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

Percentage Accurate: 85.7% → 92.9%

Time: 14.3s

Alternatives: 20

Speedup: 1.2×

• 49.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% 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: 92.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   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

   4. Applied rewrites 94.2%

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

   if +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))

   1. Initial program 0.0%

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

   4. Applied rewrites 20.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 40.0

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 40.0

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 40.0

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

   6. Applied rewrites 40.0%

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

   7. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. associate-+l+ N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

      13. associate-*r* N/A

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

      14. distribute-rgt-in N/A

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

      15. metadata-eval N/A

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

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

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

   9. Applied rewrites 85.0%

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

4. Final simplification 93.5%

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

Alternative 2: 48.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 (- INFINITY))
     (* (* (* (* y z) x) t) 18.0)
     (if (<= t_1 5e+305)
       (fma (* -27.0 j) k (* (* t a) -4.0))
       (* (* (* (* t y) 18.0) x) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((y * z) * x) * t) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = fma((-27.0 * j), k, ((t * a) * -4.0));
	} else {
		tmp = (((t * y) * 18.0) * x) * z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(y * z) * x) * t) * 18.0);
	elseif (t_1 <= 5e+305)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * x) * z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * x), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 85.3%

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

   4. Applied rewrites 90.8%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 54.3

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

   7. Applied rewrites 54.3%

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

   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)) < 5.00000000000000009e305

   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

   4. Applied rewrites 99.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 94.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 94.7

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 94.7

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

   6. Applied rewrites 94.7%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 74.1

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

   9. Applied rewrites 74.1%

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

   10. Taylor expanded in t around inf

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

   12. Applied rewrites 52.0%

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

   if 5.00000000000000009e305 < (-.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 55.9%

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 41.8

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

   7. Applied rewrites 41.8%

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

   9. Applied rewrites 41.9%

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

   11. Applied rewrites 44.7%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+210} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (or (<= t_1 -1e+210) (not (<= t_1 5e+305)))
     (* x (* (* y 18.0) (* t z)))
     (* (* -27.0 j) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if ((t_1 <= -1e+210) || !(t_1 <= 5e+305)) {
		tmp = x * ((y * 18.0) * (t * z));
	} else {
		tmp = (-27.0 * j) * k;
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if ((t_1 <= (-1d+210)) .or. (.not. (t_1 <= 5d+305))) then
        tmp = x * ((y * 18.0d0) * (t * z))
    else
        tmp = ((-27.0d0) * j) * k
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if ((t_1 <= -1e+210) || !(t_1 <= 5e+305)) {
		tmp = x * ((y * 18.0) * (t * z));
	} else {
		tmp = (-27.0 * j) * k;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if (t_1 <= -1e+210) or not (t_1 <= 5e+305):
		tmp = x * ((y * 18.0) * (t * z))
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if ((t_1 <= -1e+210) || !(t_1 <= 5e+305))
		tmp = Float64(x * Float64(Float64(y * 18.0) * Float64(t * z)));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if ((t_1 <= -1e+210) || ~((t_1 <= 5e+305)))
		tmp = x * ((y * 18.0) * (t * z));
	else
		tmp = (-27.0 * j) * k;
	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[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+210], N[Not[LessEqual[t$95$1, 5e+305]], $MachinePrecision]], N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -9.99999999999999927e209 or 5.00000000000000009e305 < (-.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 73.1%

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

   4. Applied rewrites 79.4%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 41.0

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

   7. Applied rewrites 41.0%

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

   9. Applied rewrites 42.9%

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

   if -9.99999999999999927e209 < (-.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)) < 5.00000000000000009e305

   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 j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 39.9

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

   5. Applied rewrites 39.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -1 \cdot 10^{+210} \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+204}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 -5e+204)
     (* (* (* (* y z) x) t) 18.0)
     (if (<= t_1 5e+305) (* (* -27.0 j) k) (* (* (* (* t y) 18.0) x) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -5e+204) {
		tmp = (((y * z) * x) * t) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (((t * y) * 18.0) * x) * z;
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= (-5d+204)) then
        tmp = (((y * z) * x) * t) * 18.0d0
    else if (t_1 <= 5d+305) then
        tmp = ((-27.0d0) * j) * k
    else
        tmp = (((t * y) * 18.0d0) * x) * z
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -5e+204) {
		tmp = (((y * z) * x) * t) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (((t * y) * 18.0) * x) * z;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -5e+204:
		tmp = (((y * z) * x) * t) * 18.0
	elif t_1 <= 5e+305:
		tmp = (-27.0 * j) * k
	else:
		tmp = (((t * y) * 18.0) * x) * z
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= -5e+204)
		tmp = Float64(Float64(Float64(Float64(y * z) * x) * t) * 18.0);
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(-27.0 * j) * k);
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * x) * z);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -5e+204)
		tmp = (((y * z) * x) * t) * 18.0;
	elseif (t_1 <= 5e+305)
		tmp = (-27.0 * j) * k;
	else
		tmp = (((t * y) * 18.0) * x) * z;
	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[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+204], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * x), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -5.00000000000000008e204

   1. Initial program 89.4%

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 39.7

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

   7. Applied rewrites 39.7%

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

   if -5.00000000000000008e204 < (-.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)) < 5.00000000000000009e305

   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 j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 40.0

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

   5. Applied rewrites 40.0%

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

   if 5.00000000000000009e305 < (-.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 55.9%

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 41.8

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

   7. Applied rewrites 41.8%

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

   9. Applied rewrites 41.9%

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

   11. Applied rewrites 44.7%

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

Alternative 5: 39.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+210}:\\ \;\;\;\;\left(y \cdot \left(\left(z \cdot x\right) \cdot t\right)\right) \cdot 18\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 -1e+210)
     (* (* y (* (* z x) t)) 18.0)
     (if (<= t_1 5e+305) (* (* -27.0 j) k) (* (* (* (* t y) 18.0) x) z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -1e+210) {
		tmp = (y * ((z * x) * t)) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (((t * y) * 18.0) * x) * z;
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= (-1d+210)) then
        tmp = (y * ((z * x) * t)) * 18.0d0
    else if (t_1 <= 5d+305) then
        tmp = ((-27.0d0) * j) * k
    else
        tmp = (((t * y) * 18.0d0) * x) * z
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -1e+210) {
		tmp = (y * ((z * x) * t)) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (((t * y) * 18.0) * x) * z;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -1e+210:
		tmp = (y * ((z * x) * t)) * 18.0
	elif t_1 <= 5e+305:
		tmp = (-27.0 * j) * k
	else:
		tmp = (((t * y) * 18.0) * x) * z
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= -1e+210)
		tmp = Float64(Float64(y * Float64(Float64(z * x) * t)) * 18.0);
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(-27.0 * j) * k);
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * x) * z);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -1e+210)
		tmp = (y * ((z * x) * t)) * 18.0;
	elseif (t_1 <= 5e+305)
		tmp = (-27.0 * j) * k;
	else
		tmp = (((t * y) * 18.0) * x) * z;
	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[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+210], N[(N[(y * N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * x), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -9.99999999999999927e209

   1. Initial program 89.2%

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 40.3

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

   7. Applied rewrites 40.3%

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

   9. Applied rewrites 41.2%

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

   if -9.99999999999999927e209 < (-.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)) < 5.00000000000000009e305

   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 j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 39.9

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

   5. Applied rewrites 39.9%

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

   if 5.00000000000000009e305 < (-.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 55.9%

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 41.8

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

   7. Applied rewrites 41.8%

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

   9. Applied rewrites 41.9%

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

   11. Applied rewrites 44.7%

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

Alternative 6: 38.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+210}:\\ \;\;\;\;\left(y \cdot \left(\left(z \cdot x\right) \cdot t\right)\right) \cdot 18\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 -1e+210)
     (* (* y (* (* z x) t)) 18.0)
     (if (<= t_1 5e+305) (* (* -27.0 j) k) (* x (* (* y 18.0) (* t z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -1e+210) {
		tmp = (y * ((z * x) * t)) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = x * ((y * 18.0) * (t * z));
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= (-1d+210)) then
        tmp = (y * ((z * x) * t)) * 18.0d0
    else if (t_1 <= 5d+305) then
        tmp = ((-27.0d0) * j) * k
    else
        tmp = x * ((y * 18.0d0) * (t * z))
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -1e+210) {
		tmp = (y * ((z * x) * t)) * 18.0;
	} else if (t_1 <= 5e+305) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = x * ((y * 18.0) * (t * z));
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -1e+210:
		tmp = (y * ((z * x) * t)) * 18.0
	elif t_1 <= 5e+305:
		tmp = (-27.0 * j) * k
	else:
		tmp = x * ((y * 18.0) * (t * z))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= -1e+210)
		tmp = Float64(Float64(y * Float64(Float64(z * x) * t)) * 18.0);
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(-27.0 * j) * k);
	else
		tmp = Float64(x * Float64(Float64(y * 18.0) * Float64(t * z)));
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -1e+210)
		tmp = (y * ((z * x) * t)) * 18.0;
	elseif (t_1 <= 5e+305)
		tmp = (-27.0 * j) * k;
	else
		tmp = x * ((y * 18.0) * (t * z));
	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[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+210], N[(N[(y * N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -9.99999999999999927e209

   1. Initial program 89.2%

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 40.3

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

   7. Applied rewrites 40.3%

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

   9. Applied rewrites 41.2%

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

   if -9.99999999999999927e209 < (-.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)) < 5.00000000000000009e305

   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 j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 39.9

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

   5. Applied rewrites 39.9%

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

   if 5.00000000000000009e305 < (-.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 55.9%

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

   4. Applied rewrites 64.6%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 41.8

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

   7. Applied rewrites 41.8%

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

   9. Applied rewrites 47.3%

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

Alternative 7: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(y \cdot x, z \cdot 18, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, -4 \cdot i\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1e+48)
   (fma (* -27.0 j) k (fma (fma (* y x) (* z 18.0) (* -4.0 a)) t (* b c)))
   (if (<= (* b c) 4e+125)
     (fma
      (* -27.0 j)
      k
      (fma (* -4.0 t) a (* (fma (* (* y z) t) 18.0 (* -4.0 i)) x)))
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e+48) {
		tmp = fma((-27.0 * j), k, fma(fma((y * x), (z * 18.0), (-4.0 * a)), t, (b * c)));
	} else if ((b * c) <= 4e+125) {
		tmp = fma((-27.0 * j), k, fma((-4.0 * t), a, (fma(((y * z) * t), 18.0, (-4.0 * i)) * x)));
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1e+48)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(Float64(y * x), Float64(z * 18.0), Float64(-4.0 * a)), t, Float64(b * c)));
	elseif (Float64(b * c) <= 4e+125)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * t), a, Float64(fma(Float64(Float64(y * z) * t), 18.0, Float64(-4.0 * i)) * x)));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1e+48], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(y * x), $MachinePrecision] * N[(z * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+125], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.00000000000000004e48

   1. Initial program 78.6%

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

   4. Applied rewrites 85.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 87.4

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 87.4

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 87.4

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

   6. Applied rewrites 87.4%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 85.7

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

   9. Applied rewrites 85.7%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-*l* N/A

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

       6. associate-*r* N/A

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

       7. lower-fma.f64 N/A

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

       8. lower-*.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 84.0

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

       11. lift-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 84.0

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

   11. Applied rewrites 84.0%

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

   if -1.00000000000000004e48 < (*.f64 b c) < 3.9999999999999997e125

   1. Initial program 87.6%

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

   4. Applied rewrites 90.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 90.2

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 90.2

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 90.2

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

   6. Applied rewrites 90.2%

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

   7. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. associate-+l+ N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. associate-*r* N/A

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

      13. associate-*r* N/A

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

      14. distribute-rgt-in N/A

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

      15. metadata-eval N/A

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

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

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

   9. Applied rewrites 90.9%

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

   if 3.9999999999999997e125 < (*.f64 b c)

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 93.8

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

   5. Applied rewrites 93.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(y \cdot x, z \cdot 18, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot t, a, \mathsf{fma}\left(\left(y \cdot z\right) \cdot t, 18, -4 \cdot i\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-10} \lor \neg \left(t \leq 4.2 \cdot 10^{-32}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -4.5e-10) (not (<= t 4.2e-32)))
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -4.5e-10) || !(t <= 4.2e-32)) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -4.5e-10) || !(t <= 4.2e-32))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -4.5e-10], N[Not[LessEqual[t, 4.2e-32]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e-10 or 4.1999999999999998e-32 < t

   1. Initial program 81.8%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 89.1%

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

   if -4.5e-10 < t < 4.1999999999999998e-32

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-10} \lor \neg \left(t \leq 4.2 \cdot 10^{-32}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot 18\right) \cdot z, y, a \cdot -4\right), t, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4.5e-10)
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (if (<= t 4.2e-32)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (fma (* -27.0 j) k (fma (fma (* (* x 18.0) z) y (* a -4.0)) t (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4.5e-10) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else if (t <= 4.2e-32) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(((x * 18.0) * z), y, (a * -4.0)), t, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4.5e-10)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	elseif (t <= 4.2e-32)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(Float64(Float64(x * 18.0) * z), y, Float64(a * -4.0)), t, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4.5e-10], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-32], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5e-10

   1. Initial program 71.8%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 83.8%

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

   if -4.5e-10 < t < 4.1999999999999998e-32

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   if 4.1999999999999998e-32 < t

   1. Initial program 89.2%

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

   4. Applied rewrites 95.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 97.2

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 97.2

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 97.2

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

   6. Applied rewrites 97.2%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 94.4

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

   9. Applied rewrites 94.4%

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

Alternative 10: 86.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(y \cdot x, z \cdot 18, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4.5e-10)
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (if (<= t 6.6e-34)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (fma (* -27.0 j) k (fma (fma (* y x) (* z 18.0) (* -4.0 a)) t (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4.5e-10) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else if (t <= 6.6e-34) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma(fma((y * x), (z * 18.0), (-4.0 * a)), t, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4.5e-10)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	elseif (t <= 6.6e-34)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(Float64(y * x), Float64(z * 18.0), Float64(-4.0 * a)), t, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4.5e-10], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-34], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(y * x), $MachinePrecision] * N[(z * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5e-10

   1. Initial program 71.8%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 83.8%

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

   if -4.5e-10 < t < 6.59999999999999965e-34

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   if 6.59999999999999965e-34 < t

   1. Initial program 89.2%

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

   4. Applied rewrites 95.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 97.2

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 97.2

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 97.2

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

   6. Applied rewrites 97.2%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 94.4

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

   9. Applied rewrites 94.4%

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

       1. lift-fma.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. associate-*l* N/A

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

       6. associate-*r* N/A

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

       7. lower-fma.f64 N/A

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

       8. lower-*.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 94.2

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

       11. lift-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 94.2

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

   11. Applied rewrites 94.2%

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

Alternative 11: 86.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -4.5e-10)
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (if (<= t 6.6e-34)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (fma (* -27.0 j) k (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -4.5e-10) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else if (t <= 6.6e-34) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -4.5e-10)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	elseif (t <= 6.6e-34)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -4.5e-10], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-34], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5e-10

   1. Initial program 71.8%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 83.8%

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

   if -4.5e-10 < t < 6.59999999999999965e-34

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   if 6.59999999999999965e-34 < t

   1. Initial program 89.2%

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

   4. Applied rewrites 95.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 94.2

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

   7. Applied rewrites 94.2%

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

Alternative 12: 80.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot z, t \cdot y, i \cdot -4\right) \cdot x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

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 -3.6e+183)
   (* (fma (* 18.0 z) (* t y) (* i -4.0)) x)
   (if (<= x 1.35e+165)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (* (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 <= -3.6e+183) {
		tmp = fma((18.0 * z), (t * y), (i * -4.0)) * x;
	} else if (x <= 1.35e+165) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} 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 <= -3.6e+183)
		tmp = Float64(fma(Float64(18.0 * z), Float64(t * y), Float64(i * -4.0)) * x);
	elseif (x <= 1.35e+165)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	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, -3.6e+183], N[(N[(N[(18.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.35e+165], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-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 < -3.60000000000000023e183

   1. Initial program 60.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 87.5

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

   5. Applied rewrites 87.5%

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

   7. Applied rewrites 87.5%

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

   if -3.60000000000000023e183 < x < 1.35e165

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 87.3

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

   5. Applied rewrites 87.3%

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

   if 1.35e165 < x

   1. Initial program 61.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 69.9

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

   5. Applied rewrites 69.9%

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

Alternative 13: 79.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.45 \cdot 10^{+145}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot 18, t, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 1.45e+145)
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
   (fma (* -27.0 j) k (fma (* (* (* y z) x) 18.0) t (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= 1.45e+145) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma((((y * z) * x) * 18.0), t, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 1.45e+145)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(Float64(Float64(y * z) * x) * 18.0), t, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 1.45e+145], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.45e145

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 82.7

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

   5. Applied rewrites 82.7%

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

   if 1.45e145 < z

   1. Initial program 80.7%

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

   4. Applied rewrites 91.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 78.2

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 78.2

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 78.2

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

   6. Applied rewrites 78.2%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 78.2

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

   9. Applied rewrites 78.2%

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

   10. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lower-*.f64 80.9

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

   12. Applied rewrites 80.9%

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

Alternative 14: 35.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+93} \lor \neg \left(t\_1 \leq 4000000\right):\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+93) (not (<= t_1 4000000.0)))
     (* (* -27.0 j) k)
     (* (* -4.0 x) i))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+93) || !(t_1 <= 4000000.0)) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (-4.0 * x) * i;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+93)) .or. (.not. (t_1 <= 4000000.0d0))) then
        tmp = ((-27.0d0) * j) * k
    else
        tmp = ((-4.0d0) * x) * i
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+93) || !(t_1 <= 4000000.0)) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (-4.0 * x) * i;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+93) or not (t_1 <= 4000000.0):
		tmp = (-27.0 * j) * k
	else:
		tmp = (-4.0 * x) * i
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+93) || !(t_1 <= 4000000.0))
		tmp = Float64(Float64(-27.0 * j) * k);
	else
		tmp = Float64(Float64(-4.0 * x) * i);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+93) || ~((t_1 <= 4000000.0)))
		tmp = (-27.0 * j) * k;
	else
		tmp = (-4.0 * x) * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+93], N[Not[LessEqual[t$95$1, 4000000.0]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e93 or 4e6 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 81.9%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 45.2

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

   5. Applied rewrites 45.2%

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

   if -2.00000000000000009e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4e6

   1. Initial program 87.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 25.5

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

   5. Applied rewrites 25.5%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+93} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 4000000\right):\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+93}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;t\_1 \leq 4000000:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+93)
     (* (* k j) -27.0)
     (if (<= t_1 4000000.0) (* (* -4.0 x) i) (* (* -27.0 j) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = (k * j) * -27.0;
	} else if (t_1 <= 4000000.0) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+93)) then
        tmp = (k * j) * (-27.0d0)
    else if (t_1 <= 4000000.0d0) then
        tmp = ((-4.0d0) * x) * i
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+93) {
		tmp = (k * j) * -27.0;
	} else if (t_1 <= 4000000.0) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+93:
		tmp = (k * j) * -27.0
	elif t_1 <= 4000000.0:
		tmp = (-4.0 * x) * i
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+93)
		tmp = Float64(Float64(k * j) * -27.0);
	elseif (t_1 <= 4000000.0)
		tmp = Float64(Float64(-4.0 * x) * i);
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+93)
		tmp = (k * j) * -27.0;
	elseif (t_1 <= 4000000.0)
		tmp = (-4.0 * x) * i;
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+93], N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t$95$1, 4000000.0], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e93

   1. Initial program 71.4%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 48.5

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

   5. Applied rewrites 48.5%

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

   7. Applied rewrites 48.5%

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

   if -2.00000000000000009e93 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4e6

   1. Initial program 87.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 25.5

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

   5. Applied rewrites 25.5%

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

   if 4e6 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 89.8%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 42.6

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

   5. Applied rewrites 42.6%

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

Alternative 16: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+95} \lor \neg \left(x \leq 6 \cdot 10^{+186}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -1.5e+95) (not (<= x 6e+186)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* -27.0 j) k (fma (* t a) -4.0 (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.5e+95) || !(x <= 6e+186)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((-27.0 * j), k, fma((t * a), -4.0, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.5e+95) || !(x <= 6e+186))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(t * a), -4.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.5e+95], N[Not[LessEqual[x, 6e+186]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999996e95 or 5.99999999999999964e186 < x

   1. Initial program 68.5%

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -1.49999999999999996e95 < x < 5.99999999999999964e186

   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

   4. Applied rewrites 93.3%

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

   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

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 79.3

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

   7. Applied rewrites 79.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+95} \lor \neg \left(x \leq 6 \cdot 10^{+186}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+44} \lor \neg \left(x \leq 1.36 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -5.8e+44) (not (<= x 1.36e-46)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* -27.0 j) k (* (* t a) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -5.8e+44) || !(x <= 1.36e-46)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((-27.0 * j), k, ((t * a) * -4.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -5.8e+44) || !(x <= 1.36e-46))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(t * a) * -4.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -5.8e+44], N[Not[LessEqual[x, 1.36e-46]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000004e44 or 1.3600000000000001e-46 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 61.4

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

   5. Applied rewrites 61.4%

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

   if -5.8000000000000004e44 < x < 1.3600000000000001e-46

   1. Initial program 98.2%

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

   4. Applied rewrites 98.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 98.2

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 98.2

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 98.2

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

   6. Applied rewrites 98.2%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 85.6

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

   9. Applied rewrites 85.6%

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

   10. Taylor expanded in t around inf

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

   12. Applied rewrites 59.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+44} \lor \neg \left(x \leq 1.36 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot z, t \cdot y, i \cdot -4\right) \cdot x\\ \end{array} \end{array} \]

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 -5.8e+44)
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (if (<= x 3.85e-28)
     (fma (* -27.0 j) k (* (* t a) -4.0))
     (* (fma (* 18.0 z) (* t y) (* 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 <= -5.8e+44) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else if (x <= 3.85e-28) {
		tmp = fma((-27.0 * j), k, ((t * a) * -4.0));
	} else {
		tmp = fma((18.0 * z), (t * y), (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 <= -5.8e+44)
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	elseif (x <= 3.85e-28)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(t * a) * -4.0));
	else
		tmp = Float64(fma(Float64(18.0 * z), Float64(t * y), 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, -5.8e+44], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 3.85e-28], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * z), $MachinePrecision] * N[(t * y), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8000000000000004e44

   1. Initial program 70.9%

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -5.8000000000000004e44 < x < 3.85e-28

   1. Initial program 98.3%

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

   4. Applied rewrites 98.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 98.3

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 98.3

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 98.3

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

   6. Applied rewrites 98.3%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 84.5

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

   9. Applied rewrites 84.5%

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

   10. Taylor expanded in t around inf

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

   12. Applied rewrites 59.2%

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

   if 3.85e-28 < x

   1. Initial program 74.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 49.3

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

   5. Applied rewrites 49.3%

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

   7. Applied rewrites 49.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot z, t \cdot y, i \cdot -4\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+51}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2.3e-10)
   (* x (* (* y z) (* t 18.0)))
   (if (<= t 1.15e+51)
     (- (* (* i x) -4.0) (* (* j 27.0) k))
     (fma (* -27.0 j) k (* (* t a) -4.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2.3e-10) {
		tmp = x * ((y * z) * (t * 18.0));
	} else if (t <= 1.15e+51) {
		tmp = ((i * x) * -4.0) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, ((t * a) * -4.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -2.3e-10)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)));
	elseif (t <= 1.15e+51)
		tmp = Float64(Float64(Float64(i * x) * -4.0) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(t * a) * -4.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -2.3e-10], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+51], N[(N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.30000000000000007e-10

   1. Initial program 72.3%

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   9. Applied rewrites 49.4%

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

   if -2.30000000000000007e-10 < t < 1.15000000000000003e51

   1. Initial program 88.8%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 86.7

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 51.3%

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

   if 1.15000000000000003e51 < t

   1. Initial program 88.0%

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

   4. Applied rewrites 94.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 96.5

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 96.5

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 96.5

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

   6. Applied rewrites 96.5%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 73.9

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

   9. Applied rewrites 73.9%

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

   10. Taylor expanded in t around inf

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

   12. Applied rewrites 59.4%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+51}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \left(-27 \cdot j\right) \cdot k \end{array} \]

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 (* (* -27.0 j) k))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (-27.0 * j) * k;
}

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 = ((-27.0d0) * j) * k
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 (-27.0 * j) * k;
}

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 (-27.0 * j) * k

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(-27.0 * j) * k)
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 = (-27.0 * j) * k;
end

Wolfram

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

Derivation

1. Initial program 84.9%

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

3. Taylor expanded in j around inf

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

   1. associate-*r* N/A

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

   2. lower-*.f64 N/A

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

   3. lower-*.f64 22.3

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

5. Applied rewrites 22.3%

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

Developer Target 1: 89.8% 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 2024337 
(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)))