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

Percentage Accurate: 85.2% → 94.1%

Time: 25.6s

Alternatives: 25

Speedup: 1.2×

• 50.6% 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: 85.2% 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: 94.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+42} \lor \neg \left(t \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.8e+42) (not (<= t 5e+45)))
   (fma
    (- j)
    (* k 27.0)
    (fma (* -4.0 x) i (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b))))
   (-
    (fma
     (* 18.0 x)
     (* y (* t z))
     (fma (* -4.0 a) t (fma c b (* -4.0 (* x i)))))
    (* (* j 27.0) k))))

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 ((t <= -3.8e+42) || !(t <= 5e+45)) {
		tmp = fma(-j, (k * 27.0), fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (c * b))));
	} else {
		tmp = fma((18.0 * x), (y * (t * z)), fma((-4.0 * a), t, fma(c, b, (-4.0 * (x * i))))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 ((t <= -3.8e+42) || !(t <= 5e+45))
		tmp = fma(Float64(-j), Float64(k * 27.0), fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = Float64(fma(Float64(18.0 * x), Float64(y * Float64(t * z)), fma(Float64(-4.0 * a), t, fma(c, b, Float64(-4.0 * Float64(x * i))))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.8e+42], N[Not[LessEqual[t, 5e+45]], $MachinePrecision]], N[((-j) * N[(k * 27.0), $MachinePrecision] + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * x), $MachinePrecision] * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999998e42 or 5e45 < t

   1. Initial program 88.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 89.4

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 95.5%

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

   if -3.7999999999999998e42 < t < 5e45

   1. Initial program 88.2%

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

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. lower-fma.f64 N/A

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

   4. Applied rewrites 97.2%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+42} \lor \neg \left(t \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+297} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+286}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (or (<= t_1 -2e+297) (not (<= t_1 5e+286)))
     (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
     (fma c b (* (* k j) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if ((t_1 <= -2e+297) || !(t_1 <= 5e+286)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 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))
	tmp = 0.0
	if ((t_1 <= -2e+297) || !(t_1 <= 5e+286))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -2e+297], N[Not[LessEqual[t$95$1, 5e+286]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $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)) < -2e297 or 5.0000000000000004e286 < (-.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 77.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if -2e297 < (-.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)) < 5.0000000000000004e286

   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. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 71.9

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -2 \cdot 10^{+297} \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+286}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+297}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 -2e+297)
     (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
     (if (<= t_1 5e+286)
       (fma c b (* (* k j) -27.0))
       (* (fma (* (* y z) t) 18.0 (* -4.0 i)) x)))))

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 * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+297) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (t_1 <= 5e+286) {
		tmp = fma(c, b, ((k * j) * -27.0));
	} else {
		tmp = fma(((y * z) * t), 18.0, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= -2e+297)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (t_1 <= 5e+286)
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	else
		tmp = Float64(fma(Float64(Float64(y * z) * t), 18.0, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(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]}, If[LessEqual[t$95$1, -2e+297], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $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)) < -2e297

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 58.8

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

   5. Applied rewrites 58.8%

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

   if -2e297 < (-.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)) < 5.0000000000000004e286

   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. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 71.9

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.8%

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

   if 5.0000000000000004e286 < (-.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 67.6%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 13.8

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

   5. Applied rewrites 13.8%

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

   6. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 63.9

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

   8. Applied rewrites 63.9%

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

Alternative 4: 91.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-j, k \cdot 27, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

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 -1.05e+172)
   (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b (* -27.0 (* k j))))
   (fma
    (- j)
    (* k 27.0)
    (fma (* -4.0 x) i (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.05e+172) {
		tmp = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	} else {
		tmp = fma(-j, (k * 27.0), fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (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 (x <= -1.05e+172)
		tmp = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, Float64(-27.0 * Float64(k * j))));
	else
		tmp = fma(Float64(-j), Float64(k * 27.0), fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, 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[x, -1.05e+172], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-j) * N[(k * 27.0), $MachinePrecision] + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0500000000000001e172

   1. Initial program 71.6%

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

   3. Taylor expanded in a around 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 96.0%

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

   if -1.0500000000000001e172 < x

   1. Initial program 90.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 91.1

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 93.3%

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

Alternative 5: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(t, \mathsf{fma}\left(\left(y \cdot z\right) \cdot 18, x, a \cdot -4\right), b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

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 1.5e+172)
   (fma
    (* x -4.0)
    i
    (fma (* -27.0 k) j (fma t (fma (* (* y z) 18.0) x (* a -4.0)) (* b c))))
   (fma
    (* -27.0 j)
    k
    (fma (* -4.0 x) i (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= 1.5e+172) {
		tmp = fma((x * -4.0), i, fma((-27.0 * k), j, fma(t, fma(((y * z) * 18.0), x, (a * -4.0)), (b * c))));
	} else {
		tmp = fma((-27.0 * j), k, fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (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 <= 1.5e+172)
		tmp = fma(Float64(x * -4.0), i, fma(Float64(-27.0 * k), j, fma(t, fma(Float64(Float64(y * z) * 18.0), x, Float64(a * -4.0)), Float64(b * c))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, 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, 1.5e+172], N[(N[(x * -4.0), $MachinePrecision] * i + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(t * N[(N[(N[(y * z), $MachinePrecision] * 18.0), $MachinePrecision] * x + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.5e172

   1. Initial program 88.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 89.3

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 91.9%

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

   6. Applied rewrites 94.9%

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

   if 1.5e172 < 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. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 83.7

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 87.7%

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

Alternative 6: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

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 -1.05e+172)
   (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b (* -27.0 (* k j))))
   (fma
    (* -27.0 j)
    k
    (fma (* -4.0 x) i (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.05e+172) {
		tmp = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	} else {
		tmp = fma((-27.0 * j), k, fma((-4.0 * x), i, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (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 (x <= -1.05e+172)
		tmp = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, Float64(-27.0 * Float64(k * j))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * x), i, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, 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[x, -1.05e+172], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0500000000000001e172

   1. Initial program 71.6%

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

   3. Taylor expanded in a around 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 96.0%

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

   if -1.0500000000000001e172 < x

   1. Initial program 90.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 91.5

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 93.7%

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

Alternative 7: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+89}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-13}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+89)
     (* -27.0 (* k j))
     (if (<= t_1 -2e-13)
       (* (* i x) -4.0)
       (if (<= t_1 1e+51) (* (* t a) -4.0) (* (* -27.0 k) j))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+89) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= -2e-13) {
		tmp = (i * x) * -4.0;
	} else if (t_1 <= 1e+51) {
		tmp = (t * a) * -4.0;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-5d+89)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= (-2d-13)) then
        tmp = (i * x) * (-4.0d0)
    else if (t_1 <= 1d+51) then
        tmp = (t * a) * (-4.0d0)
    else
        tmp = ((-27.0d0) * k) * j
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+89) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= -2e-13) {
		tmp = (i * x) * -4.0;
	} else if (t_1 <= 1e+51) {
		tmp = (t * a) * -4.0;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e+89:
		tmp = -27.0 * (k * j)
	elif t_1 <= -2e-13:
		tmp = (i * x) * -4.0
	elif t_1 <= 1e+51:
		tmp = (t * a) * -4.0
	else:
		tmp = (-27.0 * k) * j
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+89)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= -2e-13)
		tmp = Float64(Float64(i * x) * -4.0);
	elseif (t_1 <= 1e+51)
		tmp = Float64(Float64(t * a) * -4.0);
	else
		tmp = Float64(Float64(-27.0 * k) * j);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -5e+89)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= -2e-13)
		tmp = (i * x) * -4.0;
	elseif (t_1 <= 1e+51)
		tmp = (t * a) * -4.0;
	else
		tmp = (-27.0 * k) * j;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+89], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-13], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999983e89

   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 j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.5

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

   5. Applied rewrites 61.5%

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

   if -4.99999999999999983e89 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 33.4

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

   5. Applied rewrites 33.4%

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

   if -2.0000000000000001e-13 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e51

   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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 28.5%

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

   if 1e51 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.0%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.4

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

   5. Applied rewrites 49.4%

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

   7. Applied rewrites 49.4%

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

Alternative 8: 87.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00135 \lor \neg \left(x \leq 8.5 \cdot 10^{+29}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

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 (or (<= x -0.00135) (not (<= x 8.5e+29)))
   (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b (* -27.0 (* k j))))
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* x z) y) 18.0)) t (* 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 ((x <= -0.00135) || !(x <= 8.5e+29)) {
		tmp = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, (-27.0 * (k * j))));
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((x * z) * y) * 18.0)), t, (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 ((x <= -0.00135) || !(x <= 8.5e+29))
		tmp = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, Float64(-27.0 * Float64(k * j))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(x * z) * y) * 18.0)), t, 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[Or[LessEqual[x, -0.00135], N[Not[LessEqual[x, 8.5e+29]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0013500000000000001 or 8.5000000000000006e29 < x

   1. Initial program 76.7%

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

   3. Taylor expanded in 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 89.0%

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

   if -0.0013500000000000001 < x < 8.5000000000000006e29

   1. Initial program 97.0%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. unsub-neg N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate--l+ N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 88.3%

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

   7. Applied rewrites 92.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00135 \lor \neg \left(x \leq 8.5 \cdot 10^{+29}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-42} \lor \neg \left(t \leq 8.2 \cdot 10^{-94}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \end{array} \]

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 (or (<= t -1.75e-42) (not (<= t 8.2e-94)))
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* x z) y) 18.0)) t (* c b)))
   (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((t <= -1.75e-42) || !(t <= 8.2e-94)) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((x * z) * y) * 18.0)), t, (c * b)));
	} else {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 ((t <= -1.75e-42) || !(t <= 8.2e-94))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(x * z) * y) * 18.0)), t, Float64(c * b)));
	else
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.75e-42], N[Not[LessEqual[t, 8.2e-94]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7500000000000001e-42 or 8.20000000000000001e-94 < t

   1. Initial program 88.3%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. unsub-neg N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate--l+ N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 89.3%

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

   7. Applied rewrites 91.1%

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

   if -1.7500000000000001e-42 < t < 8.20000000000000001e-94

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

   5. Applied rewrites 92.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-42} \lor \neg \left(t \leq 8.2 \cdot 10^{-94}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot z\right) \cdot y\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-135}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* k j) -27.0))))
   (if (<= (* b c) -5e+28)
     t_1
     (if (<= (* b c) -2e-135)
       (* (* (* (* y z) x) t) 18.0)
       (if (<= (* b c) 5e+28) (fma (* -27.0 j) k (* (* i x) -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, ((k * j) * -27.0));
	double tmp;
	if ((b * c) <= -5e+28) {
		tmp = t_1;
	} else if ((b * c) <= -2e-135) {
		tmp = (((y * z) * x) * t) * 18.0;
	} else if ((b * c) <= 5e+28) {
		tmp = fma((-27.0 * j), k, ((i * x) * -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(Float64(k * j) * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -5e+28)
		tmp = t_1;
	elseif (Float64(b * c) <= -2e-135)
		tmp = Float64(Float64(Float64(Float64(y * z) * x) * t) * 18.0);
	elseif (Float64(b * c) <= 5e+28)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(i * x) * -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[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+28], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2e-135], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+28], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.99999999999999957e28 or 4.99999999999999957e28 < (*.f64 b c)

   1. Initial program 88.2%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 77.1

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.8%

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

   if -4.99999999999999957e28 < (*.f64 b c) < -2.0000000000000001e-135

   1. Initial program 91.3%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. unsub-neg N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate--l+ N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 48.2%

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

   if -2.0000000000000001e-135 < (*.f64 b c) < 4.99999999999999957e28

   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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 89.4

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 91.3%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.4

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

   7. Applied rewrites 58.4%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 57.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-135}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+232}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 62000000:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \mathsf{fma}\left(j \cdot k, -27, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(\left(y \cdot x\right) \cdot -18, z, 4 \cdot a\right)\\ \end{array} \end{array} \]

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 (fma c b (fma (* -27.0 j) k (* (* a t) -4.0)))))
   (if (<= t -5e+232)
     (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
     (if (<= t -3e+29)
       t_1
       (if (<= t 62000000.0)
         (fma (* x -4.0) i (fma (* j k) -27.0 (* c b)))
         (if (<= t 2.3e+158)
           t_1
           (* (- t) (fma (* (* y x) -18.0) z (* 4.0 a)))))))))

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((-27.0 * j), k, ((a * t) * -4.0)));
	double tmp;
	if (t <= -5e+232) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= -3e+29) {
		tmp = t_1;
	} else if (t <= 62000000.0) {
		tmp = fma((x * -4.0), i, fma((j * k), -27.0, (c * b)));
	} else if (t <= 2.3e+158) {
		tmp = t_1;
	} else {
		tmp = -t * fma(((y * x) * -18.0), z, (4.0 * a));
	}
	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(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0)))
	tmp = 0.0
	if (t <= -5e+232)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= -3e+29)
		tmp = t_1;
	elseif (t <= 62000000.0)
		tmp = fma(Float64(x * -4.0), i, fma(Float64(j * k), -27.0, Float64(c * b)));
	elseif (t <= 2.3e+158)
		tmp = t_1;
	else
		tmp = Float64(Float64(-t) * fma(Float64(Float64(y * x) * -18.0), z, Float64(4.0 * a)));
	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[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+232], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -3e+29], t$95$1, If[LessEqual[t, 62000000.0], N[(N[(x * -4.0), $MachinePrecision] * i + N[(N[(j * k), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+158], t$95$1, N[((-t) * N[(N[(N[(y * x), $MachinePrecision] * -18.0), $MachinePrecision] * z + N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.99999999999999987e232

   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 j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 6.6

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

   5. Applied rewrites 6.6%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 90.8

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

   8. Applied rewrites 90.8%

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

   if -4.99999999999999987e232 < t < -2.9999999999999999e29 or 6.2e7 < t < 2.29999999999999986e158

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 76.6

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

   5. Applied rewrites 76.6%

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

   if -2.9999999999999999e29 < t < 6.2e7

   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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 89.7

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 89.8%

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

   6. Applied rewrites 89.8%

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

   7. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 82.9

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

   9. Applied rewrites 82.9%

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

   if 2.29999999999999986e158 < t

   1. Initial program 78.5%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 18.5

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

   5. Applied rewrites 18.5%

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

   6. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. associate-*r* N/A

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

      5. neg-mul-1 N/A

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

      6. distribute-lft-in N/A

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

      7. +-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

   8. Applied rewrites 83.8%

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

Alternative 12: 72.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)\\ t_2 := \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -5 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 62000000:\\ \;\;\;\;\mathsf{fma}\left(x \cdot -4, i, \mathsf{fma}\left(j \cdot k, -27, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 c b (fma (* -27.0 j) k (* (* a t) -4.0))))
        (t_2 (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)))
   (if (<= t -5e+232)
     t_2
     (if (<= t -3e+29)
       t_1
       (if (<= t 62000000.0)
         (fma (* x -4.0) i (fma (* j k) -27.0 (* c b)))
         (if (<= t 2.3e+158) 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(c, b, fma((-27.0 * j), k, ((a * t) * -4.0)));
	double t_2 = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -5e+232) {
		tmp = t_2;
	} else if (t <= -3e+29) {
		tmp = t_1;
	} else if (t <= 62000000.0) {
		tmp = fma((x * -4.0), i, fma((j * k), -27.0, (c * b)));
	} else if (t <= 2.3e+158) {
		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(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0)))
	t_2 = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -5e+232)
		tmp = t_2;
	elseif (t <= -3e+29)
		tmp = t_1;
	elseif (t <= 62000000.0)
		tmp = fma(Float64(x * -4.0), i, fma(Float64(j * k), -27.0, Float64(c * b)));
	elseif (t <= 2.3e+158)
		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[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5e+232], t$95$2, If[LessEqual[t, -3e+29], t$95$1, If[LessEqual[t, 62000000.0], N[(N[(x * -4.0), $MachinePrecision] * i + N[(N[(j * k), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+158], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999987e232 or 2.29999999999999986e158 < t

   1. Initial program 82.2%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 14.6

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

   5. Applied rewrites 14.6%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 86.0

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

   8. Applied rewrites 86.0%

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

   if -4.99999999999999987e232 < t < -2.9999999999999999e29 or 6.2e7 < t < 2.29999999999999986e158

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 76.6

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

   5. Applied rewrites 76.6%

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

   if -2.9999999999999999e29 < t < 6.2e7

   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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

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

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

      8. lower-fma.f64 N/A

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

      9. lower-neg.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 89.7

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 89.8%

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

   6. Applied rewrites 89.8%

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

   7. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 82.9

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

   9. Applied rewrites 82.9%

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

Alternative 13: 72.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)\\ t_2 := \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -5 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 62000000:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 c b (fma (* -27.0 j) k (* (* a t) -4.0))))
        (t_2 (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)))
   (if (<= t -5e+232)
     t_2
     (if (<= t -3.8e+86)
       t_1
       (if (<= t 62000000.0)
         (fma c b (fma (* -27.0 j) k (* (* i x) -4.0)))
         (if (<= t 2.3e+158) 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(c, b, fma((-27.0 * j), k, ((a * t) * -4.0)));
	double t_2 = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -5e+232) {
		tmp = t_2;
	} else if (t <= -3.8e+86) {
		tmp = t_1;
	} else if (t <= 62000000.0) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((i * x) * -4.0)));
	} else if (t <= 2.3e+158) {
		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(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0)))
	t_2 = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -5e+232)
		tmp = t_2;
	elseif (t <= -3.8e+86)
		tmp = t_1;
	elseif (t <= 62000000.0)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(i * x) * -4.0)));
	elseif (t <= 2.3e+158)
		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[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5e+232], t$95$2, If[LessEqual[t, -3.8e+86], t$95$1, If[LessEqual[t, 62000000.0], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+158], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999987e232 or 2.29999999999999986e158 < t

   1. Initial program 82.2%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 14.6

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

   5. Applied rewrites 14.6%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 86.0

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

   8. Applied rewrites 86.0%

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

   if -4.99999999999999987e232 < t < -3.79999999999999978e86 or 6.2e7 < t < 2.29999999999999986e158

   1. Initial program 91.4%

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

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -3.79999999999999978e86 < t < 6.2e7

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 81.2

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

   5. Applied rewrites 81.2%

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

Alternative 14: 82.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+92} \lor \neg \left(y \leq 2.65 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(y \cdot \left(\left(z \cdot x\right) \cdot t\right), 18, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \end{array} \]

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 (or (<= y -5.2e+92) (not (<= y 2.65e+17)))
   (fma (* -27.0 j) k (fma (* y (* (* z x) t)) 18.0 (* b c)))
   (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((y <= -5.2e+92) || !(y <= 2.65e+17)) {
		tmp = fma((-27.0 * j), k, fma((y * ((z * x) * t)), 18.0, (b * c)));
	} else {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((y <= -5.2e+92) || !(y <= 2.65e+17))
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(y * Float64(Float64(z * x) * t)), 18.0, Float64(b * c)));
	else
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[y, -5.2e+92], N[Not[LessEqual[y, 2.65e+17]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(y * N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e92 or 2.65e17 < y

   1. Initial program 79.8%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. unsub-neg N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate--l+ N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 74.5%

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

   10. Applied rewrites 80.5%

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

   if -5.1999999999999998e92 < y < 2.65e17

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

   5. Applied rewrites 90.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+92} \lor \neg \left(y \leq 2.65 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(y \cdot \left(\left(z \cdot x\right) \cdot t\right), 18, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t, 18, b \cdot c\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(y \cdot \left(\left(z \cdot x\right) \cdot t\right), 18, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -5.8e+75)
   (fma (* -27.0 j) k (fma (* (* (* y z) x) t) 18.0 (* b c)))
   (if (<= y 2.65e+17)
     (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))
     (fma (* -27.0 j) k (fma (* y (* (* z x) t)) 18.0 (* b c))))))

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 (y <= -5.8e+75) {
		tmp = fma((-27.0 * j), k, fma((((y * z) * x) * t), 18.0, (b * c)));
	} else if (y <= 2.65e+17) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	} else {
		tmp = fma((-27.0 * j), k, fma((y * ((z * x) * t)), 18.0, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -5.8e+75)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(Float64(Float64(y * z) * x) * t), 18.0, Float64(b * c)));
	elseif (y <= 2.65e+17)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(y * Float64(Float64(z * x) * t)), 18.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -5.8e+75], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+17], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(y * N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999997e75

   1. Initial program 79.4%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. unsub-neg N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate--l+ N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 84.2%

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

   if -5.7999999999999997e75 < y < 2.65e17

   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 y around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

   5. Applied rewrites 90.5%

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

   if 2.65e17 < y

   1. Initial program 81.8%

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

   3. Taylor expanded in i around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. unsub-neg N/A

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

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

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

      6. metadata-eval N/A

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

      7. associate--l+ N/A

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

      8. +-commutative N/A

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

      9. associate--l+ N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 77.0%

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

Alternative 16: 79.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+237}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(\left(y \cdot x\right) \cdot -18, z, 4 \cdot a\right)\\ \end{array} \end{array} \]

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 (<= t -1.35e+237)
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (if (<= t 2.3e+158)
     (fma c b (fma (fma i x (* a t)) -4.0 (* -27.0 (* k j))))
     (* (- t) (fma (* (* y x) -18.0) z (* 4.0 a))))))

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 (t <= -1.35e+237) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= 2.3e+158) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, (-27.0 * (k * j))));
	} else {
		tmp = -t * fma(((y * x) * -18.0), z, (4.0 * a));
	}
	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 (t <= -1.35e+237)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 2.3e+158)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(-27.0 * Float64(k * j))));
	else
		tmp = Float64(Float64(-t) * fma(Float64(Float64(y * x) * -18.0), z, Float64(4.0 * a)));
	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[t, -1.35e+237], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.3e+158], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(N[(N[(y * x), $MachinePrecision] * -18.0), $MachinePrecision] * z + N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e237

   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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 6.9

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

   5. Applied rewrites 6.9%

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

   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 94.8

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

   8. Applied rewrites 94.8%

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

   if -1.35e237 < t < 2.29999999999999986e158

   1. Initial program 90.4%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

   5. Applied rewrites 85.2%

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

   if 2.29999999999999986e158 < t

   1. Initial program 78.5%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 18.5

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

   5. Applied rewrites 18.5%

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

   6. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. associate-*r* N/A

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

      5. neg-mul-1 N/A

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

      6. distribute-lft-in N/A

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

      7. +-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. associate-*r* N/A

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

      14. metadata-eval N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

   8. Applied rewrites 83.8%

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

Alternative 17: 35.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+47} \lor \neg \left(t\_1 \leq 10^{+51}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -1e+47) (not (<= t_1 1e+51)))
     (* -27.0 (* k j))
     (* (* 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 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+47) || !(t_1 <= 1e+51)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = (t * a) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-1d+47)) .or. (.not. (t_1 <= 1d+51))) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = (t * a) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+47) || !(t_1 <= 1e+51)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = (t * a) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -1e+47) or not (t_1 <= 1e+51):
		tmp = -27.0 * (k * j)
	else:
		tmp = (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(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -1e+47) || !(t_1 <= 1e+51))
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(Float64(t * a) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -1e+47) || ~((t_1 <= 1e+51)))
		tmp = -27.0 * (k * j);
	else
		tmp = (t * a) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+47], N[Not[LessEqual[t$95$1, 1e+51]], $MachinePrecision]], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e47 or 1e51 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.0%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 52.8

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

   5. Applied rewrites 52.8%

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

   if -1e47 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e51

   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 x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 50.0

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 26.6%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+47} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 10^{+51}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+47}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+47)
     (* -27.0 (* k j))
     (if (<= t_1 1e+51) (* (* t a) -4.0) (* (* -27.0 k) j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+47) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 1e+51) {
		tmp = (t * a) * -4.0;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+47)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= 1d+51) then
        tmp = (t * a) * (-4.0d0)
    else
        tmp = ((-27.0d0) * k) * j
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+47) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 1e+51) {
		tmp = (t * a) * -4.0;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+47:
		tmp = -27.0 * (k * j)
	elif t_1 <= 1e+51:
		tmp = (t * a) * -4.0
	else:
		tmp = (-27.0 * k) * j
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+47)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 1e+51)
		tmp = Float64(Float64(t * a) * -4.0);
	else
		tmp = Float64(Float64(-27.0 * k) * j);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+47)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 1e+51)
		tmp = (t * a) * -4.0;
	else
		tmp = (-27.0 * k) * j;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+47], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e47

   1. Initial program 86.0%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 56.4

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

   5. Applied rewrites 56.4%

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

   if -1e47 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e51

   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 x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 50.0

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 26.6%

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

   if 1e51 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 86.0%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.4

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

   5. Applied rewrites 49.4%

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

   7. Applied rewrites 49.4%

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

Alternative 19: 71.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -6.5e+194)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x 1.1e+63)
     (fma c b (fma (* -27.0 j) k (* (* a t) -4.0)))
     (* (fma (* (* y z) t) 18.0 (* -4.0 i)) x))))

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 <= -6.5e+194) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= 1.1e+63) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((a * t) * -4.0)));
	} else {
		tmp = fma(((y * z) * t), 18.0, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -6.5e+194)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= 1.1e+63)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(a * t) * -4.0)));
	else
		tmp = Float64(fma(Float64(Float64(y * z) * t), 18.0, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -6.5e+194], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.1e+63], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000005e194

   1. Initial program 77.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -6.50000000000000005e194 < x < 1.0999999999999999e63

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

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

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

      10. metadata-eval N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 71.5

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 71.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   if 1.0999999999999999e63 < x

   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 j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 18.4

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 18.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot i\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(y \cdot z\right), 18, -4 \cdot i\right)} \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot t}, 18, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot t}, 18, -4 \cdot i\right) \cdot x \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right)} \cdot t, 18, -4 \cdot i\right) \cdot x \]

      12. lower-*.f64 72.3

          \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, \color{blue}{-4 \cdot i}\right) \cdot x \]

   8. Applied rewrites 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, -4 \cdot i\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 57.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+72} \lor \neg \left(t \leq 2.2 \cdot 10^{-117}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.12e+72) (not (<= t 2.2e-117)))
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (fma c b (* (* k j) -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((t <= -1.12e+72) || !(t <= 2.2e-117)) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.12e+72) || !(t <= 2.2e-117))
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.12e+72], N[Not[LessEqual[t, 2.2e-117]], $MachinePrecision]], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12000000000000001e72 or 2.2000000000000001e-117 < t

   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 j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 21.0

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 21.0%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   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. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

      12. lower-*.f64 66.0

          \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   8. Applied rewrites 66.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]

   if -1.12000000000000001e72 < t < 2.2000000000000001e-117

   1. Initial program 89.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 62.7

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 62.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 59.8%

      \[\leadsto \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+72} \lor \neg \left(t \leq 2.2 \cdot 10^{-117}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+72} \lor \neg \left(z \leq 3.5 \cdot 10^{+214}\right):\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= z -2.7e+72) (not (<= z 3.5e+214)))
   (* x (* (* y 18.0) (* t z)))
   (fma c b (* (* k j) -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.7e+72) || !(z <= 3.5e+214)) {
		tmp = x * ((y * 18.0) * (t * z));
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((z <= -2.7e+72) || !(z <= 3.5e+214))
		tmp = Float64(x * Float64(Float64(y * 18.0) * Float64(t * z)));
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[z, -2.7e+72], N[Not[LessEqual[z, 3.5e+214]], $MachinePrecision]], N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7000000000000001e72 or 3.5e214 < z

   1. Initial program 85.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 54.8%

      \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 49.4%

       \[\leadsto x \cdot \left(\left(y \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   if -2.7000000000000001e72 < z < 3.5e214

   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 x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 67.5

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 48.0%

      \[\leadsto \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+72} \lor \neg \left(z \leq 3.5 \cdot 10^{+214}\right):\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 48.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(\left(18 \cdot x\right) \cdot t\right)\\ \end{array} \end{array} \]

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 -2.7e+72)
   (* x (* (* y 18.0) (* t z)))
   (if (<= z 6.5e+214)
     (fma c b (* (* k j) -27.0))
     (* (* z y) (* (* 18.0 x) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -2.7e+72) {
		tmp = x * ((y * 18.0) * (t * z));
	} else if (z <= 6.5e+214) {
		tmp = fma(c, b, ((k * j) * -27.0));
	} else {
		tmp = (z * y) * ((18.0 * x) * t);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -2.7e+72)
		tmp = Float64(x * Float64(Float64(y * 18.0) * Float64(t * z)));
	elseif (z <= 6.5e+214)
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	else
		tmp = Float64(Float64(z * y) * Float64(Float64(18.0 * x) * t));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -2.7e+72], N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+214], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(N[(18.0 * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000001e72

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 52.3%

      \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.4%

       \[\leadsto x \cdot \left(\left(y \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   if -2.7000000000000001e72 < z < 6.5000000000000001e214

   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 x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 67.5

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 48.0%

      \[\leadsto \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right) \]

   if 6.5000000000000001e214 < z

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 67.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.7%

      \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 61.7%

       \[\leadsto \left(z \cdot y\right) \cdot \left(\left(18 \cdot x\right) \cdot \color{blue}{t}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(\left(18 \cdot x\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 48.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(y \cdot 18\right)\\ \end{array} \end{array} \]

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 -2.7e+72)
   (* x (* (* y 18.0) (* t z)))
   (if (<= z 1.3e+94)
     (fma c b (* (* k j) -27.0))
     (* (* t (* z x)) (* y 18.0)))))

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 <= -2.7e+72) {
		tmp = x * ((y * 18.0) * (t * z));
	} else if (z <= 1.3e+94) {
		tmp = fma(c, b, ((k * j) * -27.0));
	} else {
		tmp = (t * (z * x)) * (y * 18.0);
	}
	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 <= -2.7e+72)
		tmp = Float64(x * Float64(Float64(y * 18.0) * Float64(t * z)));
	elseif (z <= 1.3e+94)
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	else
		tmp = Float64(Float64(t * Float64(z * x)) * Float64(y * 18.0));
	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, -2.7e+72], N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+94], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z * x), $MachinePrecision]), $MachinePrecision] * N[(y * 18.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000001e72

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 52.3%

      \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.4%

       \[\leadsto x \cdot \left(\left(y \cdot 18\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   if -2.7000000000000001e72 < z < 1.3e94

   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 x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 69.9

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 69.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 49.3%

      \[\leadsto \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right) \]

   if 1.3e94 < z

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right)} \]

      4. unsub-neg N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\color{blue}{-27} \cdot \left(j \cdot k\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      9. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

   5. Applied rewrites 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 50.8%

      \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 46.3%

       \[\leadsto \left(t \cdot \left(z \cdot x\right)\right) \cdot \left(y \cdot \color{blue}{18}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(y \cdot 18\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 47.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -6.9 \cdot 10^{+53} \lor \neg \left(i \leq 8.6 \cdot 10^{+230}\right):\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -6.9e+53) (not (<= i 8.6e+230)))
   (* (* i x) -4.0)
   (fma c b (* (* k j) -27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -6.9e+53) || !(i <= 8.6e+230)) {
		tmp = (i * x) * -4.0;
	} else {
		tmp = fma(c, b, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -6.9e+53) || !(i <= 8.6e+230))
		tmp = Float64(Float64(i * x) * -4.0);
	else
		tmp = fma(c, b, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -6.9e+53], N[Not[LessEqual[i, 8.6e+230]], $MachinePrecision]], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.9000000000000002e53 or 8.59999999999999918e230 < i

   1. Initial program 84.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      3. lower-*.f64 51.8

         \[\leadsto \color{blue}{\left(i \cdot x\right)} \cdot -4 \]

   5. Applied rewrites 51.8%

      \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

   if -6.9000000000000002e53 < i < 8.59999999999999918e230

   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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

      15. lower-*.f64 68.3

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

   5. Applied rewrites 68.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.7%

      \[\leadsto \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.9 \cdot 10^{+53} \lor \neg \left(i \leq 8.6 \cdot 10^{+230}\right):\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \left(t \cdot a\right) \cdot -4 \end{array} \]

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 (* (* 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) {
	return (t * a) * -4.0;
}

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 = (t * a) * (-4.0d0)
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 (t * a) * -4.0;
}

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 (t * a) * -4.0

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(Float64(t * a) * -4.0)
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 = (t * a) * -4.0;
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[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

1. Initial program 88.3%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

   4. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

   5. distribute-neg-in N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

   6. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

   7. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

   8. associate-*r* N/A

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

   9. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

   11. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

   12. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, -4 \cdot \left(a \cdot t\right)\right)\right) \]

   13. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

   14. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \]

   15. lower-*.f64 62.7

       \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(a \cdot t\right)} \cdot -4\right)\right) \]

5. Applied rewrites 62.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(a \cdot t\right) \cdot -4\right)\right)} \]

6. Taylor expanded in t around inf

   \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 21.7%

   \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{-4} \]
9. Add Preprocessing

Developer Target 1: 89.3% 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 2024318 
(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)))