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

Percentage Accurate: 85.2% → 93.4%

Time: 15.4s

Alternatives: 23

Speedup: 1.2×

• 51.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-35} \lor \neg \left(t \leq 1.55 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, t\_1\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 x) i))))
   (if (or (<= t -2e-35) (not (<= t 1.55e-60)))
     (fma (* -27.0 j) k (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t t_1))
     (-
      (fma y (* (* 18.0 x) (* t z)) (fma (* -4.0 a) t t_1))
      (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((-4.0 * x) * i));
	double tmp;
	if ((t <= -2e-35) || !(t <= 1.55e-60)) {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, t_1));
	} else {
		tmp = fma(y, ((18.0 * x) * (t * z)), fma((-4.0 * a), t, t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * x) * i))
	tmp = 0.0
	if ((t <= -2e-35) || !(t <= 1.55e-60))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, t_1));
	else
		tmp = Float64(fma(y, Float64(Float64(18.0 * x) * Float64(t * z)), fma(Float64(-4.0 * a), t, t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2e-35], N[Not[LessEqual[t, 1.55e-60]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(18.0 * x), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000002e-35 or 1.54999999999999994e-60 < t

   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

   4. Applied rewrites 95.4%

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

   if -2.00000000000000002e-35 < t < 1.54999999999999994e-60

   1. Initial program 81.5%

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

      1. lift--.f64 N/A

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

      2. 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. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

   4. Applied rewrites 95.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-35} \lor \neg \left(t \leq 1.55 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-88} \lor \neg \left(t \leq 3.4 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, t\_1\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 x) i))))
   (if (or (<= t -2e-88) (not (<= t 3.4e-60)))
     (fma (* -27.0 j) k (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t t_1))
     (-
      (fma x (* (* y 18.0) (* t z)) (fma (* -4.0 a) t t_1))
      (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((-4.0 * x) * i));
	double tmp;
	if ((t <= -2e-88) || !(t <= 3.4e-60)) {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, t_1));
	} else {
		tmp = fma(x, ((y * 18.0) * (t * z)), fma((-4.0 * a), t, t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * x) * i))
	tmp = 0.0
	if ((t <= -2e-88) || !(t <= 3.4e-60))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, t_1));
	else
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), fma(Float64(-4.0 * a), t, t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2e-88], N[Not[LessEqual[t, 3.4e-60]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.99999999999999987e-88 or 3.40000000000000007e-60 < t

   1. Initial program 88.6%

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

   4. Applied rewrites 95.2%

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

   if -1.99999999999999987e-88 < t < 3.40000000000000007e-60

   1. Initial program 79.3%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. associate-*l* N/A

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

   4. Applied rewrites 95.3%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-88} \lor \neg \left(t \leq 3.4 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+238}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t \cdot -4, a, k \cdot \left(j \cdot -27\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= (* b c) -4e+81)
   (fma (* -27.0 j) k (fma c b (* (fma (* (* y z) x) 18.0 (* a -4.0)) t)))
   (if (<= (* b c) 4e+238)
     (-
      (fma (* -4.0 t) a (* (fma -4.0 i (* (* (* z y) t) 18.0)) x))
      (* (* j 27.0) k))
     (fma c b (fma (* t -4.0) a (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+81) {
		tmp = fma((-27.0 * j), k, fma(c, b, (fma(((y * z) * x), 18.0, (a * -4.0)) * t)));
	} else if ((b * c) <= 4e+238) {
		tmp = fma((-4.0 * t), a, (fma(-4.0, i, (((z * y) * t) * 18.0)) * x)) - ((j * 27.0) * k);
	} else {
		tmp = fma(c, b, fma((t * -4.0), a, (k * (j * -27.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+81)
		tmp = fma(Float64(-27.0 * j), k, fma(c, b, Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t)));
	elseif (Float64(b * c) <= 4e+238)
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(c, b, fma(Float64(t * -4.0), a, Float64(k * Float64(j * -27.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+81], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+238], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(t * -4.0), $MachinePrecision] * a + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -3.99999999999999969e81

   1. Initial program 87.4%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 93.7%

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

   7. Applied rewrites 93.7%

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

   if -3.99999999999999969e81 < (*.f64 b c) < 4.0000000000000002e238

   1. Initial program 86.4%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 88.9%

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

   if 4.0000000000000002e238 < (*.f64 b c)

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 85.2

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

   5. Applied rewrites 85.2%

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

   7. Applied rewrites 96.3%

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

Alternative 4: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, x, a \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot t, z, t\_1 \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot t\_1\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma i x (* a t))))
   (if (<= (* b c) -5e+121)
     (fma (* -27.0 j) k (fma c b (* (fma (* (* y z) x) 18.0 (* a -4.0)) t)))
     (if (<= (* b c) 5e+72)
       (fma (* k j) -27.0 (fma (* (* (* 18.0 x) y) t) z (* t_1 -4.0)))
       (- (fma c b (* -4.0 t_1)) (* (* j 27.0) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(i, x, (a * t));
	double tmp;
	if ((b * c) <= -5e+121) {
		tmp = fma((-27.0 * j), k, fma(c, b, (fma(((y * z) * x), 18.0, (a * -4.0)) * t)));
	} else if ((b * c) <= 5e+72) {
		tmp = fma((k * j), -27.0, fma((((18.0 * x) * y) * t), z, (t_1 * -4.0)));
	} else {
		tmp = fma(c, b, (-4.0 * t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(i, x, Float64(a * t))
	tmp = 0.0
	if (Float64(b * c) <= -5e+121)
		tmp = fma(Float64(-27.0 * j), k, fma(c, b, Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t)));
	elseif (Float64(b * c) <= 5e+72)
		tmp = fma(Float64(k * j), -27.0, fma(Float64(Float64(Float64(18.0 * x) * y) * t), z, Float64(t_1 * -4.0)));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+121], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+72], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * t), $MachinePrecision] * z + N[(t$95$1 * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.00000000000000007e121

   1. Initial program 86.0%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 93.0%

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

   7. Applied rewrites 93.0%

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

   if -5.00000000000000007e121 < (*.f64 b c) < 4.99999999999999992e72

   1. Initial program 87.2%

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

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. associate-*l* N/A

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

   4. Applied rewrites 87.6%

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

   5. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.7

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

   7. Applied rewrites 85.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 85.8

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

   9. Applied rewrites 85.9%

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

   if 4.99999999999999992e72 < (*.f64 b c)

   1. Initial program 78.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.4

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

   5. Applied rewrites 89.4%

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

Alternative 5: 84.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot y\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \left(i \cdot x\right) \cdot -4\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2
         (fma
          (* -27.0 j)
          k
          (fma (fma -4.0 a (* (* (* x y) z) 18.0)) t (* c b)))))
   (if (<= z -3.05e-6)
     t_2
     (if (<= z 4.8e+55)
       (- (fma c b (* -4.0 (fma i x (* a t)))) t_1)
       (if (<= z 5.5e+285)
         t_2
         (- (fma x (* (* y 18.0) (* t z)) (* (* i x) -4.0)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = fma((-27.0 * j), k, fma(fma(-4.0, a, (((x * y) * z) * 18.0)), t, (c * b)));
	double tmp;
	if (z <= -3.05e-6) {
		tmp = t_2;
	} else if (z <= 4.8e+55) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - t_1;
	} else if (z <= 5.5e+285) {
		tmp = t_2;
	} else {
		tmp = fma(x, ((y * 18.0) * (t * z)), ((i * x) * -4.0)) - 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(Float64(j * 27.0) * k)
	t_2 = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(x * y) * z) * 18.0)), t, Float64(c * b)))
	tmp = 0.0
	if (z <= -3.05e-6)
		tmp = t_2;
	elseif (z <= 4.8e+55)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - t_1);
	elseif (z <= 5.5e+285)
		tmp = t_2;
	else
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), Float64(Float64(i * x) * -4.0)) - 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[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.05e-6], t$95$2, If[LessEqual[z, 4.8e+55], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 5.5e+285], t$95$2, N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.05000000000000002e-6 or 4.7999999999999998e55 < z < 5.50000000000000029e285

   1. Initial program 87.0%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 80.6%

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

   7. Applied rewrites 84.6%

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

   if -3.05000000000000002e-6 < z < 4.7999999999999998e55

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if 5.50000000000000029e285 < z

   1. Initial program 34.8%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. associate-*l* N/A

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

   4. Applied rewrites 82.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 92.4

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

   7. Applied rewrites 92.4%

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

Alternative 6: 85.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot y\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+285}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\left(t \cdot z\right) \cdot \left(y \cdot x\right), 18, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* -27.0 j)
          k
          (fma (fma -4.0 a (* (* (* x y) z) 18.0)) t (* c b)))))
   (if (<= z -3.05e-6)
     t_1
     (if (<= z 4.8e+55)
       (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
       (if (<= z 1.65e+285)
         t_1
         (fma (* -27.0 j) k (fma (* (* t z) (* y x)) 18.0 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, fma(fma(-4.0, a, (((x * y) * z) * 18.0)), t, (c * b)));
	double tmp;
	if (z <= -3.05e-6) {
		tmp = t_1;
	} else if (z <= 4.8e+55) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else if (z <= 1.65e+285) {
		tmp = t_1;
	} else {
		tmp = fma((-27.0 * j), k, fma(((t * z) * (y * x)), 18.0, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(x * y) * z) * 18.0)), t, Float64(c * b)))
	tmp = 0.0
	if (z <= -3.05e-6)
		tmp = t_1;
	elseif (z <= 4.8e+55)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	elseif (z <= 1.65e+285)
		tmp = t_1;
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(Float64(t * z) * Float64(y * x)), 18.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.05e-6], t$95$1, If[LessEqual[z, 4.8e+55], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+285], t$95$1, N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(t * z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.05000000000000002e-6 or 4.7999999999999998e55 < z < 1.6499999999999999e285

   1. Initial program 87.0%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 80.6%

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

   7. Applied rewrites 84.6%

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

   if -3.05000000000000002e-6 < z < 4.7999999999999998e55

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if 1.6499999999999999e285 < z

   1. Initial program 34.8%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 34.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 34.8%

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

   10. Applied rewrites 83.3%

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

Alternative 7: 89.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+285}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \left(i \cdot x\right) \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 5.5e+285)
   (fma
    (* -27.0 j)
    k
    (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (fma c b (* (* -4.0 x) i))))
   (- (fma x (* (* y 18.0) (* t z)) (* (* i x) -4.0)) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= 5.5e+285) {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, fma(c, b, ((-4.0 * x) * i))));
	} else {
		tmp = fma(x, ((y * 18.0) * (t * z)), ((i * x) * -4.0)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 5.5e+285)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, fma(c, b, Float64(Float64(-4.0 * x) * i))));
	else
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), Float64(Float64(i * x) * -4.0)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 5.5e+285], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.50000000000000029e285

   1. Initial program 86.5%

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

   4. Applied rewrites 91.7%

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

   if 5.50000000000000029e285 < z

   1. Initial program 34.8%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      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. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. associate-*l* N/A

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

   4. Applied rewrites 82.6%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 92.4

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

   7. Applied rewrites 92.4%

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

Alternative 8: 35.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-27 \cdot j\right) \cdot k\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* -27.0 j) k)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+142)
     t_1
     (if (<= t_2 -1e-307)
       (* (* t a) -4.0)
       (if (<= t_2 2e+92) (* (* -4.0 x) i) 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 = (-27.0 * j) * k;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+142) {
		tmp = t_1;
	} else if (t_2 <= -1e-307) {
		tmp = (t * a) * -4.0;
	} else if (t_2 <= 2e+92) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = ((-27.0d0) * j) * k
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+142)) then
        tmp = t_1
    else if (t_2 <= (-1d-307)) then
        tmp = (t * a) * (-4.0d0)
    else if (t_2 <= 2d+92) then
        tmp = ((-4.0d0) * x) * i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = (-27.0 * j) * k;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+142) {
		tmp = t_1;
	} else if (t_2 <= -1e-307) {
		tmp = (t * a) * -4.0;
	} else if (t_2 <= 2e+92) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-27.0 * j) * k
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+142:
		tmp = t_1
	elif t_2 <= -1e-307:
		tmp = (t * a) * -4.0
	elif t_2 <= 2e+92:
		tmp = (-4.0 * x) * i
	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(Float64(-27.0 * j) * k)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+142)
		tmp = t_1;
	elseif (t_2 <= -1e-307)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (t_2 <= 2e+92)
		tmp = Float64(Float64(-4.0 * x) * i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-27.0 * j) * k;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+142)
		tmp = t_1;
	elseif (t_2 <= -1e-307)
		tmp = (t * a) * -4.0;
	elseif (t_2 <= 2e+92)
		tmp = (-4.0 * x) * i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+142], t$95$1, If[LessEqual[t$95$2, -1e-307], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+92], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e142 or 2.0000000000000001e92 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.7%

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

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if -2.0000000000000001e142 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999909e-308

   1. Initial program 83.8%

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

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

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 27.9%

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

   if -9.99999999999999909e-308 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e92

   1. Initial program 89.2%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 29.9

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

   5. Applied rewrites 29.9%

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

Alternative 9: 86.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+70} \lor \neg \left(x \leq 3.4 \cdot 10^{+79}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot y\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.26e+70) (not (<= x 3.4e+79)))
   (- (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (* c b)) (* (* j 27.0) k))
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* x y) z) 18.0)) t (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.26e+70) || !(x <= 3.4e+79)) {
		tmp = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, (c * b)) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((x * y) * z) * 18.0)), t, (c * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.26e+70) || !(x <= 3.4e+79))
		tmp = Float64(fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, Float64(c * b)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(x * y) * z) * 18.0)), t, Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.26e+70], N[Not[LessEqual[x, 3.4e+79]], $MachinePrecision]], N[(N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.26000000000000001e70 or 3.40000000000000032e79 < x

   1. Initial program 74.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*l* N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. metadata-eval N/A

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

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

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 89.1%

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

   if -1.26000000000000001e70 < x < 3.40000000000000032e79

   1. Initial program 92.5%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 85.0%

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

   7. Applied rewrites 88.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+70} \lor \neg \left(x \leq 3.4 \cdot 10^{+79}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(x \cdot y\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -7600000 \lor \neg \left(i \leq 1.3 \cdot 10^{+123}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -7600000.0) (not (<= i 1.3e+123)))
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
   (fma (* -27.0 j) k (fma c b (* (fma (* (* y z) x) 18.0 (* a -4.0)) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -7600000.0) || !(i <= 1.3e+123)) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma(c, b, (fma(((y * z) * x), 18.0, (a * -4.0)) * t)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -7600000.0) || !(i <= 1.3e+123))
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(c, b, Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -7600000.0], N[Not[LessEqual[i, 1.3e+123]], $MachinePrecision]], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.6e6 or 1.29999999999999993e123 < i

   1. Initial program 84.2%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -7.6e6 < i < 1.29999999999999993e123

   1. Initial program 86.1%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 87.5%

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

   7. Applied rewrites 87.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7600000 \lor \neg \left(i \leq 1.3 \cdot 10^{+123}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.75 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\left(t \cdot z\right) \cdot \left(y \cdot x\right), 18, b \cdot c\right)\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(-4, \mathsf{fma}\left(i, x, t \cdot a\right), \mathsf{fma}\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t, 18, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.75e-41)
   (fma (* -27.0 j) k (fma (* (* t z) (* y x)) 18.0 (* b c)))
   (if (<= k 7e+32)
     (fma -4.0 (fma i x (* t a)) (fma (* (* (* y z) x) t) 18.0 (* b c)))
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.75e-41) {
		tmp = fma((-27.0 * j), k, fma(((t * z) * (y * x)), 18.0, (b * c)));
	} else if (k <= 7e+32) {
		tmp = fma(-4.0, fma(i, x, (t * a)), fma((((y * z) * x) * t), 18.0, (b * c)));
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.75e-41)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(Float64(t * z) * Float64(y * x)), 18.0, Float64(b * c)));
	elseif (k <= 7e+32)
		tmp = fma(-4.0, fma(i, x, Float64(t * a)), fma(Float64(Float64(Float64(y * z) * x) * t), 18.0, Float64(b * c)));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.75e-41], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(t * z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7e+32], N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.75e-41

   1. Initial program 88.6%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 80.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 67.9%

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

   10. Applied rewrites 70.4%

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

   if -1.75e-41 < k < 7.0000000000000002e32

   1. Initial program 86.8%

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

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 10.5

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

   5. Applied rewrites 10.5%

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

   6. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

   8. Applied rewrites 80.8%

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

   if 7.0000000000000002e32 < k

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 82.5

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

   5. Applied rewrites 82.5%

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

Alternative 12: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\left(t \cdot z\right) \cdot \left(y \cdot x\right), 18, b \cdot c\right)\right)\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) \cdot 18\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -3.5e+120)
   (fma (* -27.0 j) k (fma (* (* t z) (* y x)) 18.0 (* b c)))
   (if (<= y 6.1e+94)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (* (* y (* z (* t x))) 18.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -3.5e+120) {
		tmp = fma((-27.0 * j), k, fma(((t * z) * (y * x)), 18.0, (b * c)));
	} else if (y <= 6.1e+94) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = (y * (z * (t * x))) * 18.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -3.5e+120)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(Float64(t * z) * Float64(y * x)), 18.0, Float64(b * c)));
	elseif (y <= 6.1e+94)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(y * Float64(z * Float64(t * x))) * 18.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -3.5e+120], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(t * z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e+94], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000007e120

   1. Initial program 73.6%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 71.8%

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

   10. Applied rewrites 80.7%

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

   if -3.50000000000000007e120 < y < 6.10000000000000035e94

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if 6.10000000000000035e94 < y

   1. Initial program 74.5%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.0%

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

   10. Applied rewrites 45.6%

       \[\leadsto \left(y \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) \cdot 18 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 34.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+142} \lor \neg \left(t\_1 \leq 10^{+202}\right):\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+142) (not (<= t_1 1e+202)))
     (* (* -27.0 j) k)
     (* (* t a) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+142) || !(t_1 <= 1e+202)) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (t * a) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+142)) .or. (.not. (t_1 <= 1d+202))) then
        tmp = ((-27.0d0) * j) * k
    else
        tmp = (t * a) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+142) || !(t_1 <= 1e+202)) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (t * a) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+142) or not (t_1 <= 1e+202):
		tmp = (-27.0 * j) * k
	else:
		tmp = (t * a) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+142) || !(t_1 <= 1e+202))
		tmp = Float64(Float64(-27.0 * j) * k);
	else
		tmp = Float64(Float64(t * a) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+142) || ~((t_1 <= 1e+202)))
		tmp = (-27.0 * j) * k;
	else
		tmp = (t * a) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+142], N[Not[LessEqual[t$95$1, 1e+202]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e142 or 9.999999999999999e201 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.7%

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

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

   if -2.0000000000000001e142 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.999999999999999e201

   1. Initial program 86.5%

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

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 55.0

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

   5. Applied rewrites 55.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 25.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+142} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 10^{+202}\right):\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 78.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{+195}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t 1e+195)
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= 1e+195) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= 1e+195)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, 1e+195], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.99999999999999977e194

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if 9.99999999999999977e194 < t

   1. Initial program 79.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 15.4

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

   5. Applied rewrites 15.4%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 80.4

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

   8. Applied rewrites 80.4%

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

Alternative 15: 73.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+106} \lor \neg \left(x \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, \left(-4 \cdot a\right) \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.6e+106) (not (<= x 4.5e+71)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* -27.0 j) k (fma c b (* (* -4.0 a) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.6e+106) || !(x <= 4.5e+71)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((-27.0 * j), k, fma(c, b, ((-4.0 * a) * t)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.6e+106) || !(x <= 4.5e+71))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(-27.0 * j), k, fma(c, b, Float64(Float64(-4.0 * a) * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.6e+106], N[Not[LessEqual[x, 4.5e+71]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b + N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6000000000000002e106 or 4.50000000000000043e71 < x

   1. Initial program 73.3%

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

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -2.6000000000000002e106 < x < 4.50000000000000043e71

   1. Initial program 92.5%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 84.5%

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

   7. Applied rewrites 85.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 79.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+106} \lor \neg \left(x \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, \left(-4 \cdot a\right) \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+106} \lor \neg \left(x \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t \cdot -4, a, k \cdot \left(j \cdot -27\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.6e+106) (not (<= x 4.5e+71)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma c b (fma (* t -4.0) a (* k (* j -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.6e+106) || !(x <= 4.5e+71)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma(c, b, fma((t * -4.0), a, (k * (j * -27.0))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.6e+106) || !(x <= 4.5e+71))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(c, b, fma(Float64(t * -4.0), a, Float64(k * Float64(j * -27.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.6e+106], N[Not[LessEqual[x, 4.5e+71]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(c * b + N[(N[(t * -4.0), $MachinePrecision] * a + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6000000000000002e106 or 4.50000000000000043e71 < x

   1. Initial program 73.3%

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

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -2.6000000000000002e106 < x < 4.50000000000000043e71

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 77.8

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

   5. Applied rewrites 77.8%

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

   7. Applied rewrites 79.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+106} \lor \neg \left(x \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(t \cdot -4, a, k \cdot \left(j \cdot -27\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+55} \lor \neg \left(t \leq 6.6 \cdot 10^{+156}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.05e+55) (not (<= t 6.6e+156)))
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (fma (* k j) -27.0 (* b c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.05e+55) || !(t <= 6.6e+156)) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else {
		tmp = fma((k * j), -27.0, (b * c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.05e+55) || !(t <= 6.6e+156))
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	else
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.05e+55], N[Not[LessEqual[t, 6.6e+156]], $MachinePrecision]], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e55 or 6.5999999999999997e156 < t

   1. Initial program 85.6%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 17.3

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

   5. Applied rewrites 17.3%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 73.7

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

   8. Applied rewrites 73.7%

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

   if -1.05e55 < t < 6.5999999999999997e156

   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 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 58.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+55} \lor \neg \left(t \leq 6.6 \cdot 10^{+156}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -115000000 \lor \neg \left(x \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -115000000.0) (not (<= x 4.5e+71)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* k j) -27.0 (* b c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -115000000.0) || !(x <= 4.5e+71)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((k * j), -27.0, (b * c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -115000000.0) || !(x <= 4.5e+71))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -115000000.0], N[Not[LessEqual[x, 4.5e+71]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e8 or 4.50000000000000043e71 < x

   1. Initial program 76.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if -1.15e8 < x < 4.50000000000000043e71

   1. Initial program 93.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 61.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -115000000 \lor \neg \left(x \leq 4.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \left(\left(18 \cdot x\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) \cdot 18\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -9.5e+146)
   (* y (* (* 18.0 x) (* t z)))
   (if (<= t -3.8e+104)
     (* (* t a) -4.0)
     (if (<= t 8e+194)
       (fma (* k -27.0) j (* b c))
       (* (* y (* z (* t x))) 18.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -9.5e+146) {
		tmp = y * ((18.0 * x) * (t * z));
	} else if (t <= -3.8e+104) {
		tmp = (t * a) * -4.0;
	} else if (t <= 8e+194) {
		tmp = fma((k * -27.0), j, (b * c));
	} else {
		tmp = (y * (z * (t * x))) * 18.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -9.5e+146)
		tmp = Float64(y * Float64(Float64(18.0 * x) * Float64(t * z)));
	elseif (t <= -3.8e+104)
		tmp = Float64(Float64(t * a) * -4.0);
	elseif (t <= 8e+194)
		tmp = fma(Float64(k * -27.0), j, Float64(b * c));
	else
		tmp = Float64(Float64(y * Float64(z * Float64(t * x))) * 18.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -9.5e+146], N[(y * N[(N[(18.0 * x), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e+104], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t, 8e+194], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.49999999999999926e146

   1. Initial program 85.6%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.7%

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

   10. Applied rewrites 55.3%

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

   if -9.49999999999999926e146 < t < -3.79999999999999969e104

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 88.9

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 79.4%

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

   if -3.79999999999999969e104 < t < 7.99999999999999956e194

   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 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 64.5

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

   5. Applied rewrites 64.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 13.5%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 55.7%

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

   13. Applied rewrites 56.3%

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

   if 7.99999999999999956e194 < t

   1. Initial program 79.9%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 51.2%

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

   10. Applied rewrites 60.5%

       \[\leadsto \left(y \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) \cdot 18 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 20: 47.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.4 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\left(z \cdot t\right) \cdot 18\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 8.4e+159) (fma (* k j) -27.0 (* b c)) (* y (* (* (* z t) 18.0) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= 8.4e+159) {
		tmp = fma((k * j), -27.0, (b * c));
	} else {
		tmp = y * (((z * t) * 18.0) * x);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 8.4e+159)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	else
		tmp = Float64(y * Float64(Float64(Float64(z * t) * 18.0) * x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 8.4e+159], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(z * t), $MachinePrecision] * 18.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.39999999999999956e159

   1. Initial program 85.6%

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

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

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 64.2

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 50.1%

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

   if 8.39999999999999956e159 < z

   1. Initial program 83.7%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 45.5%

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

   10. Applied rewrites 63.1%

       \[\leadsto \left(y \cdot \left(z \cdot \left(t \cdot x\right)\right)\right) \cdot 18 \]
   11. Step-by-step derivation

   12. Applied rewrites 68.1%

       \[\leadsto y \cdot \left(\left(\left(z \cdot t\right) \cdot 18\right) \cdot \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 47.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.4 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(18 \cdot x\right) \cdot \left(t \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 8.4e+159) (fma (* k j) -27.0 (* b c)) (* y (* (* 18.0 x) (* t 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 (z <= 8.4e+159) {
		tmp = fma((k * j), -27.0, (b * c));
	} else {
		tmp = y * ((18.0 * x) * (t * 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 (z <= 8.4e+159)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	else
		tmp = Float64(y * Float64(Float64(18.0 * x) * Float64(t * 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[z, 8.4e+159], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(18.0 * x), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.39999999999999956e159

   1. Initial program 85.6%

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

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

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(a \cdot t\right) \cdot -4} + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot t}, -4, b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right) - 27 \cdot \left(j \cdot k\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right) - 27 \cdot \left(j \cdot k\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

      14. lower-*.f64 64.2

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

   6. Taylor expanded in t around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(k \cdot j, \color{blue}{-27}, b \cdot c\right) \]

   if 8.39999999999999956e159 < z

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)} \]

      2. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right)} \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \color{blue}{\left(\mathsf{neg}\left(-27\right)\right)} \cdot \left(j \cdot k\right)\right) - 4 \cdot \left(a \cdot t\right) \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -27 \cdot \left(j \cdot k\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-27 \cdot \left(j \cdot k\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 4 \cdot \left(a \cdot t\right) \]

      6. associate--l+ N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-27 \cdot j}, k, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - 4 \cdot \left(a \cdot t\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right)}\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(a \cdot t\right)\right) + b \cdot c}\right) \]

   5. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.5%

      \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot \color{blue}{18} \]
   9. Step-by-step derivation

   10. Applied rewrites 68.0%

       \[\leadsto y \cdot \left(\left(18 \cdot x\right) \cdot \color{blue}{\left(t \cdot z\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 45.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 2.5e+79) (fma (* k -27.0) j (* 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 <= 2.5e+79) {
		tmp = fma((k * -27.0), j, (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 <= 2.5e+79)
		tmp = fma(Float64(k * -27.0), j, Float64(b * c));
	else
		tmp = Float64(Float64(-4.0 * x) * i);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 2.5e+79], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.5e79

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      4. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(a \cdot t\right) \cdot -4} + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot t}, -4, b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right) - 27 \cdot \left(j \cdot k\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right) - 27 \cdot \left(j \cdot k\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

      14. lower-*.f64 68.6

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   5. Applied rewrites 68.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

   6. Taylor expanded in t around inf

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 22.6%

      \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{-4} \]

   9. Taylor expanded in t around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 53.2%

       \[\leadsto \mathsf{fma}\left(k \cdot j, \color{blue}{-27}, c \cdot b\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 53.6%

       \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]

   if 2.5e79 < x

   1. Initial program 66.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot x\right) \cdot i} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot x\right) \cdot i} \]

      4. lower-*.f64 43.4

         \[\leadsto \color{blue}{\left(-4 \cdot x\right)} \cdot i \]

   5. Applied rewrites 43.4%

      \[\leadsto \color{blue}{\left(-4 \cdot x\right) \cdot i} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 21.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \left(t \cdot a\right) \cdot -4 \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* (* t a) -4.0))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (t * a) * -4.0;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (t * a) * (-4.0d0)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (t * a) * -4.0;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return (t * a) * -4.0

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(t * a) * -4.0)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (t * a) * -4.0;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

1. Initial program 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 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. associate--r+ N/A

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   2. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   3. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

   4. metadata-eval N/A

      \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(j \cdot k\right) \]

   5. +-commutative N/A

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\color{blue}{\left(a \cdot t\right) \cdot -4} + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

   8. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot t}, -4, b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

   9. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right) - 27 \cdot \left(j \cdot k\right) \]

   10. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(a \cdot t, -4, \color{blue}{c \cdot b}\right) - 27 \cdot \left(j \cdot k\right) \]

   11. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

   12. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

   13. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   14. lower-*.f64 62.0

       \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

5. Applied rewrites 62.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

6. Taylor expanded in t around inf

   \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 21.2%

   \[\leadsto \left(t \cdot a\right) \cdot \color{blue}{-4} \]
9. Add Preprocessing

Developer Target 1: 89.2% 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 2024326 
(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)))