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

Percentage Accurate: 85.8% → 91.3%

Time: 32.5s

Alternatives: 23

Speedup: 1.2×

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.3% accurate, 0.5× speedup

Math

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

FPCore

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 96.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

4. Final simplification 94.2%

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

Alternative 2: 90.6% accurate, 0.5× speedup

Math

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

FPCore

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-+l+ N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. lower-fma.f64 N/A

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

   4. Applied rewrites 94.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

4. Final simplification 92.4%

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

Alternative 3: 90.5% accurate, 0.5× speedup

Math

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

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 18.0) y) z) t) (* t (* a 4.0))) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (fma
    (* j k)
    -27.0
    (fma x (* i -4.0) (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (* b c))))
   (* t (fma -4.0 a (* 18.0 (* z (* x y)))))))

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 95.4

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 94.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

4. Final simplification 92.4%

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

Alternative 4: 87.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\\ t_2 := \mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), t\_1\right)\\ \mathbf{if}\;x \leq -6.1 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 b c (* j (* k -27.0))))
        (t_2 (fma x (fma -4.0 i (* t (* 18.0 (* y z)))) t_1)))
   (if (<= x -6.1e-27)
     t_2
     (if (<= x 4.6e-6) (fma t (fma -4.0 a (* 18.0 (* z (* x y)))) 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(b, c, (j * (k * -27.0)));
	double t_2 = fma(x, fma(-4.0, i, (t * (18.0 * (y * z)))), t_1);
	double tmp;
	if (x <= -6.1e-27) {
		tmp = t_2;
	} else if (x <= 4.6e-6) {
		tmp = fma(t, fma(-4.0, a, (18.0 * (z * (x * y)))), 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(b, c, Float64(j * Float64(k * -27.0)))
	t_2 = fma(x, fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))), t_1)
	tmp = 0.0
	if (x <= -6.1e-27)
		tmp = t_2;
	elseif (x <= 4.6e-6)
		tmp = fma(t, fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))), 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[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x, -6.1e-27], t$95$2, If[LessEqual[x, 4.6e-6], N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0999999999999999e-27 or 4.6e-6 < x

   1. Initial program 76.9%

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

   3. Taylor expanded in 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 89.3%

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

   if -6.0999999999999999e-27 < x < 4.6e-6

   1. Initial program 93.7%

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

   3. Taylor expanded in i around 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. associate--r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

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

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 92.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, a \cdot -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          t
          (fma -4.0 a (* 18.0 (* z (* x y))))
          (fma b c (* j (* k -27.0))))))
   (if (<= t -1.36e+23)
     t_1
     (if (<= t 1.3e+128)
       (fma (* j k) -27.0 (fma x (* i -4.0) (fma t (* a -4.0) (* b c))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(t, fma(-4.0, a, (18.0 * (z * (x * y)))), fma(b, c, (j * (k * -27.0))));
	double tmp;
	if (t <= -1.36e+23) {
		tmp = t_1;
	} else if (t <= 1.3e+128) {
		tmp = fma((j * k), -27.0, fma(x, (i * -4.0), fma(t, (a * -4.0), (b * c))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(t, fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))), fma(b, c, Float64(j * Float64(k * -27.0))))
	tmp = 0.0
	if (t <= -1.36e+23)
		tmp = t_1;
	elseif (t <= 1.3e+128)
		tmp = fma(Float64(j * k), -27.0, fma(x, Float64(i * -4.0), fma(t, Float64(a * -4.0), Float64(b * c))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e+23], t$95$1, If[LessEqual[t, 1.3e+128], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(x * N[(i * -4.0), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.36e23 or 1.3e128 < t

   1. Initial program 81.3%

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

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

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

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 88.2%

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

   if -1.36e23 < t < 1.3e128

   1. Initial program 88.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 88.6

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 89.8

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

   7. Applied rewrites 89.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, a \cdot -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.58 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, a \cdot -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 -8.8e+167)
   (* x (fma -4.0 i (* y (* z (* 18.0 t)))))
   (if (<= x 1.58e+218)
     (fma (* j k) -27.0 (fma x (* i -4.0) (fma t (* a -4.0) (* b c))))
     (* x (fma -4.0 i (* t (* 18.0 (* y z))))))))

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 <= -8.8e+167) {
		tmp = x * fma(-4.0, i, (y * (z * (18.0 * t))));
	} else if (x <= 1.58e+218) {
		tmp = fma((j * k), -27.0, fma(x, (i * -4.0), fma(t, (a * -4.0), (b * c))));
	} else {
		tmp = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	}
	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 <= -8.8e+167)
		tmp = Float64(x * fma(-4.0, i, Float64(y * Float64(z * Float64(18.0 * t)))));
	elseif (x <= 1.58e+218)
		tmp = fma(Float64(j * k), -27.0, fma(x, Float64(i * -4.0), fma(t, Float64(a * -4.0), Float64(b * c))));
	else
		tmp = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))));
	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, -8.8e+167], N[(x * N[(-4.0 * i + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.58e+218], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(x * N[(i * -4.0), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.80000000000000013e167

   1. Initial program 57.4%

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

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 1.5

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

   5. Applied rewrites 1.5%

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

   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. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 89.3

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

   8. Applied rewrites 89.3%

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

   if -8.80000000000000013e167 < x < 1.58e218

   1. Initial program 90.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 91.3

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 84.2

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

   7. Applied rewrites 84.2%

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

   if 1.58e218 < x

   1. Initial program 71.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 95.1

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

   5. Applied rewrites 95.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.58 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, a \cdot -4, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 -6.2e-27)
   (* x (fma -4.0 i (* y (* z (* 18.0 t)))))
   (if (<= x -1.9e-252)
     (* t (fma -4.0 a (* 18.0 (* z (* x y)))))
     (if (<= x 6.5e+106)
       (fma (* j -27.0) k (* b c))
       (* x (fma -4.0 i (* t (* 18.0 (* y z)))))))))

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 <= -6.2e-27) {
		tmp = x * fma(-4.0, i, (y * (z * (18.0 * t))));
	} else if (x <= -1.9e-252) {
		tmp = t * fma(-4.0, a, (18.0 * (z * (x * y))));
	} else if (x <= 6.5e+106) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	}
	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 <= -6.2e-27)
		tmp = Float64(x * fma(-4.0, i, Float64(y * Float64(z * Float64(18.0 * t)))));
	elseif (x <= -1.9e-252)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))));
	elseif (x <= 6.5e+106)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))));
	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, -6.2e-27], N[(x * N[(-4.0 * i + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-252], N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+106], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.1999999999999997e-27

   1. Initial program 74.9%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 10.6

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

   5. Applied rewrites 10.6%

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

   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. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 78.4

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

   8. Applied rewrites 78.4%

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

   if -6.1999999999999997e-27 < x < -1.9e-252

   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 t around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   if -1.9e-252 < x < 6.5000000000000003e106

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 70.3

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

   5. Applied rewrites 70.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 70.3%

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

   if 6.5000000000000003e106 < x

   1. Initial program 75.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 77.1

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

   5. Applied rewrites 77.1%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* t (* 18.0 (* y z)))))))
   (if (<= x -9.2e-27)
     t_1
     (if (<= x -1.9e-252)
       (* t (fma -4.0 a (* 18.0 (* z (* x y)))))
       (if (<= x 6.5e+106) (fma (* j -27.0) k (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	double tmp;
	if (x <= -9.2e-27) {
		tmp = t_1;
	} else if (x <= -1.9e-252) {
		tmp = t * fma(-4.0, a, (18.0 * (z * (x * y))));
	} else if (x <= 6.5e+106) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (x <= -9.2e-27)
		tmp = t_1;
	elseif (x <= -1.9e-252)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))));
	elseif (x <= 6.5e+106)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e-27], t$95$1, If[LessEqual[x, -1.9e-252], N[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+106], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.1999999999999998e-27 or 6.5000000000000003e106 < x

   1. Initial program 75.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 76.0

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

   5. Applied rewrites 76.0%

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

   if -9.1999999999999998e-27 < x < -1.9e-252

   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 t around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   if -1.9e-252 < x < 6.5000000000000003e106

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 70.3

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

   5. Applied rewrites 70.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 70.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-255}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 -8.6e+167)
   (* z (* (* 18.0 y) (* x t)))
   (if (<= x -1e-26)
     (fma (* j k) -27.0 (* x (* i -4.0)))
     (if (<= x -1.1e-255)
       (fma (* j k) -27.0 (* -4.0 (* t a)))
       (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) (* -4.0 (* x i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -8.6e+167) {
		tmp = z * ((18.0 * y) * (x * t));
	} else if (x <= -1e-26) {
		tmp = fma((j * k), -27.0, (x * (i * -4.0)));
	} else if (x <= -1.1e-255) {
		tmp = fma((j * k), -27.0, (-4.0 * (t * a)));
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = -4.0 * (x * i);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -8.6e+167)
		tmp = Float64(z * Float64(Float64(18.0 * y) * Float64(x * t)));
	elseif (x <= -1e-26)
		tmp = fma(Float64(j * k), -27.0, Float64(x * Float64(i * -4.0)));
	elseif (x <= -1.1e-255)
		tmp = fma(Float64(j * k), -27.0, Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = Float64(-4.0 * Float64(x * i));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -8.6e+167], N[(z * N[(N[(18.0 * y), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-26], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-255], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.6000000000000004e167

   1. Initial program 57.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 19.3

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

   5. Applied rewrites 19.3%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 58.1

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

   8. Applied rewrites 58.1%

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

   10. Applied rewrites 64.8%

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

   if -8.6000000000000004e167 < x < -1e-26

   1. Initial program 93.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 93.1

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if -1e-26 < x < -1.1e-255

   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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 90.4

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 88.8%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.9

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

   7. Applied rewrites 57.9%

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

   if -1.1e-255 < x < 2.1000000000000002e215

   1. Initial program 90.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 63.7

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

   5. Applied rewrites 63.7%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 63.7%

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

   if 2.1000000000000002e215 < x

   1. Initial program 74.2%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.7

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

   5. Applied rewrites 70.7%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, x \cdot \left(i \cdot -4\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-255}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 -6.2e+46)
   (* x (fma -4.0 i (* y (* z (* 18.0 t)))))
   (if (<= x 9.2e+136)
     (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
     (* x (fma -4.0 i (* t (* 18.0 (* y z))))))))

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 <= -6.2e+46) {
		tmp = x * fma(-4.0, i, (y * (z * (18.0 * t))));
	} else if (x <= 9.2e+136) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	}
	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 <= -6.2e+46)
		tmp = Float64(x * fma(-4.0, i, Float64(y * Float64(z * Float64(18.0 * t)))));
	elseif (x <= 9.2e+136)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))));
	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, -6.2e+46], N[(x * N[(-4.0 * i + N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+136], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999995e46

   1. Initial program 71.2%

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

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 7.8

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

   5. Applied rewrites 7.8%

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

   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. lower-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. associate-*r* N/A

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

      10. lower-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 83.5

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

   8. Applied rewrites 83.5%

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

   if -6.1999999999999995e46 < x < 9.2e136

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. lower-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 81.2

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

   5. Applied rewrites 81.2%

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

   if 9.2e136 < x

   1. Initial program 76.3%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, y \cdot \left(z \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;t \leq -110000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* t (fma -4.0 a (* 18.0 (* z (* x y)))))))
   (if (<= t -110000.0)
     t_1
     (if (<= t 1.3e+128) (fma (* j -27.0) k (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = t * fma(-4.0, a, (18.0 * (z * (x * y))));
	double tmp;
	if (t <= -110000.0) {
		tmp = t_1;
	} else if (t <= 1.3e+128) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(t * fma(-4.0, a, Float64(18.0 * Float64(z * Float64(x * y)))))
	tmp = 0.0
	if (t <= -110000.0)
		tmp = t_1;
	elseif (t <= 1.3e+128)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(t * N[(-4.0 * a + N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -110000.0], t$95$1, If[LessEqual[t, 1.3e+128], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e5 or 1.3e128 < t

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -1.1e5 < t < 1.3e128

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 60.8

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

   5. Applied rewrites 60.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 60.8%

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

Alternative 12: 31.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-176}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -1.5e-43)
   (* b c)
   (if (<= c 5.9e-176)
     (* (* j k) -27.0)
     (if (<= c 1.22e-49)
       (* -4.0 (* t a))
       (if (<= c 6.8e+148) (* -4.0 (* x i)) (* 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 (c <= -1.5e-43) {
		tmp = b * c;
	} else if (c <= 5.9e-176) {
		tmp = (j * k) * -27.0;
	} else if (c <= 1.22e-49) {
		tmp = -4.0 * (t * a);
	} else if (c <= 6.8e+148) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (c <= (-1.5d-43)) then
        tmp = b * c
    else if (c <= 5.9d-176) then
        tmp = (j * k) * (-27.0d0)
    else if (c <= 1.22d-49) then
        tmp = (-4.0d0) * (t * a)
    else if (c <= 6.8d+148) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= -1.5e-43) {
		tmp = b * c;
	} else if (c <= 5.9e-176) {
		tmp = (j * k) * -27.0;
	} else if (c <= 1.22e-49) {
		tmp = -4.0 * (t * a);
	} else if (c <= 6.8e+148) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= -1.5e-43:
		tmp = b * c
	elif c <= 5.9e-176:
		tmp = (j * k) * -27.0
	elif c <= 1.22e-49:
		tmp = -4.0 * (t * a)
	elif c <= 6.8e+148:
		tmp = -4.0 * (x * i)
	else:
		tmp = 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 (c <= -1.5e-43)
		tmp = Float64(b * c);
	elseif (c <= 5.9e-176)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (c <= 1.22e-49)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (c <= 6.8e+148)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (c <= -1.5e-43)
		tmp = b * c;
	elseif (c <= 5.9e-176)
		tmp = (j * k) * -27.0;
	elseif (c <= 1.22e-49)
		tmp = -4.0 * (t * a);
	elseif (c <= 6.8e+148)
		tmp = -4.0 * (x * i);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, -1.5e-43], N[(b * c), $MachinePrecision], If[LessEqual[c, 5.9e-176], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[c, 1.22e-49], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e+148], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.50000000000000002e-43 or 6.8000000000000006e148 < c

   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 b around inf

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

      1. lower-*.f64 43.8

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

   5. Applied rewrites 43.8%

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

   if -1.50000000000000002e-43 < c < 5.8999999999999997e-176

   1. Initial program 84.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 37.2

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

   5. Applied rewrites 37.2%

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

   7. Applied rewrites 37.2%

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

   if 5.8999999999999997e-176 < c < 1.2199999999999999e-49

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 38.5

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

   5. Applied rewrites 38.5%

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

   if 1.2199999999999999e-49 < c < 6.8000000000000006e148

   1. Initial program 73.7%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 28.2

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

   5. Applied rewrites 28.2%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-176}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-176}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -1.5e-43)
   (* b c)
   (if (<= c 5.9e-176)
     (* k (* j -27.0))
     (if (<= c 1.22e-49)
       (* -4.0 (* t a))
       (if (<= c 6.8e+148) (* -4.0 (* x i)) (* 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 (c <= -1.5e-43) {
		tmp = b * c;
	} else if (c <= 5.9e-176) {
		tmp = k * (j * -27.0);
	} else if (c <= 1.22e-49) {
		tmp = -4.0 * (t * a);
	} else if (c <= 6.8e+148) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (c <= (-1.5d-43)) then
        tmp = b * c
    else if (c <= 5.9d-176) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 1.22d-49) then
        tmp = (-4.0d0) * (t * a)
    else if (c <= 6.8d+148) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= -1.5e-43) {
		tmp = b * c;
	} else if (c <= 5.9e-176) {
		tmp = k * (j * -27.0);
	} else if (c <= 1.22e-49) {
		tmp = -4.0 * (t * a);
	} else if (c <= 6.8e+148) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= -1.5e-43:
		tmp = b * c
	elif c <= 5.9e-176:
		tmp = k * (j * -27.0)
	elif c <= 1.22e-49:
		tmp = -4.0 * (t * a)
	elif c <= 6.8e+148:
		tmp = -4.0 * (x * i)
	else:
		tmp = 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 (c <= -1.5e-43)
		tmp = Float64(b * c);
	elseif (c <= 5.9e-176)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 1.22e-49)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (c <= 6.8e+148)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (c <= -1.5e-43)
		tmp = b * c;
	elseif (c <= 5.9e-176)
		tmp = k * (j * -27.0);
	elseif (c <= 1.22e-49)
		tmp = -4.0 * (t * a);
	elseif (c <= 6.8e+148)
		tmp = -4.0 * (x * i);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, -1.5e-43], N[(b * c), $MachinePrecision], If[LessEqual[c, 5.9e-176], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.22e-49], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e+148], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.50000000000000002e-43 or 6.8000000000000006e148 < c

   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 b around inf

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

      1. lower-*.f64 43.8

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

   5. Applied rewrites 43.8%

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

   if -1.50000000000000002e-43 < c < 5.8999999999999997e-176

   1. Initial program 84.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 37.2

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

   5. Applied rewrites 37.2%

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

   7. Applied rewrites 36.2%

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

   if 5.8999999999999997e-176 < c < 1.2199999999999999e-49

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 38.5

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

   5. Applied rewrites 38.5%

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

   if 1.2199999999999999e-49 < c < 6.8000000000000006e148

   1. Initial program 73.7%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 28.2

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

   5. Applied rewrites 28.2%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-176}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= c -1.5e-43)
   (* b c)
   (if (<= c 5.9e-176)
     (* j (* k -27.0))
     (if (<= c 1.22e-49)
       (* -4.0 (* t a))
       (if (<= c 6.8e+148) (* -4.0 (* x i)) (* 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 (c <= -1.5e-43) {
		tmp = b * c;
	} else if (c <= 5.9e-176) {
		tmp = j * (k * -27.0);
	} else if (c <= 1.22e-49) {
		tmp = -4.0 * (t * a);
	} else if (c <= 6.8e+148) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (c <= (-1.5d-43)) then
        tmp = b * c
    else if (c <= 5.9d-176) then
        tmp = j * (k * (-27.0d0))
    else if (c <= 1.22d-49) then
        tmp = (-4.0d0) * (t * a)
    else if (c <= 6.8d+148) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (c <= -1.5e-43) {
		tmp = b * c;
	} else if (c <= 5.9e-176) {
		tmp = j * (k * -27.0);
	} else if (c <= 1.22e-49) {
		tmp = -4.0 * (t * a);
	} else if (c <= 6.8e+148) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if c <= -1.5e-43:
		tmp = b * c
	elif c <= 5.9e-176:
		tmp = j * (k * -27.0)
	elif c <= 1.22e-49:
		tmp = -4.0 * (t * a)
	elif c <= 6.8e+148:
		tmp = -4.0 * (x * i)
	else:
		tmp = 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 (c <= -1.5e-43)
		tmp = Float64(b * c);
	elseif (c <= 5.9e-176)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (c <= 1.22e-49)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (c <= 6.8e+148)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (c <= -1.5e-43)
		tmp = b * c;
	elseif (c <= 5.9e-176)
		tmp = j * (k * -27.0);
	elseif (c <= 1.22e-49)
		tmp = -4.0 * (t * a);
	elseif (c <= 6.8e+148)
		tmp = -4.0 * (x * i);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[c, -1.5e-43], N[(b * c), $MachinePrecision], If[LessEqual[c, 5.9e-176], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.22e-49], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e+148], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.50000000000000002e-43 or 6.8000000000000006e148 < c

   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 b around inf

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

      1. lower-*.f64 43.8

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

   5. Applied rewrites 43.8%

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

   if -1.50000000000000002e-43 < c < 5.8999999999999997e-176

   1. Initial program 84.7%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 37.2

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

   5. Applied rewrites 37.2%

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

   if 5.8999999999999997e-176 < c < 1.2199999999999999e-49

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 38.5

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

   5. Applied rewrites 38.5%

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

   if 1.2199999999999999e-49 < c < 6.8000000000000006e148

   1. Initial program 73.7%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 28.2

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

   5. Applied rewrites 28.2%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-255}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 -8e+83)
   (* z (* (* 18.0 y) (* x t)))
   (if (<= x -1.1e-255)
     (fma (* j k) -27.0 (* -4.0 (* t a)))
     (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) (* -4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -8e+83) {
		tmp = z * ((18.0 * y) * (x * t));
	} else if (x <= -1.1e-255) {
		tmp = fma((j * k), -27.0, (-4.0 * (t * a)));
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = -4.0 * (x * i);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -8e+83)
		tmp = Float64(z * Float64(Float64(18.0 * y) * Float64(x * t)));
	elseif (x <= -1.1e-255)
		tmp = fma(Float64(j * k), -27.0, Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = Float64(-4.0 * Float64(x * i));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -8e+83], N[(z * N[(N[(18.0 * y), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-255], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.00000000000000025e83

   1. Initial program 69.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 17.1

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

   5. Applied rewrites 17.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 45.8

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

   8. Applied rewrites 45.8%

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

   10. Applied rewrites 54.1%

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

   if -8.00000000000000025e83 < x < -1.1e-255

   1. Initial program 91.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

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

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 92.0

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 90.6%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 53.7

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

   7. Applied rewrites 53.7%

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

   if -1.1e-255 < x < 2.1000000000000002e215

   1. Initial program 90.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 63.7

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

   5. Applied rewrites 63.7%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 63.7%

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

   if 2.1000000000000002e215 < x

   1. Initial program 74.2%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.7

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

   5. Applied rewrites 70.7%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-255}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -6e+166)
     (* z (* (* 18.0 y) (* x t)))
     (if (<= x -1.5e+119)
       t_1
       (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -6e+166) {
		tmp = z * ((18.0 * y) * (x * t));
	} else if (x <= -1.5e+119) {
		tmp = t_1;
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -6e+166)
		tmp = Float64(z * Float64(Float64(18.0 * y) * Float64(x * t)));
	elseif (x <= -1.5e+119)
		tmp = t_1;
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+166], N[(z * N[(N[(18.0 * y), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+119], t$95$1, If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.99999999999999997e166

   1. Initial program 57.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 19.3

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

   5. Applied rewrites 19.3%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 58.1

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

   8. Applied rewrites 58.1%

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

   10. Applied rewrites 64.8%

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

   if -5.99999999999999997e166 < x < -1.50000000000000001e119 or 2.1000000000000002e215 < x

   1. Initial program 80.1%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 74.6

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

   5. Applied rewrites 74.6%

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

   if -1.50000000000000001e119 < x < 2.1000000000000002e215

   1. Initial program 90.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 55.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+166}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -6e+166)
     (* y (* (* x 18.0) (* z t)))
     (if (<= x -1.5e+119)
       t_1
       (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -6e+166) {
		tmp = y * ((x * 18.0) * (z * t));
	} else if (x <= -1.5e+119) {
		tmp = t_1;
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -6e+166)
		tmp = Float64(y * Float64(Float64(x * 18.0) * Float64(z * t)));
	elseif (x <= -1.5e+119)
		tmp = t_1;
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+166], N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+119], t$95$1, If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.99999999999999997e166

   1. Initial program 57.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 19.3

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

   5. Applied rewrites 19.3%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 58.1

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

   8. Applied rewrites 58.1%

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

   10. Applied rewrites 61.4%

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

   if -5.99999999999999997e166 < x < -1.50000000000000001e119 or 2.1000000000000002e215 < x

   1. Initial program 80.1%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 74.6

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

   5. Applied rewrites 74.6%

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

   if -1.50000000000000001e119 < x < 2.1000000000000002e215

   1. Initial program 90.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

   7. Applied rewrites 55.1%

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

Alternative 18: 48.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -3.55 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -3.55e+171)
     (* t (* y (* 18.0 (* x z))))
     (if (<= x -1.5e+119)
       t_1
       (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -3.55e+171) {
		tmp = t * (y * (18.0 * (x * z)));
	} else if (x <= -1.5e+119) {
		tmp = t_1;
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -3.55e+171)
		tmp = Float64(t * Float64(y * Float64(18.0 * Float64(x * z))));
	elseif (x <= -1.5e+119)
		tmp = t_1;
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.55e+171], N[(t * N[(y * N[(18.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+119], t$95$1, If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.54999999999999985e171

   1. Initial program 52.3%

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

   3. Taylor expanded in j around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 1.4

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

   5. Applied rewrites 1.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 64.7

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

   8. Applied rewrites 64.7%

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

   if -3.54999999999999985e171 < x < -1.50000000000000001e119 or 2.1000000000000002e215 < x

   1. Initial program 81.7%

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

   3. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

   if -1.50000000000000001e119 < x < 2.1000000000000002e215

   1. Initial program 90.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 55.1

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

   5. Applied rewrites 55.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} \]

      5. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right)\right) \cdot k \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot c + \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)} \cdot k \]

      7. metadata-eval N/A

         \[\leadsto b \cdot c + \left(j \cdot \color{blue}{-27}\right) \cdot k \]

      8. associate-*r* N/A

         \[\leadsto b \cdot c + \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

      9. *-commutative N/A

         \[\leadsto b \cdot c + j \cdot \color{blue}{\left(k \cdot -27\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto b \cdot c + j \cdot \color{blue}{\left(k \cdot -27\right)} \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot c + \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      12. +-commutative N/A

          \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right) + b \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + b \cdot c \]

      14. lift-*.f64 N/A

          \[\leadsto j \cdot \color{blue}{\left(k \cdot -27\right)} + b \cdot c \]

      15. *-commutative N/A

          \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + b \cdot c \]

      16. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot -27\right) \cdot k} + b \cdot c \]

   7. Applied rewrites 55.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+166}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -6e+166)
     (* 18.0 (* t (* z (* x y))))
     (if (<= x -1.5e+119)
       t_1
       (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -6e+166) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else if (x <= -1.5e+119) {
		tmp = t_1;
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -6e+166)
		tmp = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))));
	elseif (x <= -1.5e+119)
		tmp = t_1;
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+166], N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+119], t$95$1, If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.99999999999999997e166

   1. Initial program 57.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(z \cdot \left(x \cdot y\right)\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(z \cdot \left(x \cdot y\right)\right)}\right) \]

      6. lower-*.f64 58.1

         \[\leadsto 18 \cdot \left(t \cdot \left(z \cdot \color{blue}{\left(x \cdot y\right)}\right)\right) \]

   5. Applied rewrites 58.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)} \]

   if -5.99999999999999997e166 < x < -1.50000000000000001e119 or 2.1000000000000002e215 < x

   1. Initial program 80.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

      3. lower-*.f64 74.6

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   5. Applied rewrites 74.6%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]

   if -1.50000000000000001e119 < x < 2.1000000000000002e215

   1. Initial program 90.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. lower-*.f64 55.1

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 55.1%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{b \cdot c - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} \]

      5. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right)\right) \cdot k \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot c + \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)} \cdot k \]

      7. metadata-eval N/A

         \[\leadsto b \cdot c + \left(j \cdot \color{blue}{-27}\right) \cdot k \]

      8. associate-*r* N/A

         \[\leadsto b \cdot c + \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

      9. *-commutative N/A

         \[\leadsto b \cdot c + j \cdot \color{blue}{\left(k \cdot -27\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto b \cdot c + j \cdot \color{blue}{\left(k \cdot -27\right)} \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot c + \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      12. +-commutative N/A

          \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right) + b \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + b \cdot c \]

      14. lift-*.f64 N/A

          \[\leadsto j \cdot \color{blue}{\left(k \cdot -27\right)} + b \cdot c \]

      15. *-commutative N/A

          \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + b \cdot c \]

      16. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot -27\right) \cdot k} + b \cdot c \]

   7. Applied rewrites 55.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 35.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.85 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{+28}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (<= (* b c) -1.85e+148)
   (* b c)
   (if (<= (* b c) 3.2e+28) (* -4.0 (* x i)) (* 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 ((b * c) <= -1.85e+148) {
		tmp = b * c;
	} else if ((b * c) <= 3.2e+28) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.85d+148)) then
        tmp = b * c
    else if ((b * c) <= 3.2d+28) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.85e+148) {
		tmp = b * c;
	} else if ((b * c) <= 3.2e+28) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.85e+148:
		tmp = b * c
	elif (b * c) <= 3.2e+28:
		tmp = -4.0 * (x * i)
	else:
		tmp = 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 (Float64(b * c) <= -1.85e+148)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 3.2e+28)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.85e+148)
		tmp = b * c;
	elseif ((b * c) <= 3.2e+28)
		tmp = -4.0 * (x * i);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.85e+148], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.2e+28], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.8500000000000001e148 or 3.2e28 < (*.f64 b c)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. lower-*.f64 60.8

         \[\leadsto \color{blue}{b \cdot c} \]

   5. Applied rewrites 60.8%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.8500000000000001e148 < (*.f64 b c) < 3.2e28

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

      3. lower-*.f64 27.3

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   5. Applied rewrites 27.3%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 35.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+156}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.8 \cdot 10^{+28}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (<= (* b c) -1.5e+156)
   (* b c)
   (if (<= (* b c) 2.8e+28) (* -4.0 (* t a)) (* 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 ((b * c) <= -1.5e+156) {
		tmp = b * c;
	} else if ((b * c) <= 2.8e+28) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.5d+156)) then
        tmp = b * c
    else if ((b * c) <= 2.8d+28) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.5e+156) {
		tmp = b * c;
	} else if ((b * c) <= 2.8e+28) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.5e+156:
		tmp = b * c
	elif (b * c) <= 2.8e+28:
		tmp = -4.0 * (t * a)
	else:
		tmp = 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 (Float64(b * c) <= -1.5e+156)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 2.8e+28)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.5e+156)
		tmp = b * c;
	elseif ((b * c) <= 2.8e+28)
		tmp = -4.0 * (t * a);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.5e+156], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.8e+28], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.5e156 or 2.8000000000000001e28 < (*.f64 b c)

   1. Initial program 85.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. lower-*.f64 61.4

         \[\leadsto \color{blue}{b \cdot c} \]

   5. Applied rewrites 61.4%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.5e156 < (*.f64 b c) < 2.8000000000000001e28

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

      2. lower-*.f64 22.2

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

   5. Applied rewrites 22.2%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.5 \cdot 10^{+156}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 2.8 \cdot 10^{+28}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -1.5e+119)
     t_1
     (if (<= x 2.1e+215) (fma (* j -27.0) k (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -1.5e+119) {
		tmp = t_1;
	} else if (x <= 2.1e+215) {
		tmp = fma((j * -27.0), k, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -1.5e+119)
		tmp = t_1;
	elseif (x <= 2.1e+215)
		tmp = fma(Float64(j * -27.0), k, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+119], t$95$1, If[LessEqual[x, 2.1e+215], N[(N[(j * -27.0), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000001e119 or 2.1000000000000002e215 < x

   1. Initial program 70.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

      3. lower-*.f64 57.5

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   5. Applied rewrites 57.5%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]

   if -1.50000000000000001e119 < x < 2.1000000000000002e215

   1. Initial program 90.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. lower-*.f64 55.1

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 55.1%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{b \cdot c - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} \]

      5. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right)\right) \cdot k \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot c + \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)} \cdot k \]

      7. metadata-eval N/A

         \[\leadsto b \cdot c + \left(j \cdot \color{blue}{-27}\right) \cdot k \]

      8. associate-*r* N/A

         \[\leadsto b \cdot c + \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

      9. *-commutative N/A

         \[\leadsto b \cdot c + j \cdot \color{blue}{\left(k \cdot -27\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto b \cdot c + j \cdot \color{blue}{\left(k \cdot -27\right)} \]

      11. lift-*.f64 N/A

          \[\leadsto b \cdot c + \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      12. +-commutative N/A

          \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right) + b \cdot c} \]

      13. lift-*.f64 N/A

          \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + b \cdot c \]

      14. lift-*.f64 N/A

          \[\leadsto j \cdot \color{blue}{\left(k \cdot -27\right)} + b \cdot c \]

      15. *-commutative N/A

          \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + b \cdot c \]

      16. associate-*r* N/A

          \[\leadsto \color{blue}{\left(j \cdot -27\right) \cdot k} + b \cdot c \]

   7. Applied rewrites 55.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j \cdot -27, k, b \cdot c\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 23.8% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

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 (* 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) {
	return b * c;
}

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 = b * c
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 b * c;
}

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 b * c

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(b * c)
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 = b * c;
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[(b * c), $MachinePrecision]

Derivation

1. Initial program 85.3%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. lower-*.f64 24.8

      \[\leadsto \color{blue}{b \cdot c} \]

5. Applied rewrites 24.8%

   \[\leadsto \color{blue}{b \cdot c} \]
6. Add Preprocessing

Developer Target 1: 89.7% 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 2024233 
(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)))