))) - t_1);
	else
		tmp = Float64(Float64(fma(Float64(Float64(Float64(z * y) * t) / i), 18.0, -4.0) * x) * i);
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(t$95$2 * z), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], Infinity], N[(N[(N[(t$95$2 * t), $MachinePrecision] * z + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] / i), $MachinePrecision] * 18.0 + -4.0), $MachinePrecision] * x), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 94.6%

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

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

   1. Initial program 0.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 15.8

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

      12. lift-+.f64 N/A

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

   4. Applied rewrites 21.1%

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

   5. Taylor expanded in i around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 57.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 63.7%

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

4. Final simplification 92.3%

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

Alternative 3: 91.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	t_2 = Float64(Float64(18.0 * x) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(t_2 * z)) - Float64(Float64(4.0 * a) * t))) - Float64(i * Float64(4.0 * x))) - t_1) <= Inf)
		tmp = Float64(fma(Float64(-4.0 * x), i, fma(fma(z, t_2, Float64(-4.0 * a)), t, Float64(c * b))) - t_1);
	else
		tmp = Float64(Float64(fma(Float64(Float64(Float64(z * y) * t) / i), 18.0, -4.0) * x) * i);
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(t$95$2 * z), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], Infinity], N[(N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * t$95$2 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] / i), $MachinePrecision] * 18.0 + -4.0), $MachinePrecision] * x), $MachinePrecision] * i), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 94.6

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

      12. lift-+.f64 N/A

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

   4. Applied rewrites 94.6%

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

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

   1. Initial program 0.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 15.8

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

      12. lift-+.f64 N/A

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

   4. Applied rewrites 21.1%

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

   5. Taylor expanded in i around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 57.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 63.7%

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

4. Final simplification 92.3%

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

Alternative 4: 91.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(18.0 * x) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(t_1 * z)) - Float64(Float64(4.0 * a) * t))) - Float64(i * Float64(4.0 * x))) - Float64(k * Float64(27.0 * j))) <= Inf)
		tmp = fma(Float64(k * j), -27.0, fma(Float64(i * x), -4.0, fma(fma(z, t_1, Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = Float64(Float64(fma(Float64(Float64(Float64(z * y) * t) / i), 18.0, -4.0) * x) * i);
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(z * t$95$1 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] / i), $MachinePrecision] * 18.0 + -4.0), $MachinePrecision] * x), $MachinePrecision] * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 95.0

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 95.0%

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

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

   1. Initial program 0.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 15.8

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

      12. lift-+.f64 N/A

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

   4. Applied rewrites 21.1%

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

   5. Taylor expanded in i around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 57.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 63.7%

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

4. Final simplification 92.7%

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

Alternative 5: 82.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right) \cdot t\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))))
   (if (<= t_1 -1e-67)
     (fma (* k j) -27.0 (fma c b (* (fma (* (* z x) y) 18.0 (* -4.0 a)) t)))
     (if (<= t_1 5e+194)
       (fma c b (fma (fma (* (* z y) x) 18.0 (* -4.0 a)) t (* (* i x) -4.0)))
       (fma c b (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e-67) {
		tmp = fma((k * j), -27.0, fma(c, b, (fma(((z * x) * y), 18.0, (-4.0 * a)) * t)));
	} else if (t_1 <= 5e+194) {
		tmp = fma(c, b, fma(fma(((z * y) * x), 18.0, (-4.0 * a)), t, ((i * x) * -4.0)));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e-67)
		tmp = fma(Float64(k * j), -27.0, fma(c, b, Float64(fma(Float64(Float64(z * x) * y), 18.0, Float64(-4.0 * a)) * t)));
	elseif (t_1 <= 5e+194)
		tmp = fma(c, b, fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-67], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b + N[(N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+194], N[(c * b + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999943e-68

   1. Initial program 85.2%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 86.3

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 86.4%

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

   5. Taylor expanded in i around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 77.6

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

   7. Applied rewrites 77.6%

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

   9. Applied rewrites 80.0%

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

   if -9.99999999999999943e-68 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e194

   1. Initial program 90.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 23.8

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

   5. Applied rewrites 23.8%

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

   6. Taylor expanded in k around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

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

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

      5. metadata-eval N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-+r+ N/A

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

      13. associate-*r* N/A

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

   8. Applied rewrites 88.5%

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

   if 4.99999999999999989e194 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 96.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right) \cdot t\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, t\_1 \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x)) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -1e+97)
     (fma (* -27.0 k) j (fma (fma -4.0 a (* t_1 18.0)) t (* c b)))
     (if (<= t_2 5e+194)
       (fma c b (fma (fma t_1 18.0 (* -4.0 a)) t (* (* i x) -4.0)))
       (fma c b (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * x;
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -1e+97) {
		tmp = fma((-27.0 * k), j, fma(fma(-4.0, a, (t_1 * 18.0)), t, (c * b)));
	} else if (t_2 <= 5e+194) {
		tmp = fma(c, b, fma(fma(t_1, 18.0, (-4.0 * a)), t, ((i * x) * -4.0)));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -1e+97)
		tmp = fma(Float64(-27.0 * k), j, fma(fma(-4.0, a, Float64(t_1 * 18.0)), t, Float64(c * b)));
	elseif (t_2 <= 5e+194)
		tmp = fma(c, b, fma(fma(t_1, 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+97], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(-4.0 * a + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+194], N[(c * b + N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e97

   1. Initial program 83.2%

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

   3. Taylor expanded in 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. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

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

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate--l+ N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 85.5%

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

   if -1.0000000000000001e97 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e194

   1. Initial program 90.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 23.7

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

   5. Applied rewrites 23.7%

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

   6. Taylor expanded in k around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

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

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

      5. metadata-eval N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-+r+ N/A

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

      13. associate-*r* N/A

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

   8. Applied rewrites 86.3%

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

   if 4.99999999999999989e194 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 96.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, t\_1 \cdot 18\right) \cdot t - t\_2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x)) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -1e+97)
     (- (* (fma -4.0 a (* t_1 18.0)) t) t_2)
     (if (<= t_2 5e+194)
       (fma c b (fma (fma t_1 18.0 (* -4.0 a)) t (* (* i x) -4.0)))
       (fma c b (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * x;
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -1e+97) {
		tmp = (fma(-4.0, a, (t_1 * 18.0)) * t) - t_2;
	} else if (t_2 <= 5e+194) {
		tmp = fma(c, b, fma(fma(t_1, 18.0, (-4.0 * a)), t, ((i * x) * -4.0)));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -1e+97)
		tmp = Float64(Float64(fma(-4.0, a, Float64(t_1 * 18.0)) * t) - t_2);
	elseif (t_2 <= 5e+194)
		tmp = fma(c, b, fma(fma(t_1, 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+97], N[(N[(N[(-4.0 * a + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 5e+194], N[(c * b + N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.0000000000000001e97

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 72.2

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

   5. Applied rewrites 72.2%

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

   if -1.0000000000000001e97 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e194

   1. Initial program 90.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 23.7

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

   5. Applied rewrites 23.7%

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

   6. Taylor expanded in k around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

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

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

      5. metadata-eval N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-+r+ N/A

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

      13. associate-*r* N/A

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

   8. Applied rewrites 86.3%

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

   if 4.99999999999999989e194 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 96.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+97}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t - k \cdot \left(27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))))
   (if (<= t_1 -1e+198)
     (fma (* k j) -27.0 (fma c b (* (* (* (* z y) x) t) 18.0)))
     (if (<= t_1 5e+194)
       (fma c b (fma (fma (* (* z x) y) 18.0 (* -4.0 a)) t (* (* i x) -4.0)))
       (fma c b (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e+198) {
		tmp = fma((k * j), -27.0, fma(c, b, ((((z * y) * x) * t) * 18.0)));
	} else if (t_1 <= 5e+194) {
		tmp = fma(c, b, fma(fma(((z * x) * y), 18.0, (-4.0 * a)), t, ((i * x) * -4.0)));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e+198)
		tmp = fma(Float64(k * j), -27.0, fma(c, b, Float64(Float64(Float64(Float64(z * y) * x) * t) * 18.0)));
	elseif (t_1 <= 5e+194)
		tmp = fma(c, b, fma(fma(Float64(Float64(z * x) * y), 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+198], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+194], N[(c * b + N[(N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000002e198

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 86.4

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 86.4%

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

   5. Taylor expanded in i around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 83.3

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

   7. Applied rewrites 83.3%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 81.3%

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

   if -1.00000000000000002e198 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e194

   1. Initial program 89.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 22.4

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

   5. Applied rewrites 22.4%

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

   6. Taylor expanded in k around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

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

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

      5. metadata-eval N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-+r+ N/A

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

      13. associate-*r* N/A

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

   8. Applied rewrites 84.0%

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

   10. Applied rewrites 85.3%

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

   if 4.99999999999999989e194 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 96.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;c \cdot b \leq -4 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 100000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(-4, a, t\_1 \cdot 18\right) \cdot t - i \cdot \left(4 \cdot x\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \mathsf{fma}\left(t\_1, 18, -4 \cdot a\right) \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x)))
   (if (<= (* c b) -4e-29)
     (fma c b (fma (fma (* (* z x) y) 18.0 (* -4.0 a)) t (* (* i x) -4.0)))
     (if (<= (* c b) 100000000000.0)
       (- (- (* (fma -4.0 a (* t_1 18.0)) t) (* i (* 4.0 x))) (* k (* 27.0 j)))
       (fma (* k j) -27.0 (fma c b (* (fma t_1 18.0 (* -4.0 a)) t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * x;
	double tmp;
	if ((c * b) <= -4e-29) {
		tmp = fma(c, b, fma(fma(((z * x) * y), 18.0, (-4.0 * a)), t, ((i * x) * -4.0)));
	} else if ((c * b) <= 100000000000.0) {
		tmp = ((fma(-4.0, a, (t_1 * 18.0)) * t) - (i * (4.0 * x))) - (k * (27.0 * j));
	} else {
		tmp = fma((k * j), -27.0, fma(c, b, (fma(t_1, 18.0, (-4.0 * a)) * t)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	tmp = 0.0
	if (Float64(c * b) <= -4e-29)
		tmp = fma(c, b, fma(fma(Float64(Float64(z * x) * y), 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)));
	elseif (Float64(c * b) <= 100000000000.0)
		tmp = Float64(Float64(Float64(fma(-4.0, a, Float64(t_1 * 18.0)) * t) - Float64(i * Float64(4.0 * x))) - Float64(k * Float64(27.0 * j)));
	else
		tmp = fma(Float64(k * j), -27.0, fma(c, b, Float64(fma(t_1, 18.0, Float64(-4.0 * a)) * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -4e-29], N[(c * b + N[(N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(-4.0 * a + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(i * N[(4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b + N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -3.99999999999999977e-29

   1. Initial program 85.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 42.4

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

   5. Applied rewrites 42.4%

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

   6. Taylor expanded in k around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-out N/A

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

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

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

      5. metadata-eval N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. +-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-+r+ N/A

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

      13. associate-*r* N/A

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

   8. Applied rewrites 80.9%

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

   10. Applied rewrites 85.1%

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

   if -3.99999999999999977e-29 < (*.f64 b c) < 1e11

   1. Initial program 88.4%

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

   3. Taylor expanded in c around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if 1e11 < (*.f64 b c)

   1. Initial program 88.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 88.1

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 90.1%

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

   5. Taylor expanded in i around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 88.4

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

   7. Applied rewrites 88.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -4 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 100000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t - i \cdot \left(4 \cdot x\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, t, \frac{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\right)}{y}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot t, z, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \left(i \cdot x\right) \cdot -4\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -1.06e+15)
   (*
    (fma
     (* (* z x) 18.0)
     t
     (/ (fma c b (fma (fma i x (* a t)) -4.0 (* (* k j) -27.0))) y))
    y)
   (-
    (fma
     (* (* (* 18.0 x) y) t)
     z
     (fma (* a t) -4.0 (fma c b (* (* i x) -4.0))))
    (* k (* 27.0 j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -1.06e+15) {
		tmp = fma(((z * x) * 18.0), t, (fma(c, b, fma(fma(i, x, (a * t)), -4.0, ((k * j) * -27.0))) / y)) * y;
	} else {
		tmp = fma((((18.0 * x) * y) * t), z, fma((a * t), -4.0, fma(c, b, ((i * x) * -4.0)))) - (k * (27.0 * 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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -1.06e+15)
		tmp = Float64(fma(Float64(Float64(z * x) * 18.0), t, Float64(fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(Float64(k * j) * -27.0))) / y)) * y);
	else
		tmp = Float64(fma(Float64(Float64(Float64(18.0 * x) * y) * t), z, fma(Float64(a * t), -4.0, fma(c, b, Float64(Float64(i * x) * -4.0)))) - Float64(k * Float64(27.0 * 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -1.06e+15], N[(N[(N[(N[(z * x), $MachinePrecision] * 18.0), $MachinePrecision] * t + N[(N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e15

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.8%

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

   if -1.06e15 < y

   1. Initial program 88.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 88.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, t, \frac{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\right)}{y}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot t, z, \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \left(i \cdot x\right) \cdot -4\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 90.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (z <= 3.6e-13) {
		tmp = fma(y, ((t * z) * (18.0 * x)), fma((a * t), -4.0, fma(c, b, ((i * x) * -4.0)))) - t_1;
	} else {
		tmp = fma((-4.0 * x), i, fma(fma(z, ((18.0 * x) * y), (-4.0 * a)), t, (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (z <= 3.6e-13)
		tmp = Float64(fma(y, Float64(Float64(t * z) * Float64(18.0 * x)), fma(Float64(a * t), -4.0, fma(c, b, Float64(Float64(i * x) * -4.0)))) - t_1);
	else
		tmp = Float64(fma(Float64(-4.0 * x), i, fma(fma(z, Float64(Float64(18.0 * x) * y), Float64(-4.0 * a)), t, Float64(c * b))) - t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3.6e-13], N[(N[(y * N[(N[(t * z), $MachinePrecision] * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 3.5999999999999998e-13

   1. Initial program 87.0%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. lower-fma.f64 N/A

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

   4. Applied rewrites 92.9%

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

   if 3.5999999999999998e-13 < z

   1. Initial program 89.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 91.3

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

      12. lift-+.f64 N/A

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

   4. Applied rewrites 93.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(t \cdot z\right) \cdot \left(18 \cdot x\right), \mathsf{fma}\left(a \cdot t, -4, \mathsf{fma}\left(c, b, \left(i \cdot x\right) \cdot -4\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(18 \cdot x\right) \cdot y, -4 \cdot a\right), t, c \cdot b\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+150}:\\ \;\;\;\;c \cdot b - t\_1\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(\left(18 \cdot x\right) \cdot t\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))))
   (if (<= t_1 -5e+150)
     (- (* c b) t_1)
     (if (<= t_1 -5e-35)
       (* (* (* (* 18.0 x) t) y) z)
       (if (<= t_1 5e+82)
         (fma c b (* (* a t) -4.0))
         (fma c b (* (* k j) -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -5e+150) {
		tmp = (c * b) - t_1;
	} else if (t_1 <= -5e-35) {
		tmp = (((18.0 * x) * t) * y) * z;
	} else if (t_1 <= 5e+82) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -5e+150)
		tmp = Float64(Float64(c * b) - t_1);
	elseif (t_1 <= -5e-35)
		tmp = Float64(Float64(Float64(Float64(18.0 * x) * t) * y) * z);
	elseif (t_1 <= 5e+82)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+150], N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -5e-35], N[(N[(N[(N[(18.0 * x), $MachinePrecision] * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+82], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000009e150

   1. Initial program 81.9%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.8

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

   5. Applied rewrites 62.8%

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

   if -5.00000000000000009e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999964e-35

   1. Initial program 85.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 33.6

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

   5. Applied rewrites 33.6%

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

   7. Applied rewrites 41.5%

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

   9. Applied rewrites 44.2%

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

   if -4.99999999999999964e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000015e82

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 54.1

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

   5. Applied rewrites 54.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 51.6%

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

   if 5.00000000000000015e82 < (*.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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 80.1

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 80.2%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{+150}:\\ \;\;\;\;c \cdot b - k \cdot \left(27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(\left(\left(18 \cdot x\right) \cdot t\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-195}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+174}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))))
   (if (<= t_1 -5e-35)
     (* (* -27.0 j) k)
     (if (<= t_1 -5e-195)
       (* c b)
       (if (<= t_1 5e+174) (* (* -4.0 i) x) (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -5e-35) {
		tmp = (-27.0 * j) * k;
	} else if (t_1 <= -5e-195) {
		tmp = c * b;
	} else if (t_1 <= 5e+174) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = (k * j) * -27.0;
	}
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (27.0d0 * j)
    if (t_1 <= (-5d-35)) then
        tmp = ((-27.0d0) * j) * k
    else if (t_1 <= (-5d-195)) then
        tmp = c * b
    else if (t_1 <= 5d+174) then
        tmp = ((-4.0d0) * i) * x
    else
        tmp = (k * j) * (-27.0d0)
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -5e-35) {
		tmp = (-27.0 * j) * k;
	} else if (t_1 <= -5e-195) {
		tmp = c * b;
	} else if (t_1 <= 5e+174) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = (k * j) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (27.0 * j)
	tmp = 0
	if t_1 <= -5e-35:
		tmp = (-27.0 * j) * k
	elif t_1 <= -5e-195:
		tmp = c * b
	elif t_1 <= 5e+174:
		tmp = (-4.0 * i) * x
	else:
		tmp = (k * j) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -5e-35)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (t_1 <= -5e-195)
		tmp = Float64(c * b);
	elseif (t_1 <= 5e+174)
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = Float64(Float64(k * j) * -27.0);
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (27.0 * j);
	tmp = 0.0;
	if (t_1 <= -5e-35)
		tmp = (-27.0 * j) * k;
	elseif (t_1 <= -5e-195)
		tmp = c * b;
	elseif (t_1 <= 5e+174)
		tmp = (-4.0 * i) * x;
	else
		tmp = (k * j) * -27.0;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-35], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t$95$1, -5e-195], N[(c * b), $MachinePrecision], If[LessEqual[t$95$1, 5e+174], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999964e-35

   1. Initial program 83.8%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 37.7

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

   5. Applied rewrites 37.7%

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

   7. Applied rewrites 36.5%

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

   if -4.99999999999999964e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000009e-195

   1. Initial program 96.6%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 49.9

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

   5. Applied rewrites 49.9%

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

   if -5.00000000000000009e-195 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e174

   1. Initial program 89.3%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 33.2

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

   5. Applied rewrites 33.2%

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

   if 4.9999999999999997e174 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 81.4%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 81.5

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

   5. Applied rewrites 81.5%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{-195}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+174}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))))
   (if (<= t_1 -5e-35)
     (* (* -27.0 j) k)
     (if (<= t_1 -2e-277)
       (* c b)
       (if (<= t_1 5e+82) (* (* a t) -4.0) (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -5e-35) {
		tmp = (-27.0 * j) * k;
	} else if (t_1 <= -2e-277) {
		tmp = c * b;
	} else if (t_1 <= 5e+82) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = (k * j) * -27.0;
	}
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (27.0d0 * j)
    if (t_1 <= (-5d-35)) then
        tmp = ((-27.0d0) * j) * k
    else if (t_1 <= (-2d-277)) then
        tmp = c * b
    else if (t_1 <= 5d+82) then
        tmp = (a * t) * (-4.0d0)
    else
        tmp = (k * j) * (-27.0d0)
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -5e-35) {
		tmp = (-27.0 * j) * k;
	} else if (t_1 <= -2e-277) {
		tmp = c * b;
	} else if (t_1 <= 5e+82) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = (k * j) * -27.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (27.0 * j)
	tmp = 0
	if t_1 <= -5e-35:
		tmp = (-27.0 * j) * k
	elif t_1 <= -2e-277:
		tmp = c * b
	elif t_1 <= 5e+82:
		tmp = (a * t) * -4.0
	else:
		tmp = (k * j) * -27.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -5e-35)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (t_1 <= -2e-277)
		tmp = Float64(c * b);
	elseif (t_1 <= 5e+82)
		tmp = Float64(Float64(a * t) * -4.0);
	else
		tmp = Float64(Float64(k * j) * -27.0);
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (27.0 * j);
	tmp = 0.0;
	if (t_1 <= -5e-35)
		tmp = (-27.0 * j) * k;
	elseif (t_1 <= -2e-277)
		tmp = c * b;
	elseif (t_1 <= 5e+82)
		tmp = (a * t) * -4.0;
	else
		tmp = (k * j) * -27.0;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-35], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[t$95$1, -2e-277], N[(c * b), $MachinePrecision], If[LessEqual[t$95$1, 5e+82], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999964e-35

   1. Initial program 83.8%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 37.7

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

   5. Applied rewrites 37.7%

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

   7. Applied rewrites 36.5%

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

   if -4.99999999999999964e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999994e-277

   1. Initial program 97.3%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 39.8

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

   5. Applied rewrites 39.8%

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

   if -1.99999999999999994e-277 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000015e82

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 30.5

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

   5. Applied rewrites 30.5%

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

   if 5.00000000000000015e82 < (*.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. Add Preprocessing

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 67.7

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

   5. Applied rewrites 67.7%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* (* k j) -27.0)) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -5e-35)
     t_1
     (if (<= t_2 -2e-277) (* c b) (if (<= t_2 5e+82) (* (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = (k * j) * -27.0;
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -5e-35) {
		tmp = t_1;
	} else if (t_2 <= -2e-277) {
		tmp = c * b;
	} else if (t_2 <= 5e+82) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (k * j) * (-27.0d0)
    t_2 = k * (27.0d0 * j)
    if (t_2 <= (-5d-35)) then
        tmp = t_1
    else if (t_2 <= (-2d-277)) then
        tmp = c * b
    else if (t_2 <= 5d+82) then
        tmp = (a * t) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * j) * -27.0;
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -5e-35) {
		tmp = t_1;
	} else if (t_2 <= -2e-277) {
		tmp = c * b;
	} else if (t_2 <= 5e+82) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (k * j) * -27.0
	t_2 = k * (27.0 * j)
	tmp = 0
	if t_2 <= -5e-35:
		tmp = t_1
	elif t_2 <= -2e-277:
		tmp = c * b
	elif t_2 <= 5e+82:
		tmp = (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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * j) * -27.0)
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -5e-35)
		tmp = t_1;
	elseif (t_2 <= -2e-277)
		tmp = Float64(c * b);
	elseif (t_2 <= 5e+82)
		tmp = Float64(Float64(a * t) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (k * j) * -27.0;
	t_2 = k * (27.0 * j);
	tmp = 0.0;
	if (t_2 <= -5e-35)
		tmp = t_1;
	elseif (t_2 <= -2e-277)
		tmp = c * b;
	elseif (t_2 <= 5e+82)
		tmp = (a * t) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-35], t$95$1, If[LessEqual[t$95$2, -2e-277], N[(c * b), $MachinePrecision], If[LessEqual[t$95$2, 5e+82], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999964e-35 or 5.00000000000000015e82 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.1%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.1

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

   5. Applied rewrites 49.1%

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

   if -4.99999999999999964e-35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999994e-277

   1. Initial program 97.3%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 39.8

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

   5. Applied rewrites 39.8%

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

   if -1.99999999999999994e-277 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000015e82

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 30.5

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

   5. Applied rewrites 30.5%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(a \cdot t\right) \cdot -4\\ \mathbf{if}\;c \cdot b \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t\_1\right)\\ \mathbf{elif}\;c \cdot b \leq -4 \cdot 10^{-75}:\\ \;\;\;\;\left(\left(\left(18 \cdot x\right) \cdot t\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;c \cdot b \leq 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* (* a t) -4.0)))
   (if (<= (* c b) -5e-31)
     (fma c b t_1)
     (if (<= (* c b) -4e-75)
       (* (* (* (* 18.0 x) t) y) z)
       (if (<= (* c b) 1e+116)
         (fma (* -27.0 j) k t_1)
         (fma c b (* (* k j) -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = (a * t) * -4.0;
	double tmp;
	if ((c * b) <= -5e-31) {
		tmp = fma(c, b, t_1);
	} else if ((c * b) <= -4e-75) {
		tmp = (((18.0 * x) * t) * y) * z;
	} else if ((c * b) <= 1e+116) {
		tmp = fma((-27.0 * j), k, t_1);
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(a * t) * -4.0)
	tmp = 0.0
	if (Float64(c * b) <= -5e-31)
		tmp = fma(c, b, t_1);
	elseif (Float64(c * b) <= -4e-75)
		tmp = Float64(Float64(Float64(Float64(18.0 * x) * t) * y) * z);
	elseif (Float64(c * b) <= 1e+116)
		tmp = fma(Float64(-27.0 * j), k, t_1);
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -5e-31], N[(c * b + t$95$1), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -4e-75], N[(N[(N[(N[(18.0 * x), $MachinePrecision] * t), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 1e+116], N[(N[(-27.0 * j), $MachinePrecision] * k + t$95$1), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5e-31

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 70.8

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 62.0%

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

   if -5e-31 < (*.f64 b c) < -3.9999999999999998e-75

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.2

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

   5. Applied rewrites 68.2%

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

   7. Applied rewrites 84.0%

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

   9. Applied rewrites 100.0%

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

   if -3.9999999999999998e-75 < (*.f64 b c) < 1.00000000000000002e116

   1. Initial program 88.4%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 52.4

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

   5. Applied rewrites 52.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-*.f64 53.1

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

   7. Applied rewrites 53.1%

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

   if 1.00000000000000002e116 < (*.f64 b c)

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 67.7

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

   5. Applied rewrites 67.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 67.7%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq -4 \cdot 10^{-75}:\\ \;\;\;\;\left(\left(\left(18 \cdot x\right) \cdot t\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;c \cdot b \leq 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+187}:\\ \;\;\;\;c \cdot b - t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* k (* 27.0 j))))
   (if (<= t_1 -2e+187)
     (- (* c b) t_1)
     (if (<= t_1 5e+82)
       (fma c b (* (* a t) -4.0))
       (fma c b (* (* k j) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -2e+187) {
		tmp = (c * b) - t_1;
	} else if (t_1 <= 5e+82) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -2e+187)
		tmp = Float64(Float64(c * b) - t_1);
	elseif (t_1 <= 5e+82)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+187], N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e+82], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999981e187

   1. Initial program 81.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 67.8

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

   5. Applied rewrites 67.8%

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

   if -1.99999999999999981e187 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000015e82

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 46.5%

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

   if 5.00000000000000015e82 < (*.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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 80.1

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 80.2%

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+187}:\\ \;\;\;\;c \cdot b - k \cdot \left(27 \cdot j\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* k j) -27.0))) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -2e+187)
     t_1
     (if (<= t_2 5e+82) (fma c b (* (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((k * j) * -27.0));
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -2e+187) {
		tmp = t_1;
	} else if (t_2 <= 5e+82) {
		tmp = fma(c, b, ((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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(c, b, Float64(Float64(k * j) * -27.0))
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -2e+187)
		tmp = t_1;
	elseif (t_2 <= 5e+82)
		tmp = fma(c, b, 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+187], t$95$1, If[LessEqual[t$95$2, 5e+82], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999981e187 or 5.00000000000000015e82 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 78.3

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 78.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 76.2%

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right) \]

   if -1.99999999999999981e187 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000015e82

   1. Initial program 89.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 52.7

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 52.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 46.5%

      \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -5 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq 10^{+119}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= (* c b) -5e+160)
   (fma c b (* (* a t) -4.0))
   (if (<= (* c b) 1e+119)
     (- (* (* -4.0 i) x) (* k (* 27.0 j)))
     (fma c b (* (* k j) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((c * b) <= -5e+160) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else if ((c * b) <= 1e+119) {
		tmp = ((-4.0 * i) * x) - (k * (27.0 * j));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(c * b) <= -5e+160)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	elseif (Float64(c * b) <= 1e+119)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(k * Float64(27.0 * j)));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(c * b), $MachinePrecision], -5e+160], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 1e+119], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.0000000000000002e160

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 87.4

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.2%

      \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

   if -5.0000000000000002e160 < (*.f64 b c) < 9.99999999999999944e118

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 53.9

         \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 53.9%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]

   if 9.99999999999999944e118 < (*.f64 b c)

   1. Initial program 87.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 69.6

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 69.6%

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -5 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq 10^{+119}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 55.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -5 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= (* c b) -5e+160)
   (fma c b (* (* a t) -4.0))
   (if (<= (* c b) 1e+119)
     (fma (* k j) -27.0 (* (* i x) -4.0))
     (fma c b (* (* k j) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((c * b) <= -5e+160) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else if ((c * b) <= 1e+119) {
		tmp = fma((k * j), -27.0, ((i * x) * -4.0));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(c * b) <= -5e+160)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	elseif (Float64(c * b) <= 1e+119)
		tmp = fma(Float64(k * j), -27.0, Float64(Float64(i * x) * -4.0));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(c * b), $MachinePrecision], -5e+160], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 1e+119], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.0000000000000002e160

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 87.4

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.2%

      \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

   if -5.0000000000000002e160 < (*.f64 b c) < 9.99999999999999944e118

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{k \cdot \left(j \cdot 27\right)}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(k \cdot \color{blue}{\left(j \cdot 27\right)}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(k \cdot j\right) \cdot 27}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot \left(\mathsf{neg}\left(27\right)\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot j, \mathsf{neg}\left(27\right), \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{k \cdot j}, \mathsf{neg}\left(27\right), \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 89.2

          \[\leadsto \mathsf{fma}\left(k \cdot j, \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   5. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{-4 \cdot \left(i \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(i \cdot x\right) \cdot -4}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(i \cdot x\right) \cdot -4}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(x \cdot i\right)} \cdot -4\right) \]

      4. lower-*.f64 54.4

         \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(x \cdot i\right)} \cdot -4\right) \]

   7. Applied rewrites 54.4%

      \[\leadsto \mathsf{fma}\left(k \cdot j, -27, \color{blue}{\left(x \cdot i\right) \cdot -4}\right) \]

   if 9.99999999999999944e118 < (*.f64 b c)

   1. Initial program 87.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 69.6

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 69.6%

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -5 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq 10^{+119}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 i (* (* (* z y) t) 18.0)) x)))
   (if (<= x -1.8e+36)
     t_1
     (if (<= x 1.75e+110)
       (fma c b (fma (* -27.0 k) j (* (* 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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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, i, (((z * y) * t) * 18.0)) * x;
	double tmp;
	if (x <= -1.8e+36) {
		tmp = t_1;
	} else if (x <= 1.75e+110) {
		tmp = fma(c, b, fma((-27.0 * k), j, ((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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x)
	tmp = 0.0
	if (x <= -1.8e+36)
		tmp = t_1;
	elseif (x <= 1.75e+110)
		tmp = fma(c, b, fma(Float64(-27.0 * k), j, 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.8e+36], t$95$1, If[LessEqual[x, 1.75e+110], N[(c * b + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e36 or 1.75e110 < x

   1. Initial program 78.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 81.2

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 81.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]

   if -1.7999999999999999e36 < x < 1.75e110

   1. Initial program 93.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 79.1

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 57.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+69}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 i (* (* (* z y) t) 18.0)) x)))
   (if (<= x -1.75e+36)
     t_1
     (if (<= x 1.6e+69) (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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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, i, (((z * y) * t) * 18.0)) * x;
	double tmp;
	if (x <= -1.75e+36) {
		tmp = t_1;
	} else if (x <= 1.6e+69) {
		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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x)
	tmp = 0.0
	if (x <= -1.75e+36)
		tmp = t_1;
	elseif (x <= 1.6e+69)
		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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.75e+36], t$95$1, If[LessEqual[x, 1.6e+69], 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 x < -1.7499999999999999e36 or 1.59999999999999992e69 < x

   1. Initial program 77.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 78.2

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 78.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]

   if -1.7499999999999999e36 < x < 1.59999999999999992e69

   1. Initial program 94.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 59.3

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 59.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + -4 \cdot \left(a \cdot t\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + -4 \cdot \left(a \cdot t\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + -4 \cdot \left(a \cdot t\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, -4 \cdot \left(a \cdot t\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, -4 \cdot \left(a \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, -4 \cdot \left(a \cdot t\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, -4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-*.f64 59.3

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right) \]

   7. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 55.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -1 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+173}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -1e-25)
     t_1
     (if (<= t 1.3e+173) (- (* (* -4.0 i) x) (* k (* 27.0 j))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -1e-25) {
		tmp = t_1;
	} else if (t <= 1.3e+173) {
		tmp = ((-4.0 * i) * x) - (k * (27.0 * 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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -1e-25)
		tmp = t_1;
	elseif (t <= 1.3e+173)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(k * Float64(27.0 * 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -1e-25], t$95$1, If[LessEqual[t, 1.3e+173], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000004e-25 or 1.2999999999999999e173 < t

   1. Initial program 87.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \cdot t \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \cdot t \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

      12. lower-*.f64 68.4

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

   5. Applied rewrites 68.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t} \]

   if -1.00000000000000004e-25 < t < 1.2999999999999999e173

   1. Initial program 87.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]

      3. lower-*.f64 58.6

         \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+173}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 37.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+32}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 10^{+72}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= (* c b) -1e+32)
   (* c b)
   (if (<= (* c b) 1e+72) (* (* k j) -27.0) (* c b))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((c * b) <= -1e+32) {
		tmp = c * b;
	} else if ((c * b) <= 1e+72) {
		tmp = (k * j) * -27.0;
	} 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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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 ((c * b) <= (-1d+32)) then
        tmp = c * b
    else if ((c * b) <= 1d+72) then
        tmp = (k * j) * (-27.0d0)
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((c * b) <= -1e+32) {
		tmp = c * b;
	} else if ((c * b) <= 1e+72) {
		tmp = (k * j) * -27.0;
	} 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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 (c * b) <= -1e+32:
		tmp = c * b
	elif (c * b) <= 1e+72:
		tmp = (k * j) * -27.0
	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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(c * b) <= -1e+32)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= 1e+72)
		tmp = Float64(Float64(k * j) * -27.0);
	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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 ((c * b) <= -1e+32)
		tmp = c * b;
	elseif ((c * b) <= 1e+72)
		tmp = (k * j) * -27.0;
	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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(c * b), $MachinePrecision], -1e+32], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 1e+72], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.00000000000000005e32 or 9.99999999999999944e71 < (*.f64 b c)

   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. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} \]

      2. lower-*.f64 47.1

         \[\leadsto \color{blue}{c \cdot b} \]

   5. Applied rewrites 47.1%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -1.00000000000000005e32 < (*.f64 b c) < 9.99999999999999944e71

   1. Initial program 88.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 32.4

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 32.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+32}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 10^{+72}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 45.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot i\right) \cdot x\\ \mathbf{if}\;i \leq -1 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 i) x)))
   (if (<= i -1e+151)
     t_1
     (if (<= i 1.85e-17) (fma c b (* (* k j) -27.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * i) * x;
	double tmp;
	if (i <= -1e+151) {
		tmp = t_1;
	} else if (i <= 1.85e-17) {
		tmp = fma(c, b, ((k * j) * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * i) * x)
	tmp = 0.0
	if (i <= -1e+151)
		tmp = t_1;
	elseif (i <= 1.85e-17)
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[i, -1e+151], t$95$1, If[LessEqual[i, 1.85e-17], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.00000000000000002e151 or 1.8499999999999999e-17 < i

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      3. lower-*.f64 51.3

         \[\leadsto \color{blue}{\left(-4 \cdot i\right)} \cdot x \]

   5. Applied rewrites 51.3%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

   if -1.00000000000000002e151 < i < 1.8499999999999999e-17

   1. Initial program 87.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 69.6

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 69.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.9%

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+151}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 23.9% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 87.6%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{c \cdot b} \]

   2. lower-*.f64 21.1

      \[\leadsto \color{blue}{c \cdot b} \]

5. Applied rewrites 21.1%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024257 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))