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

Percentage Accurate: 85.9% → 91.7%

Time: 30.2s

Alternatives: 26

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z \cdot x, y \cdot 18, -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)}{x} - \mathsf{fma}\left(-18 \cdot \left(z \cdot y\right), t, i \cdot 4\right)\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.5e+111)
   (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b))
   (if (<= x 1.15e+123)
     (fma
      (* -27.0 j)
      k
      (fma (* i x) -4.0 (fma (fma (* z x) (* y 18.0) (* -4.0 a)) t (* c b))))
     (*
      (- (/ (fma (* -27.0 j) k (* c b)) x) (fma (* -18.0 (* z y)) t (* i 4.0)))
      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 (x <= -1.5e+111) {
		tmp = fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b));
	} else if (x <= 1.15e+123) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, fma(fma((z * x), (y * 18.0), (-4.0 * a)), t, (c * b))));
	} else {
		tmp = ((fma((-27.0 * j), k, (c * b)) / x) - fma((-18.0 * (z * y)), t, (i * 4.0))) * 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 (x <= -1.5e+111)
		tmp = fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b));
	elseif (x <= 1.15e+123)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, fma(fma(Float64(z * x), Float64(y * 18.0), Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = Float64(Float64(Float64(fma(Float64(-27.0 * j), k, Float64(c * b)) / x) - fma(Float64(-18.0 * Float64(z * y)), t, Float64(i * 4.0))) * 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[x, -1.5e+111], N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+123], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(N[(z * x), $MachinePrecision] * N[(y * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - N[(N[(-18.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] * t + N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e111

   1. Initial program 60.2%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 90.6%

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

   if -1.5e111 < x < 1.14999999999999995e123

   1. Initial program 91.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 92.7

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 95.5%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 96.1

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 96.1

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

   6. Applied rewrites 96.1%

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

   if 1.14999999999999995e123 < x

   1. Initial program 67.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + -1 \cdot \frac{-27 \cdot \left(j \cdot k\right) + b \cdot c}{x}\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 90.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z \cdot x, y \cdot 18, -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)}{x} - \mathsf{fma}\left(-18 \cdot \left(z \cdot y\right), t, i \cdot 4\right)\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ t_2 := \left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot t\right) \cdot 18\right) \cdot y\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* a t) -4.0)))
        (t_2
         (-
          (+ (* c b) (- (* (* (* (* 18.0 x) y) z) t) (* (* 4.0 a) t)))
          (* (* 4.0 x) i))))
   (if (<= t_2 (- INFINITY))
     (* (* (* (* z x) t) 18.0) y)
     (if (<= t_2 -5e+215)
       t_1
       (if (<= t_2 1e+94) (fma (* -27.0 j) k (* (* i x) -4.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((a * t) * -4.0));
	double t_2 = ((c * b) + (((((18.0 * x) * y) * z) * t) - ((4.0 * a) * t))) - ((4.0 * x) * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((z * x) * t) * 18.0) * y;
	} else if (t_2 <= -5e+215) {
		tmp = t_1;
	} else if (t_2 <= 1e+94) {
		tmp = fma((-27.0 * j), k, ((i * x) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(a * t) * -4.0))
	t_2 = Float64(Float64(Float64(c * b) + Float64(Float64(Float64(Float64(Float64(18.0 * x) * y) * z) * t) - Float64(Float64(4.0 * a) * t))) - Float64(Float64(4.0 * x) * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(z * x) * t) * 18.0) * y);
	elseif (t_2 <= -5e+215)
		tmp = t_1;
	elseif (t_2 <= 1e+94)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(i * x) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(c * b), $MachinePrecision] + N[(N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$2, -5e+215], t$95$1, If[LessEqual[t$95$2, 1e+94], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 78.0%

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 69.8%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 67.7%

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

   11. Taylor expanded in t around inf

       \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 57.5%

       \[\leadsto \left(\left(\left(z \cdot x\right) \cdot t\right) \cdot 18\right) \cdot y \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -5.0000000000000001e215 or 1e94 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 77.2%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 55.9%

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

   if -5.0000000000000001e215 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 1e94

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 99.8

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 64.3

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

   7. Applied rewrites 64.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot t\right) \cdot 18\right) \cdot y\\ \mathbf{elif}\;\left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i \leq -5 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;\left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i \leq 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ t_2 := \left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+301}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b)))
        (t_2
         (-
          (+ (* c b) (- (* (* (* (* 18.0 x) y) z) t) (* (* 4.0 a) t)))
          (* (* 4.0 x) i))))
   (if (<= t_2 -4e+294)
     t_1
     (if (<= t_2 1e+301)
       (fma c b (fma (fma i x (* a t)) -4.0 (* (* k j) -27.0)))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b));
	double t_2 = ((c * b) + (((((18.0 * x) * y) * z) * t) - ((4.0 * a) * t))) - ((4.0 * x) * i);
	double tmp;
	if (t_2 <= -4e+294) {
		tmp = t_1;
	} else if (t_2 <= 1e+301) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, ((k * j) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b))
	t_2 = Float64(Float64(Float64(c * b) + Float64(Float64(Float64(Float64(Float64(18.0 * x) * y) * z) * t) - Float64(Float64(4.0 * a) * t))) - Float64(Float64(4.0 * x) * i))
	tmp = 0.0
	if (t_2 <= -4e+294)
		tmp = t_1;
	elseif (t_2 <= 1e+301)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, Float64(Float64(k * j) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(c * b), $MachinePrecision] + N[(N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+294], t$95$1, If[LessEqual[t$95$2, 1e+301], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -4.00000000000000027e294 or 1.00000000000000005e301 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 65.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 79.3%

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

   if -4.00000000000000027e294 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 1.00000000000000005e301

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 90.4

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

   5. Applied rewrites 90.4%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i \leq -4 \cdot 10^{+294}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;\left(c \cdot b + \left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot z\right) \cdot t - \left(4 \cdot a\right) \cdot t\right)\right) - \left(4 \cdot x\right) \cdot i \leq 10^{+301}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ t_2 := \left(27 \cdot j\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot t\right) \cdot 18\right) \cdot y\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* c b))) (t_2 (* (* 27.0 j) k)))
   (if (<= t_2 -1e+86)
     t_1
     (if (<= t_2 -2e+41)
       (* (* (* (* z x) t) 18.0) y)
       (if (<= t_2 -5e-59)
         (fma c b (* (* a t) -4.0))
         (if (<= t_2 1e+156) (fma (* -4.0 i) x (* c b)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, (c * b));
	double t_2 = (27.0 * j) * k;
	double tmp;
	if (t_2 <= -1e+86) {
		tmp = t_1;
	} else if (t_2 <= -2e+41) {
		tmp = (((z * x) * t) * 18.0) * y;
	} else if (t_2 <= -5e-59) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else if (t_2 <= 1e+156) {
		tmp = fma((-4.0 * i), x, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(c * b))
	t_2 = Float64(Float64(27.0 * j) * k)
	tmp = 0.0
	if (t_2 <= -1e+86)
		tmp = t_1;
	elseif (t_2 <= -2e+41)
		tmp = Float64(Float64(Float64(Float64(z * x) * t) * 18.0) * y);
	elseif (t_2 <= -5e-59)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	elseif (t_2 <= 1e+156)
		tmp = fma(Float64(-4.0 * i), x, Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+86], t$95$1, If[LessEqual[t$95$2, -2e+41], N[(N[(N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$2, -5e-59], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+156], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e86 or 9.9999999999999998e155 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 81.1%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. +-commutative N/A

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

   7. Applied rewrites 64.3%

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

   if -1e86 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000001e41

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 88.0

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

   5. Applied rewrites 88.0%

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

   7. Applied rewrites 88.2%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 88.0%

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

   11. Taylor expanded in t around inf

       \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right) \cdot y \]
   12. Step-by-step derivation

   13. Applied rewrites 75.8%

       \[\leadsto \left(\left(\left(z \cdot x\right) \cdot t\right) \cdot 18\right) \cdot y \]

   if -2.00000000000000001e41 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e-59

   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. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 83.1

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

   5. Applied rewrites 83.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 69.5%

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

   if -5.0000000000000001e-59 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999998e155

   1. Initial program 84.4%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 68.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 53.8%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(27 \cdot j\right) \cdot k \leq -1 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(\left(z \cdot x\right) \cdot t\right) \cdot 18\right) \cdot y\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq -5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ t_2 := \left(27 \cdot j\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* c b))) (t_2 (* (* 27.0 j) k)))
   (if (<= t_2 -1e+147)
     t_1
     (if (<= t_2 -2e+41)
       (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
       (if (<= t_2 5e+161) (fma c b (* (fma i x (* a t)) -4.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, (c * b));
	double t_2 = (27.0 * j) * k;
	double tmp;
	if (t_2 <= -1e+147) {
		tmp = t_1;
	} else if (t_2 <= -2e+41) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (t_2 <= 5e+161) {
		tmp = fma(c, b, (fma(i, x, (a * t)) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(c * b))
	t_2 = Float64(Float64(27.0 * j) * k)
	tmp = 0.0
	if (t_2 <= -1e+147)
		tmp = t_1;
	elseif (t_2 <= -2e+41)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (t_2 <= 5e+161)
		tmp = fma(c, b, Float64(fma(i, x, Float64(a * t)) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+147], t$95$1, If[LessEqual[t$95$2, -2e+41], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+161], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999998e146 or 4.9999999999999997e161 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.4

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

   5. Applied rewrites 65.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. +-commutative N/A

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

   7. Applied rewrites 68.3%

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

   if -9.9999999999999998e146 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000001e41

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 66.1

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

   5. Applied rewrites 66.1%

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

   if -2.00000000000000001e41 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e161

   1. Initial program 85.0%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 72.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(27 \cdot j\right) \cdot k \leq -1 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ t_2 := \left(27 \cdot j\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* c b))) (t_2 (* (* 27.0 j) k)))
   (if (<= t_2 -5e+267)
     t_1
     (if (<= t_2 -4e+19)
       (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)
       (if (<= t_2 5e+161) (fma c b (* (fma i x (* a t)) -4.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, (c * b));
	double t_2 = (27.0 * j) * k;
	double tmp;
	if (t_2 <= -5e+267) {
		tmp = t_1;
	} else if (t_2 <= -4e+19) {
		tmp = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	} else if (t_2 <= 5e+161) {
		tmp = fma(c, b, (fma(i, x, (a * t)) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(c * b))
	t_2 = Float64(Float64(27.0 * j) * k)
	tmp = 0.0
	if (t_2 <= -5e+267)
		tmp = t_1;
	elseif (t_2 <= -4e+19)
		tmp = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t);
	elseif (t_2 <= 5e+161)
		tmp = fma(c, b, Float64(fma(i, x, Float64(a * t)) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+267], t$95$1, If[LessEqual[t$95$2, -4e+19], N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, 5e+161], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999999e267 or 4.9999999999999997e161 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.8

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

   5. Applied rewrites 69.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. +-commutative N/A

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

   7. Applied rewrites 73.2%

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

   if -4.9999999999999999e267 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4e19

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

   if -4e19 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e161

   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 z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 72.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(27 \cdot j\right) \cdot k \leq -5 \cdot 10^{+267}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq -4 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot t\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z \cdot x, y \cdot 18, -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, t\_1 \cdot 18\right), x, \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

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 (* (* z y) t)))
   (if (<= x -1.5e+111)
     (fma (fma t_1 18.0 (* -4.0 i)) x (* c b))
     (if (<= x 1.15e+123)
       (fma
        (* -27.0 j)
        k
        (fma (* i x) -4.0 (fma (fma (* z x) (* y 18.0) (* -4.0 a)) t (* c b))))
       (fma (fma -4.0 i (* t_1 18.0)) x (fma c b (* (* k j) -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * t;
	double tmp;
	if (x <= -1.5e+111) {
		tmp = fma(fma(t_1, 18.0, (-4.0 * i)), x, (c * b));
	} else if (x <= 1.15e+123) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, fma(fma((z * x), (y * 18.0), (-4.0 * a)), t, (c * b))));
	} else {
		tmp = fma(fma(-4.0, i, (t_1 * 18.0)), x, fma(c, b, ((k * j) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * t)
	tmp = 0.0
	if (x <= -1.5e+111)
		tmp = fma(fma(t_1, 18.0, Float64(-4.0 * i)), x, Float64(c * b));
	elseif (x <= 1.15e+123)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, fma(fma(Float64(z * x), Float64(y * 18.0), Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = fma(fma(-4.0, i, Float64(t_1 * 18.0)), x, fma(c, b, Float64(Float64(k * j) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -1.5e+111], N[(N[(t$95$1 * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+123], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(N[(z * x), $MachinePrecision] * N[(y * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e111

   1. Initial program 60.2%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 90.6%

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

   if -1.5e111 < x < 1.14999999999999995e123

   1. Initial program 91.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 92.7

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 95.5%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 96.1

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 96.1

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

   6. Applied rewrites 96.1%

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

   if 1.14999999999999995e123 < x

   1. Initial program 67.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z \cdot x, y \cdot 18, -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot t\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(18 \cdot x\right) \cdot y, -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, t\_1 \cdot 18\right), x, \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

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 (* (* z y) t)))
   (if (<= x -6.6e+109)
     (fma (fma t_1 18.0 (* -4.0 i)) x (* c b))
     (if (<= x 2.3e+122)
       (fma
        (* -27.0 j)
        k
        (fma (* i x) -4.0 (fma (fma z (* (* 18.0 x) y) (* -4.0 a)) t (* c b))))
       (fma (fma -4.0 i (* t_1 18.0)) x (fma c b (* (* k j) -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * t;
	double tmp;
	if (x <= -6.6e+109) {
		tmp = fma(fma(t_1, 18.0, (-4.0 * i)), x, (c * b));
	} else if (x <= 2.3e+122) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, fma(fma(z, ((18.0 * x) * y), (-4.0 * a)), t, (c * b))));
	} else {
		tmp = fma(fma(-4.0, i, (t_1 * 18.0)), x, fma(c, b, ((k * j) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * t)
	tmp = 0.0
	if (x <= -6.6e+109)
		tmp = fma(fma(t_1, 18.0, Float64(-4.0 * i)), x, Float64(c * b));
	elseif (x <= 2.3e+122)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, fma(fma(z, Float64(Float64(18.0 * x) * y), Float64(-4.0 * a)), t, Float64(c * b))));
	else
		tmp = fma(fma(-4.0, i, Float64(t_1 * 18.0)), x, fma(c, b, Float64(Float64(k * j) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -6.6e+109], N[(N[(t$95$1 * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+122], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(z * N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(t$95$1 * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5999999999999998e109

   1. Initial program 60.2%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 90.6%

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

   if -6.5999999999999998e109 < x < 2.3000000000000001e122

   1. Initial program 91.1%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. metadata-eval 92.7

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

   4. Applied rewrites 95.5%

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

   if 2.3000000000000001e122 < x

   1. Initial program 67.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 90.6%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, \left(18 \cdot x\right) \cdot y, -4 \cdot a\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ t_2 := \left(27 \cdot j\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* c b))) (t_2 (* (* 27.0 j) k)))
   (if (<= t_2 -1e+59)
     t_1
     (if (<= t_2 -5e-59)
       (fma c b (* (* a t) -4.0))
       (if (<= t_2 1e+156) (fma (* -4.0 i) x (* c b)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, (c * b));
	double t_2 = (27.0 * j) * k;
	double tmp;
	if (t_2 <= -1e+59) {
		tmp = t_1;
	} else if (t_2 <= -5e-59) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else if (t_2 <= 1e+156) {
		tmp = fma((-4.0 * i), x, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(c * b))
	t_2 = Float64(Float64(27.0 * j) * k)
	tmp = 0.0
	if (t_2 <= -1e+59)
		tmp = t_1;
	elseif (t_2 <= -5e-59)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	elseif (t_2 <= 1e+156)
		tmp = fma(Float64(-4.0 * i), x, Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+59], t$95$1, If[LessEqual[t$95$2, -5e-59], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+156], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999972e58 or 9.9999999999999998e155 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.6

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

   5. Applied rewrites 60.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. +-commutative N/A

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

   7. Applied rewrites 62.9%

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

   if -9.99999999999999972e58 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000001e-59

   1. Initial program 83.4%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 59.0%

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

   if -5.0000000000000001e-59 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999998e155

   1. Initial program 84.4%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 68.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 53.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(27 \cdot j\right) \cdot k \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq -5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(z, \left(t \cdot y\right) \cdot 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* c b) -2e+248)
   (fma c b (* (* a t) -4.0))
   (if (<= (* c b) -5e+27)
     (* (fma z (* (* t y) 18.0) (* -4.0 i)) x)
     (if (<= (* c b) 5e+99)
       (fma (fma i x (* a t)) -4.0 (* (* k j) -27.0))
       (fma (* -4.0 i) x (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+248) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else if ((c * b) <= -5e+27) {
		tmp = fma(z, ((t * y) * 18.0), (-4.0 * i)) * x;
	} else if ((c * b) <= 5e+99) {
		tmp = fma(fma(i, x, (a * t)), -4.0, ((k * j) * -27.0));
	} else {
		tmp = fma((-4.0 * i), x, (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -2e+248)
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	elseif (Float64(c * b) <= -5e+27)
		tmp = Float64(fma(z, Float64(Float64(t * y) * 18.0), Float64(-4.0 * i)) * x);
	elseif (Float64(c * b) <= 5e+99)
		tmp = fma(fma(i, x, Float64(a * t)), -4.0, Float64(Float64(k * j) * -27.0));
	else
		tmp = fma(Float64(-4.0 * i), x, Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -2e+248], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -5e+27], N[(N[(z * N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 5e+99], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.00000000000000009e248

   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 z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 86.5%

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

   if -2.00000000000000009e248 < (*.f64 b c) < -4.99999999999999979e27

   1. Initial program 79.0%

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 58.9

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

   5. Applied rewrites 58.9%

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

   7. Applied rewrites 59.0%

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

   if -4.99999999999999979e27 < (*.f64 b c) < 5.00000000000000008e99

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in c around 0

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

   8. Applied rewrites 71.7%

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

   if 5.00000000000000008e99 < (*.f64 b c)

   1. Initial program 66.8%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 83.5%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 84.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(z, \left(t \cdot y\right) \cdot 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ t_2 := \mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, t\_1\right)\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* k j) -27.0))
        (t_2 (fma (fma -4.0 i (* (* (* z y) t) 18.0)) x (fma c b t_1))))
   (if (<= x -4.2e+80)
     t_2
     (if (<= x 4.5e-11) (fma c b (fma (fma i x (* a t)) -4.0 t_1)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * j) * -27.0;
	double t_2 = fma(fma(-4.0, i, (((z * y) * t) * 18.0)), x, fma(c, b, t_1));
	double tmp;
	if (x <= -4.2e+80) {
		tmp = t_2;
	} else if (x <= 4.5e-11) {
		tmp = fma(c, b, fma(fma(i, x, (a * t)), -4.0, t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(k * j) * -27.0)
	t_2 = fma(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)), x, fma(c, b, t_1))
	tmp = 0.0
	if (x <= -4.2e+80)
		tmp = t_2;
	elseif (x <= 4.5e-11)
		tmp = fma(c, b, fma(fma(i, x, Float64(a * t)), -4.0, t_1));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x + N[(c * b + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+80], t$95$2, If[LessEqual[x, 4.5e-11], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0 + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000003e80 or 4.5e-11 < x

   1. Initial program 72.2%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 89.0%

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

   if -4.20000000000000003e80 < x < 4.5e-11

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 85.9

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

   5. Applied rewrites 85.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, \left(k \cdot j\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+194}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{-194}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* c b) -1e+194)
   (* c b)
   (if (<= (* c b) -5e-194)
     (* (* -4.0 i) x)
     (if (<= (* c b) 2e-17)
       (* (* a t) -4.0)
       (if (<= (* c b) 5e+99) (* (* k j) -27.0) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -1e+194) {
		tmp = c * b;
	} else if ((c * b) <= -5e-194) {
		tmp = (-4.0 * i) * x;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((c * b) <= (-1d+194)) then
        tmp = c * b
    else if ((c * b) <= (-5d-194)) then
        tmp = ((-4.0d0) * i) * x
    else if ((c * b) <= 2d-17) then
        tmp = (a * t) * (-4.0d0)
    else if ((c * b) <= 5d+99) then
        tmp = (k * j) * (-27.0d0)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -1e+194) {
		tmp = c * b;
	} else if ((c * b) <= -5e-194) {
		tmp = (-4.0 * i) * x;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -1e+194:
		tmp = c * b
	elif (c * b) <= -5e-194:
		tmp = (-4.0 * i) * x
	elif (c * b) <= 2e-17:
		tmp = (a * t) * -4.0
	elif (c * b) <= 5e+99:
		tmp = (k * j) * -27.0
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -1e+194)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= -5e-194)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (Float64(c * b) <= 2e-17)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (Float64(c * b) <= 5e+99)
		tmp = Float64(Float64(k * j) * -27.0);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -1e+194)
		tmp = c * b;
	elseif ((c * b) <= -5e-194)
		tmp = (-4.0 * i) * x;
	elseif ((c * b) <= 2e-17)
		tmp = (a * t) * -4.0;
	elseif ((c * b) <= 5e+99)
		tmp = (k * j) * -27.0;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -1e+194], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -5e-194], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 2e-17], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 5e+99], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -9.99999999999999945e193 or 5.00000000000000008e99 < (*.f64 b c)

   1. Initial program 75.8%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 68.0

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

   5. Applied rewrites 68.0%

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

   if -9.99999999999999945e193 < (*.f64 b c) < -5.0000000000000002e-194

   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 i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 30.4

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

   5. Applied rewrites 30.4%

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

   if -5.0000000000000002e-194 < (*.f64 b c) < 2.00000000000000014e-17

   1. Initial program 91.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 37.0

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

   5. Applied rewrites 37.0%

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

   if 2.00000000000000014e-17 < (*.f64 b c) < 5.00000000000000008e99

   1. Initial program 92.1%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 43.4

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

   5. Applied rewrites 43.4%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -1 \cdot 10^{+194}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -5 \cdot 10^{-194}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-194}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* c b) -2e+244)
   (* c b)
   (if (<= (* c b) -2e-194)
     (* (* -27.0 k) j)
     (if (<= (* c b) 2e-17)
       (* (* a t) -4.0)
       (if (<= (* c b) 5e+99) (* (* k j) -27.0) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= -2e-194) {
		tmp = (-27.0 * k) * j;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((c * b) <= (-2d+244)) then
        tmp = c * b
    else if ((c * b) <= (-2d-194)) then
        tmp = ((-27.0d0) * k) * j
    else if ((c * b) <= 2d-17) then
        tmp = (a * t) * (-4.0d0)
    else if ((c * b) <= 5d+99) then
        tmp = (k * j) * (-27.0d0)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= -2e-194) {
		tmp = (-27.0 * k) * j;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -2e+244:
		tmp = c * b
	elif (c * b) <= -2e-194:
		tmp = (-27.0 * k) * j
	elif (c * b) <= 2e-17:
		tmp = (a * t) * -4.0
	elif (c * b) <= 5e+99:
		tmp = (k * j) * -27.0
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -2e+244)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= -2e-194)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (Float64(c * b) <= 2e-17)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (Float64(c * b) <= 5e+99)
		tmp = Float64(Float64(k * j) * -27.0);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -2e+244)
		tmp = c * b;
	elseif ((c * b) <= -2e-194)
		tmp = (-27.0 * k) * j;
	elseif ((c * b) <= 2e-17)
		tmp = (a * t) * -4.0;
	elseif ((c * b) <= 5e+99)
		tmp = (k * j) * -27.0;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -2e+244], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -2e-194], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 2e-17], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 5e+99], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.00000000000000015e244 or 5.00000000000000008e99 < (*.f64 b c)

   1. Initial program 72.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -2.00000000000000015e244 < (*.f64 b c) < -2.00000000000000004e-194

   1. Initial program 79.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 6.8

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

   5. Applied rewrites 6.8%

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

   6. Taylor expanded in k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 26.9

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

   8. Applied rewrites 26.9%

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

   10. Applied rewrites 26.9%

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

   if -2.00000000000000004e-194 < (*.f64 b c) < 2.00000000000000014e-17

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 37.3

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

   5. Applied rewrites 37.3%

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

   if 2.00000000000000014e-17 < (*.f64 b c) < 5.00000000000000008e99

   1. Initial program 92.1%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 43.4

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

   5. Applied rewrites 43.4%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-194}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-194}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* c b) -2e+244)
   (* c b)
   (if (<= (* c b) -2e-194)
     (* (* -27.0 j) k)
     (if (<= (* c b) 2e-17)
       (* (* a t) -4.0)
       (if (<= (* c b) 5e+99) (* (* k j) -27.0) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= -2e-194) {
		tmp = (-27.0 * j) * k;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((c * b) <= (-2d+244)) then
        tmp = c * b
    else if ((c * b) <= (-2d-194)) then
        tmp = ((-27.0d0) * j) * k
    else if ((c * b) <= 2d-17) then
        tmp = (a * t) * (-4.0d0)
    else if ((c * b) <= 5d+99) then
        tmp = (k * j) * (-27.0d0)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= -2e-194) {
		tmp = (-27.0 * j) * k;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -2e+244:
		tmp = c * b
	elif (c * b) <= -2e-194:
		tmp = (-27.0 * j) * k
	elif (c * b) <= 2e-17:
		tmp = (a * t) * -4.0
	elif (c * b) <= 5e+99:
		tmp = (k * j) * -27.0
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -2e+244)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= -2e-194)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (Float64(c * b) <= 2e-17)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (Float64(c * b) <= 5e+99)
		tmp = Float64(Float64(k * j) * -27.0);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -2e+244)
		tmp = c * b;
	elseif ((c * b) <= -2e-194)
		tmp = (-27.0 * j) * k;
	elseif ((c * b) <= 2e-17)
		tmp = (a * t) * -4.0;
	elseif ((c * b) <= 5e+99)
		tmp = (k * j) * -27.0;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -2e+244], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -2e-194], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 2e-17], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 5e+99], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -2.00000000000000015e244 or 5.00000000000000008e99 < (*.f64 b c)

   1. Initial program 72.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -2.00000000000000015e244 < (*.f64 b c) < -2.00000000000000004e-194

   1. Initial program 79.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 6.8

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

   5. Applied rewrites 6.8%

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

   6. Taylor expanded in k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 26.9

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

   8. Applied rewrites 26.9%

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

   10. Applied rewrites 26.9%

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

   if -2.00000000000000004e-194 < (*.f64 b c) < 2.00000000000000014e-17

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 37.3

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

   5. Applied rewrites 37.3%

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

   if 2.00000000000000014e-17 < (*.f64 b c) < 5.00000000000000008e99

   1. Initial program 92.1%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 43.4

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

   5. Applied rewrites 43.4%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-194}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(k \cdot j\right) \cdot -27\\ \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* k j) -27.0)))
   (if (<= (* c b) -2e+244)
     (* c b)
     (if (<= (* c b) -2e-194)
       t_1
       (if (<= (* c b) 2e-17)
         (* (* a t) -4.0)
         (if (<= (* c b) 5e+99) t_1 (* c b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * j) * -27.0;
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= -2e-194) {
		tmp = t_1;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (k * j) * (-27.0d0)
    if ((c * b) <= (-2d+244)) then
        tmp = c * b
    else if ((c * b) <= (-2d-194)) then
        tmp = t_1
    else if ((c * b) <= 2d-17) then
        tmp = (a * t) * (-4.0d0)
    else if ((c * b) <= 5d+99) then
        tmp = t_1
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * j) * -27.0;
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= -2e-194) {
		tmp = t_1;
	} else if ((c * b) <= 2e-17) {
		tmp = (a * t) * -4.0;
	} else if ((c * b) <= 5e+99) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (k * j) * -27.0
	tmp = 0
	if (c * b) <= -2e+244:
		tmp = c * b
	elif (c * b) <= -2e-194:
		tmp = t_1
	elif (c * b) <= 2e-17:
		tmp = (a * t) * -4.0
	elif (c * b) <= 5e+99:
		tmp = t_1
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(k * j) * -27.0)
	tmp = 0.0
	if (Float64(c * b) <= -2e+244)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= -2e-194)
		tmp = t_1;
	elseif (Float64(c * b) <= 2e-17)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (Float64(c * b) <= 5e+99)
		tmp = t_1;
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (k * j) * -27.0;
	tmp = 0.0;
	if ((c * b) <= -2e+244)
		tmp = c * b;
	elseif ((c * b) <= -2e-194)
		tmp = t_1;
	elseif ((c * b) <= 2e-17)
		tmp = (a * t) * -4.0;
	elseif ((c * b) <= 5e+99)
		tmp = t_1;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[N[(c * b), $MachinePrecision], -2e+244], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], -2e-194], t$95$1, If[LessEqual[N[(c * b), $MachinePrecision], 2e-17], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 5e+99], t$95$1, N[(c * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.00000000000000015e244 or 5.00000000000000008e99 < (*.f64 b c)

   1. Initial program 72.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -2.00000000000000015e244 < (*.f64 b c) < -2.00000000000000004e-194 or 2.00000000000000014e-17 < (*.f64 b c) < 5.00000000000000008e99

   1. Initial program 82.2%

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

   3. Taylor expanded in k around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 31.0

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

   5. Applied rewrites 31.0%

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

   if -2.00000000000000004e-194 < (*.f64 b c) < 2.00000000000000014e-17

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 37.3

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

   5. Applied rewrites 37.3%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq -2 \cdot 10^{-194}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;c \cdot b \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ t_2 := \left(27 \cdot j\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* c b))) (t_2 (* (* 27.0 j) k)))
   (if (<= t_2 -1e+147)
     t_1
     (if (<= t_2 5e+161) (fma c b (* (fma i x (* a t)) -4.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, (c * b));
	double t_2 = (27.0 * j) * k;
	double tmp;
	if (t_2 <= -1e+147) {
		tmp = t_1;
	} else if (t_2 <= 5e+161) {
		tmp = fma(c, b, (fma(i, x, (a * t)) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(c * b))
	t_2 = Float64(Float64(27.0 * j) * k)
	tmp = 0.0
	if (t_2 <= -1e+147)
		tmp = t_1;
	elseif (t_2 <= 5e+161)
		tmp = fma(c, b, Float64(fma(i, x, Float64(a * t)) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+147], t$95$1, If[LessEqual[t$95$2, 5e+161], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999998e146 or 4.9999999999999997e161 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.7%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.4

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

   5. Applied rewrites 65.4%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. +-commutative N/A

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

   7. Applied rewrites 68.3%

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

   if -9.9999999999999998e146 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e161

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-neg-in N/A

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

      6. distribute-lft-out N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

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

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 69.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(27 \cdot j\right) \cdot k \leq -1 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-27 \cdot j\right) \cdot k\\ t_2 := \left(27 \cdot j\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -27.0 j) k)) (t_2 (* (* 27.0 j) k)))
   (if (<= t_2 -1e+75)
     t_1
     (if (<= t_2 5e+167) (fma (* -4.0 i) x (* c b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-27.0 * j) * k;
	double t_2 = (27.0 * j) * k;
	double tmp;
	if (t_2 <= -1e+75) {
		tmp = t_1;
	} else if (t_2 <= 5e+167) {
		tmp = fma((-4.0 * i), x, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-27.0 * j) * k)
	t_2 = Float64(Float64(27.0 * j) * k)
	tmp = 0.0
	if (t_2 <= -1e+75)
		tmp = t_1;
	elseif (t_2 <= 5e+167)
		tmp = fma(Float64(-4.0 * i), x, Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+75], t$95$1, If[LessEqual[t$95$2, 5e+167], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999927e74 or 4.9999999999999997e167 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 80.4%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 14.2

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

   5. Applied rewrites 14.2%

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

   6. Taylor expanded in k around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 53.3

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

   8. Applied rewrites 53.3%

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

   10. Applied rewrites 53.3%

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

   if -9.99999999999999927e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e167

   1. Initial program 84.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in k around 0

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

   8. Applied rewrites 67.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 49.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(27 \cdot j\right) \cdot k \leq -1 \cdot 10^{+75}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;\left(27 \cdot j\right) \cdot k \leq 5 \cdot 10^{+167}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -4.6e+123)
     t_1
     (if (<= t -1.42e-67)
       (fma (* -27.0 j) k (fma (* -4.0 t) a (* c b)))
       (if (<= t 1.06e+76)
         (fma (* -27.0 k) j (fma (* -4.0 i) x (* c b)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -4.6e+123) {
		tmp = t_1;
	} else if (t <= -1.42e-67) {
		tmp = fma((-27.0 * j), k, fma((-4.0 * t), a, (c * b)));
	} else if (t <= 1.06e+76) {
		tmp = fma((-27.0 * k), j, fma((-4.0 * i), x, (c * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -4.6e+123)
		tmp = t_1;
	elseif (t <= -1.42e-67)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * t), a, Float64(c * b)));
	elseif (t <= 1.06e+76)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(-4.0 * i), x, Float64(c * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.6e+123], t$95$1, If[LessEqual[t, -1.42e-67], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * t), $MachinePrecision] * a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+76], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999981e123 or 1.06e76 < t

   1. Initial program 80.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \cdot t \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \cdot t \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

      12. lower-*.f64 78.7

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t} \]

   if -4.59999999999999981e123 < t < -1.42000000000000004e-67

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 91.2

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(-4 \cdot t\right) \cdot a} + b \cdot c\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot -4, a, \color{blue}{c \cdot b}\right)\right) \]

      7. lower-*.f64 70.2

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot -4, a, \color{blue}{c \cdot b}\right)\right) \]

   7. Applied rewrites 70.2%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\mathsf{fma}\left(t \cdot -4, a, c \cdot b\right)}\right) \]

   if -1.42000000000000004e-67 < t < 1.06e76

   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 c around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 52.0

         \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 52.0%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{c \cdot b - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{c \cdot b + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto c \cdot b + \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} \]

      5. lift-*.f64 N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right)\right) \cdot k \]

      6. *-commutative N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right)\right) \cdot k \]

      7. distribute-lft-neg-in N/A

         \[\leadsto c \cdot b + \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot j\right)} \cdot k \]

      8. metadata-eval N/A

         \[\leadsto c \cdot b + \left(\color{blue}{-27} \cdot j\right) \cdot k \]

      9. associate-*l* N/A

         \[\leadsto c \cdot b + \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      10. *-commutative N/A

          \[\leadsto c \cdot b + -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      11. lift-*.f64 N/A

          \[\leadsto c \cdot b + -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto c \cdot b + \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

      13. +-commutative N/A

          \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right) + c \cdot b} \]

      14. lift-*.f64 N/A

          \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} + c \cdot b \]

   7. Applied rewrites 53.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)}\right) \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{\left(-4 \cdot i\right) \cdot x} + b \cdot c\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{\mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(\color{blue}{i \cdot -4}, x, b \cdot c\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(\color{blue}{i \cdot -4}, x, b \cdot c\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(i \cdot -4, x, \color{blue}{c \cdot b}\right)\right) \]

      9. lower-*.f64 81.7

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(i \cdot -4, x, \color{blue}{c \cdot b}\right)\right) \]

   10. Applied rewrites 81.7%

       \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{\mathsf{fma}\left(i \cdot -4, x, c \cdot b\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -4.6e+123)
     t_1
     (if (<= t -1.42e-67)
       (fma (* -27.0 j) k (fma (* -4.0 t) a (* c b)))
       (if (<= t 1.06e+76)
         (fma (* -27.0 j) k (fma (* i x) -4.0 (* c b)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -4.6e+123) {
		tmp = t_1;
	} else if (t <= -1.42e-67) {
		tmp = fma((-27.0 * j), k, fma((-4.0 * t), a, (c * b)));
	} else if (t <= 1.06e+76) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, (c * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -4.6e+123)
		tmp = t_1;
	elseif (t <= -1.42e-67)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * t), a, Float64(c * b)));
	elseif (t <= 1.06e+76)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, Float64(c * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.6e+123], t$95$1, If[LessEqual[t, -1.42e-67], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * t), $MachinePrecision] * a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+76], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999981e123 or 1.06e76 < t

   1. Initial program 80.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \cdot t \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \cdot t \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

      12. lower-*.f64 78.7

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t} \]

   if -4.59999999999999981e123 < t < -1.42000000000000004e-67

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 91.2

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(-4 \cdot t\right) \cdot a} + b \cdot c\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot -4, a, \color{blue}{c \cdot b}\right)\right) \]

      7. lower-*.f64 70.2

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot -4, a, \color{blue}{c \cdot b}\right)\right) \]

   7. Applied rewrites 70.2%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\mathsf{fma}\left(t \cdot -4, a, c \cdot b\right)}\right) \]

   if -1.42000000000000004e-67 < t < 1.06e76

   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. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 85.0

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 85.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \color{blue}{c \cdot b}\right)\right) \]

      2. lower-*.f64 80.1

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \color{blue}{c \cdot b}\right)\right) \]

   7. Applied rewrites 80.1%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \color{blue}{c \cdot b}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 72.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -4.6e+123)
     t_1
     (if (<= t -1.42e-67)
       (fma (* -27.0 j) k (fma (* -4.0 t) a (* c b)))
       (if (<= t 1.06e+76)
         (fma c b (fma (* -4.0 x) i (* (* k j) -27.0)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -4.6e+123) {
		tmp = t_1;
	} else if (t <= -1.42e-67) {
		tmp = fma((-27.0 * j), k, fma((-4.0 * t), a, (c * b)));
	} else if (t <= 1.06e+76) {
		tmp = fma(c, b, fma((-4.0 * x), i, ((k * j) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -4.6e+123)
		tmp = t_1;
	elseif (t <= -1.42e-67)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * t), a, Float64(c * b)));
	elseif (t <= 1.06e+76)
		tmp = fma(c, b, fma(Float64(-4.0 * x), i, Float64(Float64(k * j) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.6e+123], t$95$1, If[LessEqual[t, -1.42e-67], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * t), $MachinePrecision] * a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+76], N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999981e123 or 1.06e76 < t

   1. Initial program 80.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \cdot t \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \cdot t \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

      12. lower-*.f64 78.7

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t} \]

   if -4.59999999999999981e123 < t < -1.42000000000000004e-67

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(j \cdot 27\right) \cdot k}\right)\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(j \cdot 27\right)\right) \cdot k} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(j \cdot 27\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{j \cdot 27}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{27 \cdot j}\right), k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot j}, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      11. metadata-eval 91.2

          \[\leadsto \mathsf{fma}\left(\color{blue}{-27} \cdot j, k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i}\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right)}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(\mathsf{neg}\left(\left(x \cdot 4\right) \cdot i\right)\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

   4. Applied rewrites 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\left(-4 \cdot t\right) \cdot a} + b \cdot c\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\mathsf{fma}\left(-4 \cdot t, a, b \cdot c\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot -4, a, \color{blue}{c \cdot b}\right)\right) \]

      7. lower-*.f64 70.2

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot -4, a, \color{blue}{c \cdot b}\right)\right) \]

   7. Applied rewrites 70.2%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \color{blue}{\mathsf{fma}\left(t \cdot -4, a, c \cdot b\right)}\right) \]

   if -1.42000000000000004e-67 < t < 1.06e76

   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 t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4} \cdot \left(i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\left(x \cdot i\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot x\right) \cdot i} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-4 \cdot x}, i, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \color{blue}{\left(k \cdot j\right)}\right)\right) \]

      15. lower-*.f64 79.2

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \color{blue}{\left(k \cdot j\right)}\right)\right) \]

   5. Applied rewrites 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \left(k \cdot j\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 72.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -4.6e+123)
     t_1
     (if (<= t -1.42e-67)
       (fma c b (fma (* -27.0 k) j (* (* a t) -4.0)))
       (if (<= t 1.06e+76)
         (fma c b (fma (* -4.0 x) i (* (* k j) -27.0)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -4.6e+123) {
		tmp = t_1;
	} else if (t <= -1.42e-67) {
		tmp = fma(c, b, fma((-27.0 * k), j, ((a * t) * -4.0)));
	} else if (t <= 1.06e+76) {
		tmp = fma(c, b, fma((-4.0 * x), i, ((k * j) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -4.6e+123)
		tmp = t_1;
	elseif (t <= -1.42e-67)
		tmp = fma(c, b, fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0)));
	elseif (t <= 1.06e+76)
		tmp = fma(c, b, fma(Float64(-4.0 * x), i, Float64(Float64(k * j) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.6e+123], t$95$1, If[LessEqual[t, -1.42e-67], N[(c * b + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e+76], N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999981e123 or 1.06e76 < t

   1. Initial program 80.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right) \cdot t} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \cdot t \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \cdot t \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

      12. lower-*.f64 78.7

          \[\leadsto \mathsf{fma}\left(-4, a, \left(\color{blue}{\left(z \cdot y\right)} \cdot x\right) \cdot 18\right) \cdot t \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t} \]

   if -4.59999999999999981e123 < t < -1.42000000000000004e-67

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 70.2

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 70.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   if -1.42000000000000004e-67 < t < 1.06e76

   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 t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4} \cdot \left(i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\left(x \cdot i\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot x\right) \cdot i} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      12. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-4 \cdot x}, i, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \color{blue}{\left(k \cdot j\right)}\right)\right) \]

      15. lower-*.f64 79.2

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \color{blue}{\left(k \cdot j\right)}\right)\right) \]

   5. Applied rewrites 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, -27 \cdot \left(k \cdot j\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot x, i, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 77.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b))))
   (if (<= x -9.4e+63)
     t_1
     (if (<= x 2.76e+17) (fma c b (fma (* -27.0 k) j (* (* a t) -4.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b));
	double tmp;
	if (x <= -9.4e+63) {
		tmp = t_1;
	} else if (x <= 2.76e+17) {
		tmp = fma(c, b, fma((-27.0 * k), j, ((a * t) * -4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b))
	tmp = 0.0
	if (x <= -9.4e+63)
		tmp = t_1;
	elseif (x <= 2.76e+17)
		tmp = fma(c, b, fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.4e+63], t$95$1, If[LessEqual[x, 2.76e+17], N[(c * b + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4000000000000006e63 or 2.76e17 < x

   1. Initial program 71.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. associate--l+ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Applied rewrites 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in k around 0

      \[\leadsto b \cdot c + \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 81.5%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, i \cdot -4\right), \color{blue}{x}, c \cdot b\right) \]

   if -9.4000000000000006e63 < x < 2.76e17

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 76.8

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 73.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(z, \left(t \cdot y\right) \cdot 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.65e+81)
   (* (fma z (* (* t y) 18.0) (* -4.0 i)) x)
   (if (<= x 2.35e+24)
     (fma c b (fma (* -27.0 k) j (* (* a t) -4.0)))
     (* (fma -4.0 i (* (* (* z y) 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 (x <= -1.65e+81) {
		tmp = fma(z, ((t * y) * 18.0), (-4.0 * i)) * x;
	} else if (x <= 2.35e+24) {
		tmp = fma(c, b, fma((-27.0 * k), j, ((a * t) * -4.0)));
	} else {
		tmp = fma(-4.0, i, (((z * y) * 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 (x <= -1.65e+81)
		tmp = Float64(fma(z, Float64(Float64(t * y) * 18.0), Float64(-4.0 * i)) * x);
	elseif (x <= 2.35e+24)
		tmp = fma(c, b, fma(Float64(-27.0 * k), j, Float64(Float64(a * t) * -4.0)));
	else
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * 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[x, -1.65e+81], N[(N[(z * N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.35e+24], N[(c * b + N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e81

   1. Initial program 65.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 80.3

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 80.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 82.9%

      \[\leadsto \mathsf{fma}\left(z, \left(t \cdot y\right) \cdot 18, -4 \cdot i\right) \cdot x \]

   if -1.65e81 < x < 2.35e24

   1. Initial program 91.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(a \cdot t\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-27} \cdot \left(j \cdot k\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \color{blue}{\left(k \cdot j\right)} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-27 \cdot k\right) \cdot j} + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot k\right) \cdot j + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{-27 \cdot k}, j, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

      15. lower-*.f64 75.9

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\right)} \]

   if 2.35e24 < x

   1. Initial program 74.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \cdot x \]

      4. metadata-eval N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \cdot x \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

      12. lower-*.f64 65.9

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 65.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(z, \left(t \cdot y\right) \cdot 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot k, j, \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 35.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* c b) -2e+244)
   (* c b)
   (if (<= (* c b) 5e+99) (* (* k j) -27.0) (* c b))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((c * b) <= (-2d+244)) then
        tmp = c * b
    else if ((c * b) <= 5d+99) then
        tmp = (k * j) * (-27.0d0)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -2e+244) {
		tmp = c * b;
	} else if ((c * b) <= 5e+99) {
		tmp = (k * j) * -27.0;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -2e+244:
		tmp = c * b
	elif (c * b) <= 5e+99:
		tmp = (k * j) * -27.0
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -2e+244)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= 5e+99)
		tmp = Float64(Float64(k * j) * -27.0);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -2e+244)
		tmp = c * b;
	elseif ((c * b) <= 5e+99)
		tmp = (k * j) * -27.0;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -2e+244], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 5e+99], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.00000000000000015e244 or 5.00000000000000008e99 < (*.f64 b c)

   1. Initial program 72.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} \]

      2. lower-*.f64 76.3

         \[\leadsto \color{blue}{c \cdot b} \]

   5. Applied rewrites 76.3%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -2.00000000000000015e244 < (*.f64 b c) < 5.00000000000000008e99

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in k around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

      3. lower-*.f64 25.5

         \[\leadsto -27 \cdot \color{blue}{\left(k \cdot j\right)} \]

   5. Applied rewrites 25.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -2 \cdot 10^{+244}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 50.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* a t) -4.0))))
   (if (<= t -1.42e-67) t_1 (if (<= t 1e+82) (fma (* -4.0 i) x (* c b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((a * t) * -4.0));
	double tmp;
	if (t <= -1.42e-67) {
		tmp = t_1;
	} else if (t <= 1e+82) {
		tmp = fma((-4.0 * i), x, (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(a * t) * -4.0))
	tmp = 0.0
	if (t <= -1.42e-67)
		tmp = t_1;
	elseif (t <= 1e+82)
		tmp = fma(Float64(-4.0 * i), x, Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.42e-67], t$95$1, If[LessEqual[t, 1e+82], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.42000000000000004e-67 or 9.9999999999999996e81 < t

   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 z around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      5. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(\color{blue}{\left(a \cdot t + i \cdot x\right) \cdot 4}\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(a \cdot t + i \cdot x\right) \cdot \left(\mathsf{neg}\left(4\right)\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot \color{blue}{-4} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot -4 + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t + i \cdot x\right) \cdot -4 + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(a \cdot t + i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{i \cdot x + a \cdot t}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}, -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right), -4, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, \color{blue}{-27 \cdot \left(j \cdot k\right)}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \color{blue}{\left(k \cdot j\right)}\right)\right) \]

      18. lower-*.f64 68.4

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \color{blue}{\left(k \cdot j\right)}\right)\right) \]

   5. Applied rewrites 68.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\mathsf{fma}\left(i, x, a \cdot t\right), -4, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 50.8%

      \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]

   if -1.42000000000000004e-67 < t < 9.9999999999999996e81

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      6. associate--l+ N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Applied rewrites 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right), x, \mathsf{fma}\left(c, b, -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   6. Taylor expanded in k around 0

      \[\leadsto b \cdot c + \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.8%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, i \cdot -4\right), \color{blue}{x}, c \cdot b\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 59.4%

       \[\leadsto \mathsf{fma}\left(i \cdot -4, x, c \cdot b\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{elif}\;t \leq 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 23.8% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = c * b
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(c * b)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = c * b;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 83.3%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{c \cdot b} \]

   2. lower-*.f64 22.1

      \[\leadsto \color{blue}{c \cdot b} \]

5. Applied rewrites 22.1%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 89.9% 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 2024249 
(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)))