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

Percentage Accurate: 85.5% → 91.3%

Time: 35.4s

Alternatives: 24

Speedup: 1.1×

• 50.9% 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: 85.5% 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: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 1e+162)
   (fma
    c
    b
    (fma
     t
     (fma x (* 18.0 (* z y)) (* a -4.0))
     (- (fma x (* 4.0 i) (* j (* 27.0 k))))))
   (-
    (fma
     (* t (* x (* 18.0 y)))
     z
     (fma t (* a -4.0) (fma b c (* x (* -4.0 i)))))
    (* 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);
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 (z <= 1e+162) {
		tmp = fma(c, b, fma(t, fma(x, (18.0 * (z * y)), (a * -4.0)), -fma(x, (4.0 * i), (j * (27.0 * k)))));
	} else {
		tmp = fma((t * (x * (18.0 * y))), z, fma(t, (a * -4.0), fma(b, c, (x * (-4.0 * i))))) - (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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 1e+162)
		tmp = fma(c, b, fma(t, fma(x, Float64(18.0 * Float64(z * y)), Float64(a * -4.0)), Float64(-fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))))));
	else
		tmp = Float64(fma(Float64(t * Float64(x * Float64(18.0 * y))), z, fma(t, Float64(a * -4.0), fma(b, c, Float64(x * Float64(-4.0 * i))))) - Float64(k * Float64(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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 1e+162], N[(c * b + N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + (-N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + N[(t * N[(a * -4.0), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.9999999999999994e161

   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. 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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.5%

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

   if 9.9999999999999994e161 < z

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. 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 91.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, x \cdot \left(-4 \cdot i\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(c \cdot b + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+294}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* c b) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
          (* i (* x 4.0)))))
   (if (<= t_1 -1e+249)
     (fma -4.0 (* x i) (fma t (fma -4.0 a (* 18.0 (* z (* x y)))) (* c b)))
     (if (<= t_1 1e+294)
       (fma c b (fma t (* a -4.0) (- (fma x (* 4.0 i) (* j (* 27.0 k))))))
       (fma c b (* x (fma (* y (* t 18.0)) z (* -4.0 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);
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 = ((c * b) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0));
	double tmp;
	if (t_1 <= -1e+249) {
		tmp = fma(-4.0, (x * i), fma(t, fma(-4.0, a, (18.0 * (z * (x * y)))), (c * b)));
	} else if (t_1 <= 1e+294) {
		tmp = fma(c, b, fma(t, (a * -4.0), -fma(x, (4.0 * i), (j * (27.0 * k)))));
	} else {
		tmp = fma(c, b, (x * fma((y * (t * 18.0)), z, (-4.0 * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0)))
	tmp = 0.0
	if (t_1 <= -1e+249)
		tmp = fma(-4.0, Float64(x * i), fma(t, fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))), Float64(c * b)));
	elseif (t_1 <= 1e+294)
		tmp = fma(c, b, fma(t, Float64(a * -4.0), Float64(-fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))))));
	else
		tmp = fma(c, b, Float64(x * fma(Float64(y * Float64(t * 18.0)), z, Float64(-4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+249], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+294], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision] + (-N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(x * N[(N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] * z + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.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)) < -9.9999999999999992e248

   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 j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Applied rewrites 84.3%

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

   if -9.9999999999999992e248 < (-.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)) < 1.00000000000000007e294

   1. Initial program 98.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 94.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 88.1

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

   7. Applied rewrites 88.1%

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

   if 1.00000000000000007e294 < (-.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))

   1. Initial program 61.7%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 81.0%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 83.5

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

   7. Applied rewrites 83.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot b + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq -1 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;\left(c \cdot b + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 10^{+294}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;\left(c \cdot b + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z, a \cdot -4\right), c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), x \cdot \left(-4 \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
       (* i (* x 4.0)))
      5e+293)
   (fma
    (* k -27.0)
    j
    (fma x (* -4.0 i) (fma t (fma (* x (* 18.0 y)) z (* a -4.0)) (* c b))))
   (fma c b (fma t (fma x (* 18.0 (* z y)) (* a -4.0)) (* x (* -4.0 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);
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) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) <= 5e+293) {
		tmp = fma((k * -27.0), j, fma(x, (-4.0 * i), fma(t, fma((x * (18.0 * y)), z, (a * -4.0)), (c * b))));
	} else {
		tmp = fma(c, b, fma(t, fma(x, (18.0 * (z * y)), (a * -4.0)), (x * (-4.0 * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(c * b) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) <= 5e+293)
		tmp = fma(Float64(k * -27.0), j, fma(x, Float64(-4.0 * i), fma(t, fma(Float64(x * Float64(18.0 * y)), z, Float64(a * -4.0)), Float64(c * b))));
	else
		tmp = fma(c, b, fma(t, fma(x, Float64(18.0 * Float64(z * y)), Float64(a * -4.0)), Float64(x * Float64(-4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(c * b), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+293], N[(N[(k * -27.0), $MachinePrecision] * j + N[(x * N[(-4.0 * i), $MachinePrecision] + N[(t * N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.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)) < 5.00000000000000033e293

   1. Initial program 95.1%

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

   4. Applied rewrites 93.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 95.1

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

   6. Applied rewrites 95.1%

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

   if 5.00000000000000033e293 < (-.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))

   1. Initial program 62.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 81.2%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 84.0

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

   7. Applied rewrites 84.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot b + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right) \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z, a \cdot -4\right), c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), x \cdot \left(-4 \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(z \cdot y\right)\\ t_2 := \mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot t\_1\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, t\_1, a \cdot -4\right), x \cdot \left(-4 \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+224}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, t \cdot \left(a \cdot -4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* z y)))
        (t_2 (fma x (fma -4.0 i (* t t_1)) (fma b c (* j (* k -27.0)))))
        (t_3 (* k (* j 27.0))))
   (if (<= t_3 -5e+55)
     t_2
     (if (<= t_3 5e+22)
       (fma c b (fma t (fma x t_1 (* a -4.0)) (* x (* -4.0 i))))
       (if (<= t_3 4e+224)
         t_2
         (fma (* k -27.0) j (fma x (* -4.0 i) (* t (* a -4.0)))))))))

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);
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 * (z * y);
	double t_2 = fma(x, fma(-4.0, i, (t * t_1)), fma(b, c, (j * (k * -27.0))));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -5e+55) {
		tmp = t_2;
	} else if (t_3 <= 5e+22) {
		tmp = fma(c, b, fma(t, fma(x, t_1, (a * -4.0)), (x * (-4.0 * i))));
	} else if (t_3 <= 4e+224) {
		tmp = t_2;
	} else {
		tmp = fma((k * -27.0), j, fma(x, (-4.0 * i), (t * (a * -4.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(18.0 * Float64(z * y))
	t_2 = fma(x, fma(-4.0, i, Float64(t * t_1)), fma(b, c, Float64(j * Float64(k * -27.0))))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= -5e+55)
		tmp = t_2;
	elseif (t_3 <= 5e+22)
		tmp = fma(c, b, fma(t, fma(x, t_1, Float64(a * -4.0)), Float64(x * Float64(-4.0 * i))));
	elseif (t_3 <= 4e+224)
		tmp = t_2;
	else
		tmp = fma(Float64(k * -27.0), j, fma(x, Float64(-4.0 * i), Float64(t * Float64(a * -4.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+55], t$95$2, If[LessEqual[t$95$3, 5e+22], N[(c * b + N[(t * N[(x * t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+224], t$95$2, N[(N[(k * -27.0), $MachinePrecision] * j + N[(x * N[(-4.0 * i), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.00000000000000046e55 or 4.9999999999999996e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999988e224

   1. Initial program 90.2%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.3%

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

   if -5.00000000000000046e55 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999996e22

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 89.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 88.4

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

   7. Applied rewrites 88.4%

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

   if 3.99999999999999988e224 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 75.0%

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

   4. Applied rewrites 91.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 95.8

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

   7. Applied rewrites 95.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), x \cdot \left(-4 \cdot i\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, t \cdot \left(a \cdot -4\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-55}:\\ \;\;\;\;\left(x \cdot 18\right) \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* j k) (* c b))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -5e+149)
     t_1
     (if (<= t_2 -1e-55)
       (* (* x 18.0) (* t (* z y)))
       (if (<= t_2 -5e-211)
         (fma c b (* x (* -4.0 i)))
         (if (<= t_2 5e+22) (fma c b (* t (* a -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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (j * k), (c * b));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -5e+149) {
		tmp = t_1;
	} else if (t_2 <= -1e-55) {
		tmp = (x * 18.0) * (t * (z * y));
	} else if (t_2 <= -5e-211) {
		tmp = fma(c, b, (x * (-4.0 * i)));
	} else if (t_2 <= 5e+22) {
		tmp = fma(c, b, (t * (a * -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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(j * k), Float64(c * b))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -5e+149)
		tmp = t_1;
	elseif (t_2 <= -1e-55)
		tmp = Float64(Float64(x * 18.0) * Float64(t * Float64(z * y)));
	elseif (t_2 <= -5e-211)
		tmp = fma(c, b, Float64(x * Float64(-4.0 * i)));
	elseif (t_2 <= 5e+22)
		tmp = fma(c, b, Float64(t * Float64(a * -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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+149], t$95$1, If[LessEqual[t$95$2, -1e-55], N[(N[(x * 18.0), $MachinePrecision] * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-211], N[(c * b + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+22], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999999e149 or 4.9999999999999996e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 66.2%

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

   if -4.9999999999999999e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999995e-56

   1. Initial program 86.6%

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

   3. Taylor expanded in y 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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 46.2

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

   5. Applied rewrites 46.2%

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

   7. Applied rewrites 53.9%

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

   if -9.99999999999999995e-56 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000002e-211

   1. Initial program 88.0%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.9

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

   7. Applied rewrites 59.9%

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

   if -5.0000000000000002e-211 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999996e22

   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. 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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 58.0

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

   7. Applied rewrites 58.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-55}:\\ \;\;\;\;\left(x \cdot 18\right) \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* j k) (* c b))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -5e+149)
     t_1
     (if (<= t_2 -1e-55)
       (* x (* t (* 18.0 (* z y))))
       (if (<= t_2 -5e-211)
         (fma c b (* x (* -4.0 i)))
         (if (<= t_2 5e+22) (fma c b (* t (* a -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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (j * k), (c * b));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -5e+149) {
		tmp = t_1;
	} else if (t_2 <= -1e-55) {
		tmp = x * (t * (18.0 * (z * y)));
	} else if (t_2 <= -5e-211) {
		tmp = fma(c, b, (x * (-4.0 * i)));
	} else if (t_2 <= 5e+22) {
		tmp = fma(c, b, (t * (a * -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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(j * k), Float64(c * b))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -5e+149)
		tmp = t_1;
	elseif (t_2 <= -1e-55)
		tmp = Float64(x * Float64(t * Float64(18.0 * Float64(z * y))));
	elseif (t_2 <= -5e-211)
		tmp = fma(c, b, Float64(x * Float64(-4.0 * i)));
	elseif (t_2 <= 5e+22)
		tmp = fma(c, b, Float64(t * Float64(a * -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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+149], t$95$1, If[LessEqual[t$95$2, -1e-55], N[(x * N[(t * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-211], N[(c * b + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+22], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999999e149 or 4.9999999999999996e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 66.2%

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

   if -4.9999999999999999e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999995e-56

   1. Initial program 86.6%

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

   3. Taylor expanded in y 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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 46.2

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

   5. Applied rewrites 46.2%

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

   7. Applied rewrites 53.9%

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

   if -9.99999999999999995e-56 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000002e-211

   1. Initial program 88.0%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 59.9

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

   7. Applied rewrites 59.9%

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

   if -5.0000000000000002e-211 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999996e22

   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. 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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 58.0

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

   7. Applied rewrites 58.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(-4 \cdot i\right)\\ t_2 := \mathsf{fma}\left(c, b, t\_1\right)\\ t_3 := t \cdot \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right)\\ \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot b \leq 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, t\_1\right)\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* -4.0 i)))
        (t_2 (fma c b t_1))
        (t_3 (* t (fma x (* 18.0 (* z y)) (* a -4.0)))))
   (if (<= (* c b) -2e+108)
     t_2
     (if (<= (* c b) -5e-320)
       t_3
       (if (<= (* c b) 1e-250)
         (fma (* k -27.0) j t_1)
         (if (<= (* c b) 2e+99) t_3 t_2))))))

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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (-4.0 * i);
	double t_2 = fma(c, b, t_1);
	double t_3 = t * fma(x, (18.0 * (z * y)), (a * -4.0));
	double tmp;
	if ((c * b) <= -2e+108) {
		tmp = t_2;
	} else if ((c * b) <= -5e-320) {
		tmp = t_3;
	} else if ((c * b) <= 1e-250) {
		tmp = fma((k * -27.0), j, t_1);
	} else if ((c * b) <= 2e+99) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(x * Float64(-4.0 * i))
	t_2 = fma(c, b, t_1)
	t_3 = Float64(t * fma(x, Float64(18.0 * Float64(z * y)), Float64(a * -4.0)))
	tmp = 0.0
	if (Float64(c * b) <= -2e+108)
		tmp = t_2;
	elseif (Float64(c * b) <= -5e-320)
		tmp = t_3;
	elseif (Float64(c * b) <= 1e-250)
		tmp = fma(Float64(k * -27.0), j, t_1);
	elseif (Float64(c * b) <= 2e+99)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * b + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -2e+108], t$95$2, If[LessEqual[N[(c * b), $MachinePrecision], -5e-320], t$95$3, If[LessEqual[N[(c * b), $MachinePrecision], 1e-250], N[(N[(k * -27.0), $MachinePrecision] * j + t$95$1), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 2e+99], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.0000000000000001e108 or 1.9999999999999999e99 < (*.f64 b c)

   1. Initial program 78.4%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 75.4

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

   7. Applied rewrites 75.4%

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

   if -2.0000000000000001e108 < (*.f64 b c) < -4.99994e-320 or 1.0000000000000001e-250 < (*.f64 b c) < 1.9999999999999999e99

   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 b around inf

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

      1. lower-*.f64 4.5

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

   5. Applied rewrites 4.5%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 60.5

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

   8. Applied rewrites 60.5%

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

   if -4.99994e-320 < (*.f64 b c) < 1.0000000000000001e-250

   1. Initial program 92.6%

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

   4. Applied rewrites 88.0%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 67.3

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

   7. Applied rewrites 67.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(-4 \cdot i\right)\\ t_2 := \mathsf{fma}\left(c, b, t\_1\right)\\ t_3 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{-192}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, t\_1\right)\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* -4.0 i)))
        (t_2 (fma c b t_1))
        (t_3 (* t (fma -4.0 a (* 18.0 (* z (* x y)))))))
   (if (<= (* c b) -2e+108)
     t_2
     (if (<= (* c b) -5e-320)
       t_3
       (if (<= (* c b) 5e-192)
         (fma (* k -27.0) j t_1)
         (if (<= (* c b) 2e+99) t_3 t_2))))))

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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (-4.0 * i);
	double t_2 = fma(c, b, t_1);
	double t_3 = t * fma(-4.0, a, (18.0 * (z * (x * y))));
	double tmp;
	if ((c * b) <= -2e+108) {
		tmp = t_2;
	} else if ((c * b) <= -5e-320) {
		tmp = t_3;
	} else if ((c * b) <= 5e-192) {
		tmp = fma((k * -27.0), j, t_1);
	} else if ((c * b) <= 2e+99) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(x * Float64(-4.0 * i))
	t_2 = fma(c, b, t_1)
	t_3 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))))
	tmp = 0.0
	if (Float64(c * b) <= -2e+108)
		tmp = t_2;
	elseif (Float64(c * b) <= -5e-320)
		tmp = t_3;
	elseif (Float64(c * b) <= 5e-192)
		tmp = fma(Float64(k * -27.0), j, t_1);
	elseif (Float64(c * b) <= 2e+99)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * b + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -2e+108], t$95$2, If[LessEqual[N[(c * b), $MachinePrecision], -5e-320], t$95$3, If[LessEqual[N[(c * b), $MachinePrecision], 5e-192], N[(N[(k * -27.0), $MachinePrecision] * j + t$95$1), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 2e+99], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.0000000000000001e108 or 1.9999999999999999e99 < (*.f64 b c)

   1. Initial program 78.4%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 75.4

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

   7. Applied rewrites 75.4%

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

   if -2.0000000000000001e108 < (*.f64 b c) < -4.99994e-320 or 5.0000000000000001e-192 < (*.f64 b c) < 1.9999999999999999e99

   1. Initial program 89.7%

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

   3. Taylor expanded in t around 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. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 60.0

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

   5. Applied rewrites 60.0%

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

   if -4.99994e-320 < (*.f64 b c) < 5.0000000000000001e-192

   1. Initial program 89.1%

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

   4. Applied rewrites 89.2%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 63.1

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

   7. Applied rewrites 63.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{-320}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{-192}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right), \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (fma t (* a -4.0) (- (fma x (* 4.0 i) (* j (* 27.0 k))))))))
   (if (<= (* c b) -1e+121)
     t_1
     (if (<= (* c b) 2e+99)
       (fma
        x
        (fma -4.0 i (* t (* 18.0 (* z y))))
        (fma -4.0 (* t a) (* j (* k -27.0))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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, fma(t, (a * -4.0), -fma(x, (4.0 * i), (j * (27.0 * k)))));
	double tmp;
	if ((c * b) <= -1e+121) {
		tmp = t_1;
	} else if ((c * b) <= 2e+99) {
		tmp = fma(x, fma(-4.0, i, (t * (18.0 * (z * y)))), fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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, fma(t, Float64(a * -4.0), Float64(-fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))))))
	tmp = 0.0
	if (Float64(c * b) <= -1e+121)
		tmp = t_1;
	elseif (Float64(c * b) <= 2e+99)
		tmp = fma(x, fma(-4.0, i, Float64(t * Float64(18.0 * Float64(z * y)))), fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(t * N[(a * -4.0), $MachinePrecision] + (-N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -1e+121], t$95$1, If[LessEqual[N[(c * b), $MachinePrecision], 2e+99], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.00000000000000004e121 or 1.9999999999999999e99 < (*.f64 b c)

   1. Initial program 77.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 87.4

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

   7. Applied rewrites 87.4%

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

   if -1.00000000000000004e121 < (*.f64 b c) < 1.9999999999999999e99

   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. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate--r+ N/A

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

      3. +-commutative N/A

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

      4. associate--r+ N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

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

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

      10. associate--r+ N/A

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

      11. sub-neg N/A

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

   5. Applied rewrites 89.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right), \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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+304)
   (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
   (fma
    (* k -27.0)
    j
    (fma x (* -4.0 i) (fma t (fma x (* 18.0 (* z y)) (* a -4.0)) (* 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);
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+304) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = fma((k * -27.0), j, fma(x, (-4.0 * i), fma(t, fma(x, (18.0 * (z * y)), (a * -4.0)), (c * b))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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+304)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = fma(Float64(k * -27.0), j, fma(x, Float64(-4.0 * i), fma(t, fma(x, Float64(18.0 * Float64(z * y)), Float64(a * -4.0)), Float64(c * b))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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+304], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(x * N[(-4.0 * i), $MachinePrecision] + N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -9.9999999999999994e303

   1. Initial program 58.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 94.1

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

   5. Applied rewrites 94.1%

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

   if -9.9999999999999994e303 < (*.f64 b c)

   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

   4. Applied rewrites 91.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), c \cdot b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+233}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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))))
   (if (<= t_1 -1e+233)
     (* j (* k -27.0))
     (if (<= t_1 -5e-211)
       (fma c b (* x (* -4.0 i)))
       (if (<= t_1 5e+22)
         (fma c b (* t (* a -4.0)))
         (fma -27.0 (* j k) (* 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);
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 tmp;
	if (t_1 <= -1e+233) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= -5e-211) {
		tmp = fma(c, b, (x * (-4.0 * i)));
	} else if (t_1 <= 5e+22) {
		tmp = fma(c, b, (t * (a * -4.0)));
	} else {
		tmp = fma(-27.0, (j * k), (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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_1 <= -1e+233)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t_1 <= -5e-211)
		tmp = fma(c, b, Float64(x * Float64(-4.0 * i)));
	elseif (t_1 <= 5e+22)
		tmp = fma(c, b, Float64(t * Float64(a * -4.0)));
	else
		tmp = fma(-27.0, Float64(j * k), Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+233], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-211], N[(c * b + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+22], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999974e232

   1. Initial program 85.8%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if -9.99999999999999974e232 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000002e-211

   1. Initial program 89.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 47.5

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

   7. Applied rewrites 47.5%

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

   if -5.0000000000000002e-211 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999996e22

   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. 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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 58.0

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

   7. Applied rewrites 58.0%

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

   if 4.9999999999999996e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 63.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+233}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6.2 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z, a \cdot -4\right), c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (<= z 6.2e+172)
   (fma
    c
    b
    (fma
     t
     (fma x (* 18.0 (* z y)) (* a -4.0))
     (- (fma x (* 4.0 i) (* j (* 27.0 k))))))
   (fma
    (* k -27.0)
    j
    (fma x (* -4.0 i) (fma t (fma (* x (* 18.0 y)) z (* a -4.0)) (* 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);
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 (z <= 6.2e+172) {
		tmp = fma(c, b, fma(t, fma(x, (18.0 * (z * y)), (a * -4.0)), -fma(x, (4.0 * i), (j * (27.0 * k)))));
	} else {
		tmp = fma((k * -27.0), j, fma(x, (-4.0 * i), fma(t, fma((x * (18.0 * y)), z, (a * -4.0)), (c * b))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 (z <= 6.2e+172)
		tmp = fma(c, b, fma(t, fma(x, Float64(18.0 * Float64(z * y)), Float64(a * -4.0)), Float64(-fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))))));
	else
		tmp = fma(Float64(k * -27.0), j, fma(x, Float64(-4.0 * i), fma(t, fma(Float64(x * Float64(18.0 * y)), z, Float64(a * -4.0)), Float64(c * b))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[z, 6.2e+172], N[(c * b + N[(t * N[(x * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + (-N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(x * N[(-4.0 * i), $MachinePrecision] + N[(t * N[(N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.19999999999999976e172

   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. 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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.7%

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

   if 6.19999999999999976e172 < z

   1. Initial program 84.3%

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

   4. Applied rewrites 84.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 93.8

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

   6. Applied rewrites 93.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.2 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(z \cdot y\right), a \cdot -4\right), -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(x, -4 \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot \left(18 \cdot y\right), z, a \cdot -4\right), c \cdot b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1350000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1350000000000.0)
   (fma x (fma -4.0 i (* t (* 18.0 (* z y)))) (fma b c (* j (* k -27.0))))
   (if (<= x 1.5e-34)
     (fma c b (fma t (* a -4.0) (- (fma x (* 4.0 i) (* j (* 27.0 k))))))
     (fma c b (* x (fma (* y (* t 18.0)) z (* -4.0 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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1350000000000.0) {
		tmp = fma(x, fma(-4.0, i, (t * (18.0 * (z * y)))), fma(b, c, (j * (k * -27.0))));
	} else if (x <= 1.5e-34) {
		tmp = fma(c, b, fma(t, (a * -4.0), -fma(x, (4.0 * i), (j * (27.0 * k)))));
	} else {
		tmp = fma(c, b, (x * fma((y * (t * 18.0)), z, (-4.0 * 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1350000000000.0)
		tmp = fma(x, fma(-4.0, i, Float64(t * Float64(18.0 * Float64(z * y)))), fma(b, c, Float64(j * Float64(k * -27.0))));
	elseif (x <= 1.5e-34)
		tmp = fma(c, b, fma(t, Float64(a * -4.0), Float64(-fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))))));
	else
		tmp = fma(c, b, Float64(x * fma(Float64(y * Float64(t * 18.0)), z, Float64(-4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1350000000000.0], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-34], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision] + (-N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(x * N[(N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] * z + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e12

   1. Initial program 75.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 87.6%

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

   if -1.35e12 < x < 1.5e-34

   1. Initial program 95.3%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 94.0%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 87.6

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

   7. Applied rewrites 87.6%

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

   if 1.5e-34 < x

   1. Initial program 75.8%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 90.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 88.9

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

   7. Applied rewrites 88.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1350000000000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* x (fma (* y (* t 18.0)) z (* -4.0 i))))))
   (if (<= x -1.35e+181)
     t_1
     (if (<= x 1.5e-34)
       (fma c b (fma t (* a -4.0) (- (fma x (* 4.0 i) (* j (* 27.0 k))))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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, (x * fma((y * (t * 18.0)), z, (-4.0 * i))));
	double tmp;
	if (x <= -1.35e+181) {
		tmp = t_1;
	} else if (x <= 1.5e-34) {
		tmp = fma(c, b, fma(t, (a * -4.0), -fma(x, (4.0 * i), (j * (27.0 * k)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(x * fma(Float64(y * Float64(t * 18.0)), z, Float64(-4.0 * i))))
	tmp = 0.0
	if (x <= -1.35e+181)
		tmp = t_1;
	elseif (x <= 1.5e-34)
		tmp = fma(c, b, fma(t, Float64(a * -4.0), Float64(-fma(x, Float64(4.0 * i), Float64(j * Float64(27.0 * k))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(x * N[(N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] * z + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+181], t$95$1, If[LessEqual[x, 1.5e-34], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision] + (-N[(x * N[(4.0 * i), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000004e181 or 1.5e-34 < x

   1. Initial program 74.8%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 86.9%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 91.1

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

   7. Applied rewrites 91.1%

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

   if -1.35000000000000004e181 < x < 1.5e-34

   1. Initial program 90.8%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 91.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 82.2

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

   7. Applied rewrites 82.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t, a \cdot -4, -\mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ t_2 := x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* j k) (* c b)))
        (t_2 (* x (fma -4.0 i (* t (* 18.0 (* z y)))))))
   (if (<= x -5.6e+22)
     t_2
     (if (<= x -5e-106)
       t_1
       (if (<= x 8.2e-182)
         (fma (* k -27.0) j (* t (* a -4.0)))
         (if (<= x 4.4e-29) t_1 t_2))))))

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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (j * k), (c * b));
	double t_2 = x * fma(-4.0, i, (t * (18.0 * (z * y))));
	double tmp;
	if (x <= -5.6e+22) {
		tmp = t_2;
	} else if (x <= -5e-106) {
		tmp = t_1;
	} else if (x <= 8.2e-182) {
		tmp = fma((k * -27.0), j, (t * (a * -4.0)));
	} else if (x <= 4.4e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(-27.0, Float64(j * k), Float64(c * b))
	t_2 = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(z * y)))))
	tmp = 0.0
	if (x <= -5.6e+22)
		tmp = t_2;
	elseif (x <= -5e-106)
		tmp = t_1;
	elseif (x <= 8.2e-182)
		tmp = fma(Float64(k * -27.0), j, Float64(t * Float64(a * -4.0)));
	elseif (x <= 4.4e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+22], t$95$2, If[LessEqual[x, -5e-106], t$95$1, If[LessEqual[x, 8.2e-182], N[(N[(k * -27.0), $MachinePrecision] * j + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.6e22 or 4.39999999999999981e-29 < x

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if -5.6e22 < x < -4.99999999999999983e-106 or 8.2000000000000003e-182 < x < 4.39999999999999981e-29

   1. Initial program 92.4%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 83.7

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.8%

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

   if -4.99999999999999983e-106 < x < 8.2000000000000003e-182

   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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 66.5

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

   7. Applied rewrites 66.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-106}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* j k) (* c b))) (t_2 (* k (* j 27.0))))
   (if (<= t_2 -1e+100)
     t_1
     (if (<= t_2 5e+22) (fma c b (* t (* a -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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (j * k), (c * b));
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t_2 <= -1e+100) {
		tmp = t_1;
	} else if (t_2 <= 5e+22) {
		tmp = fma(c, b, (t * (a * -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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(j * k), Float64(c * b))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_2 <= -1e+100)
		tmp = t_1;
	elseif (t_2 <= 5e+22)
		tmp = fma(c, b, Float64(t * Float64(a * -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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+100], t$95$1, If[LessEqual[t$95$2, 5e+22], N[(c * b + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000002e100 or 4.9999999999999996e22 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 87.4%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 72.8

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 63.0%

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

   if -1.00000000000000002e100 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999996e22

   1. Initial program 84.4%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 88.6%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 52.4

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

   7. Applied rewrites 52.4%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 78.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* x (fma (* y (* t 18.0)) z (* -4.0 i))))))
   (if (<= x -2.8e+24)
     t_1
     (if (<= x 1.35e-34) (fma b c (fma -4.0 (* t a) (* j (* k -27.0)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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, (x * fma((y * (t * 18.0)), z, (-4.0 * i))));
	double tmp;
	if (x <= -2.8e+24) {
		tmp = t_1;
	} else if (x <= 1.35e-34) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(x * fma(Float64(y * Float64(t * 18.0)), z, Float64(-4.0 * i))))
	tmp = 0.0
	if (x <= -2.8e+24)
		tmp = t_1;
	elseif (x <= 1.35e-34)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(x * N[(N[(y * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] * z + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+24], t$95$1, If[LessEqual[x, 1.35e-34], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e24 or 1.35000000000000008e-34 < x

   1. Initial program 76.0%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 85.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 82.2

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

   7. Applied rewrites 82.2%

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

   if -2.8000000000000002e24 < x < 1.35000000000000008e-34

   1. Initial program 94.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 84.9

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

   5. Applied rewrites 84.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \mathsf{fma}\left(y \cdot \left(t \cdot 18\right), z, -4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2.7 \cdot 10^{+114}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \cdot b \leq 1.3 \cdot 10^{+177}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -2.7e+114)
   (* c b)
   (if (<= (* c b) 3.3e-255)
     (* j (* k -27.0))
     (if (<= (* c b) 1.3e+177) (* -4.0 (* x i)) (* 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);
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) <= -2.7e+114) {
		tmp = c * b;
	} else if ((c * b) <= 3.3e-255) {
		tmp = j * (k * -27.0);
	} else if ((c * b) <= 1.3e+177) {
		tmp = -4.0 * (x * i);
	} 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.
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) <= (-2.7d+114)) then
        tmp = c * b
    else if ((c * b) <= 3.3d-255) then
        tmp = j * (k * (-27.0d0))
    else if ((c * b) <= 1.3d+177) then
        tmp = (-4.0d0) * (x * i)
    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;
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) <= -2.7e+114) {
		tmp = c * b;
	} else if ((c * b) <= 3.3e-255) {
		tmp = j * (k * -27.0);
	} else if ((c * b) <= 1.3e+177) {
		tmp = -4.0 * (x * i);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -2.7e+114:
		tmp = c * b
	elif (c * b) <= 3.3e-255:
		tmp = j * (k * -27.0)
	elif (c * b) <= 1.3e+177:
		tmp = -4.0 * (x * i)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -2.7e+114)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= 3.3e-255)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(c * b) <= 1.3e+177)
		tmp = Float64(-4.0 * Float64(x * i));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -2.7e+114)
		tmp = c * b;
	elseif ((c * b) <= 3.3e-255)
		tmp = j * (k * -27.0);
	elseif ((c * b) <= 1.3e+177)
		tmp = -4.0 * (x * i);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -2.7e+114], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 3.3e-255], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 1.3e+177], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.7e114 or 1.2999999999999999e177 < (*.f64 b c)

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if -2.7e114 < (*.f64 b c) < 3.29999999999999988e-255

   1. Initial program 90.5%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 34.0

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

   5. Applied rewrites 34.0%

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

   if 3.29999999999999988e-255 < (*.f64 b c) < 1.2999999999999999e177

   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 i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 29.7

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

   5. Applied rewrites 29.7%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2.7 \cdot 10^{+114}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \cdot b \leq 1.3 \cdot 10^{+177}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-322}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \cdot b \leq 1.3 \cdot 10^{+177}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -1.55e+77)
   (* c b)
   (if (<= (* c b) -2e-322)
     (* -4.0 (* t a))
     (if (<= (* c b) 1.3e+177) (* -4.0 (* x i)) (* 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);
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) <= -1.55e+77) {
		tmp = c * b;
	} else if ((c * b) <= -2e-322) {
		tmp = -4.0 * (t * a);
	} else if ((c * b) <= 1.3e+177) {
		tmp = -4.0 * (x * i);
	} 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.
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) <= (-1.55d+77)) then
        tmp = c * b
    else if ((c * b) <= (-2d-322)) then
        tmp = (-4.0d0) * (t * a)
    else if ((c * b) <= 1.3d+177) then
        tmp = (-4.0d0) * (x * i)
    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;
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) <= -1.55e+77) {
		tmp = c * b;
	} else if ((c * b) <= -2e-322) {
		tmp = -4.0 * (t * a);
	} else if ((c * b) <= 1.3e+177) {
		tmp = -4.0 * (x * i);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -1.55e+77:
		tmp = c * b
	elif (c * b) <= -2e-322:
		tmp = -4.0 * (t * a)
	elif (c * b) <= 1.3e+177:
		tmp = -4.0 * (x * i)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -1.55e+77)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= -2e-322)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (Float64(c * b) <= 1.3e+177)
		tmp = Float64(-4.0 * Float64(x * i));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -1.55e+77)
		tmp = c * b;
	elseif ((c * b) <= -2e-322)
		tmp = -4.0 * (t * a);
	elseif ((c * b) <= 1.3e+177)
		tmp = -4.0 * (x * i);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -1.55e+77], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -2e-322], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 1.3e+177], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.54999999999999999e77 or 1.2999999999999999e177 < (*.f64 b c)

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 63.7

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

   5. Applied rewrites 63.7%

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

   if -1.54999999999999999e77 < (*.f64 b c) < -1.97626e-322

   1. Initial program 89.0%

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

   3. Taylor expanded in 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 32.5

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

   5. Applied rewrites 32.5%

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

   if -1.97626e-322 < (*.f64 b c) < 1.2999999999999999e177

   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 i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.8

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

   5. Applied rewrites 26.8%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-322}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \cdot b \leq 1.3 \cdot 10^{+177}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 55.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* x (* -4.0 i)))))
   (if (<= (* c b) -1e+92)
     t_1
     (if (<= (* c b) 2e+99) (fma (* k -27.0) j (* t (* a -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);
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, (x * (-4.0 * i)));
	double tmp;
	if ((c * b) <= -1e+92) {
		tmp = t_1;
	} else if ((c * b) <= 2e+99) {
		tmp = fma((k * -27.0), j, (t * (a * -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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(x * Float64(-4.0 * i)))
	tmp = 0.0
	if (Float64(c * b) <= -1e+92)
		tmp = t_1;
	elseif (Float64(c * b) <= 2e+99)
		tmp = fma(Float64(k * -27.0), j, Float64(t * Float64(a * -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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -1e+92], t$95$1, If[LessEqual[N[(c * b), $MachinePrecision], 2e+99], N[(N[(k * -27.0), $MachinePrecision] * j + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1e92 or 1.9999999999999999e99 < (*.f64 b c)

   1. Initial program 78.7%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

   4. Applied rewrites 87.8%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 74.6

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

   7. Applied rewrites 74.6%

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

   if -1e92 < (*.f64 b c) < 1.9999999999999999e99

   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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 53.1

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

   7. Applied rewrites 53.1%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, x \cdot \left(-4 \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* t (* 18.0 (* z y)))))))
   (if (<= x -2.7e+34)
     t_1
     (if (<= x 3.5e-28) (fma b c (fma -4.0 (* t a) (* j (* k -27.0)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (t * (18.0 * (z * y))));
	double tmp;
	if (x <= -2.7e+34) {
		tmp = t_1;
	} else if (x <= 3.5e-28) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(z * y)))))
	tmp = 0.0
	if (x <= -2.7e+34)
		tmp = t_1;
	elseif (x <= 3.5e-28)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+34], t$95$1, If[LessEqual[x, 3.5e-28], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e34 or 3.5e-28 < x

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

   if -2.7e34 < x < 3.5e-28

   1. Initial program 94.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 85.0

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

   5. Applied rewrites 85.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 4.3 \cdot 10^{+109}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -1.55e+77)
   (* c b)
   (if (<= (* c b) 4.3e+109) (* -4.0 (* t a)) (* 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);
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) <= -1.55e+77) {
		tmp = c * b;
	} else if ((c * b) <= 4.3e+109) {
		tmp = -4.0 * (t * a);
	} 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.
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) <= (-1.55d+77)) then
        tmp = c * b
    else if ((c * b) <= 4.3d+109) then
        tmp = (-4.0d0) * (t * a)
    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;
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) <= -1.55e+77) {
		tmp = c * b;
	} else if ((c * b) <= 4.3e+109) {
		tmp = -4.0 * (t * a);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -1.55e+77:
		tmp = c * b
	elif (c * b) <= 4.3e+109:
		tmp = -4.0 * (t * a)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -1.55e+77)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= 4.3e+109)
		tmp = Float64(-4.0 * Float64(t * a));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -1.55e+77)
		tmp = c * b;
	elseif ((c * b) <= 4.3e+109)
		tmp = -4.0 * (t * a);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -1.55e+77], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 4.3e+109], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.54999999999999999e77 or 4.3000000000000001e109 < (*.f64 b c)

   1. Initial program 79.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 61.5

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

   5. Applied rewrites 61.5%

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

   if -1.54999999999999999e77 < (*.f64 b c) < 4.3000000000000001e109

   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 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 26.1

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

   5. Applied rewrites 26.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 4.3 \cdot 10^{+109}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* x i))))
   (if (<= x -6.2e+139)
     t_1
     (if (<= x 1.28e+85) (fma -27.0 (* j k) (* 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);
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 * (x * i);
	double tmp;
	if (x <= -6.2e+139) {
		tmp = t_1;
	} else if (x <= 1.28e+85) {
		tmp = fma(-27.0, (j * k), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -6.2e+139)
		tmp = t_1;
	elseif (x <= 1.28e+85)
		tmp = fma(-27.0, Float64(j * k), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+139], t$95$1, If[LessEqual[x, 1.28e+85], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e139 or 1.28000000000000004e85 < x

   1. Initial program 72.4%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 43.0

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

   5. Applied rewrites 43.0%

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

   if -6.2e139 < x < 1.28000000000000004e85

   1. Initial program 90.8%

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

   3. Taylor expanded in 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. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. lower-*.f64 75.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Applied rewrites 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   7. Step-by-step derivation

   8. Applied rewrites 54.7%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 24.1% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

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.
(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);
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.
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;
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])
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])
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])){:}
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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 85.7%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. lower-*.f64 23.8

      \[\leadsto \color{blue}{b \cdot c} \]

5. Applied rewrites 23.8%

   \[\leadsto \color{blue}{b \cdot c} \]

6. Final simplification 23.8%

   \[\leadsto c \cdot b \]
7. Add Preprocessing

Developer Target 1: 89.5% 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 2024234 
(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)))