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

Percentage Accurate: 85.6% → 90.2%

Time: 37.9s

Alternatives: 29

Speedup: 0.5×

• 51.0% 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: 85.6% 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: 90.2% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (fma
    (fma x (* 18.0 (* y z)) (* a -4.0))
    t
    (- (* b c) (fma x (* 4.0 i) (* 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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = fma(fma(x, (18.0 * (y * z)), (a * -4.0)), t, ((b * c) - fma(x, (4.0 * i), (27.0 * (j * k)))));
	} else {
		tmp = 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = fma(fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), t, Float64(Float64(b * c) - fma(x, Float64(4.0 * i), Float64(27.0 * Float64(j * k)))));
	else
		tmp = 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.7%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 96.1%

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

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

   1. Initial program 0.0%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 29.0%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 58.1

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

   7. Simplified 58.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 61.3

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

   9. Applied egg-rr 61.3%

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

4. Final simplification 91.9%

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

Alternative 2: 90.2% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (fma
    (* j k)
    -27.0
    (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (fma b c (* -4.0 (* x i)))))
   (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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = fma((j * k), -27.0, fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), fma(b, c, (-4.0 * (x * i)))));
	} else {
		tmp = 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = fma(Float64(j * k), -27.0, fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), fma(b, c, Float64(-4.0 * Float64(x * i)))));
	else
		tmp = 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. metadata-eval N/A

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

      9. associate--l+ N/A

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

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

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

      11. accelerator-lowering-fma.f64 N/A

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

   4. Applied egg-rr 96.1%

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

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

   1. Initial program 0.0%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 29.0%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 58.1

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

   7. Simplified 58.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 61.3

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

   9. Applied egg-rr 61.3%

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

4. Final simplification 91.9%

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

Alternative 3: 37.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -4e+174)
     t_1
     (if (<= t_2 -5e-21)
       (* b c)
       (if (<= t_2 -1e-215)
         (* -4.0 (* t a))
         (if (<= t_2 5e+122) (* b c) t_1))))))

C

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 * k) * -27.0;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+174) {
		tmp = t_1;
	} else if (t_2 <= -5e-21) {
		tmp = b * c;
	} else if (t_2 <= -1e-215) {
		tmp = -4.0 * (t * a);
	} else if (t_2 <= 5e+122) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (j * k) * (-27.0d0)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-4d+174)) then
        tmp = t_1
    else if (t_2 <= (-5d-21)) then
        tmp = b * c
    else if (t_2 <= (-1d-215)) then
        tmp = (-4.0d0) * (t * a)
    else if (t_2 <= 5d+122) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * k) * -27.0;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+174) {
		tmp = t_1;
	} else if (t_2 <= -5e-21) {
		tmp = b * c;
	} else if (t_2 <= -1e-215) {
		tmp = -4.0 * (t * a);
	} else if (t_2 <= 5e+122) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -4e+174:
		tmp = t_1
	elif t_2 <= -5e-21:
		tmp = b * c
	elif t_2 <= -1e-215:
		tmp = -4.0 * (t * a)
	elif t_2 <= 5e+122:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -4e+174)
		tmp = t_1;
	elseif (t_2 <= -5e-21)
		tmp = Float64(b * c);
	elseif (t_2 <= -1e-215)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (t_2 <= 5e+122)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -4e+174)
		tmp = t_1;
	elseif (t_2 <= -5e-21)
		tmp = b * c;
	elseif (t_2 <= -1e-215)
		tmp = -4.0 * (t * a);
	elseif (t_2 <= 5e+122)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+174], t$95$1, If[LessEqual[t$95$2, -5e-21], N[(b * c), $MachinePrecision], If[LessEqual[t$95$2, -1e-215], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+122], N[(b * c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.00000000000000028e174 or 4.99999999999999989e122 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.3%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 N/A

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

      18. *-commutative N/A

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

      19. *-lowering-*.f64 83.5

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

   5. Simplified 83.5%

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

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 61.1

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

   8. Simplified 61.1%

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

   if -4.00000000000000028e174 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999973e-21 or -1.00000000000000004e-215 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e122

   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 b around inf

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

      1. *-lowering-*.f64 32.0

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

   5. Simplified 32.0%

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

   if -4.99999999999999973e-21 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000004e-215

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 40.9

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

   5. Simplified 40.9%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+174}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -0.002:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot 18\right) \cdot z, y, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -0.002)
     (fma j (* k -27.0) (fma -4.0 (* x i) (* b c)))
     (if (<= t_1 2e+84)
       (fma (fma (* (* x 18.0) z) y (* a -4.0)) t (* b c))
       (fma (* t -4.0) a (fma j (* k -27.0) (* b c)))))))

C

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 <= -0.002) {
		tmp = fma(j, (k * -27.0), fma(-4.0, (x * i), (b * c)));
	} else if (t_1 <= 2e+84) {
		tmp = fma(fma(((x * 18.0) * z), y, (a * -4.0)), t, (b * c));
	} else {
		tmp = fma((t * -4.0), a, fma(j, (k * -27.0), (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -0.002)
		tmp = fma(j, Float64(k * -27.0), fma(-4.0, Float64(x * i), Float64(b * c)));
	elseif (t_1 <= 2e+84)
		tmp = fma(fma(Float64(Float64(x * 18.0) * z), y, Float64(a * -4.0)), t, Float64(b * c));
	else
		tmp = fma(Float64(t * -4.0), a, fma(j, Float64(k * -27.0), Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -0.002], N[(j * N[(k * -27.0), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+84], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * a + N[(j * N[(k * -27.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e-3

   1. Initial program 83.8%

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. accelerator-lowering-fma.f64 N/A

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

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

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 83.0

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

   7. Simplified 83.0%

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

   if -2e-3 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000012e84

   1. Initial program 83.4%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 86.6%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 76.0

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

   7. Simplified 76.0%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 76.0

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

   9. Applied egg-rr 76.0%

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

   if 2.00000000000000012e84 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 71.5

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

   5. Simplified 71.5%

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 77.9

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

   7. Applied egg-rr 77.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -0.002:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot 18\right) \cdot z, y, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot z\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right) - t\_2\\ \mathbf{elif}\;x \leq 0.23:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, t\_1, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* y z))) (t_2 (* (* j 27.0) k)))
   (if (<= x -4.3e+99)
     (- (* x (fma 18.0 (* z (* y t)) (* i -4.0))) t_2)
     (if (<= x 0.23)
       (fma b c (fma -4.0 (fma a t (* x i)) (* j (* k -27.0))))
       (if (<= x 2.15e+111)
         (fma (fma x t_1 (* a -4.0)) t (* b c))
         (- (* x (fma -4.0 i (* t t_1))) t_2))))))

C

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 = 18.0 * (y * z);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -4.3e+99) {
		tmp = (x * fma(18.0, (z * (y * t)), (i * -4.0))) - t_2;
	} else if (x <= 0.23) {
		tmp = fma(b, c, fma(-4.0, fma(a, t, (x * i)), (j * (k * -27.0))));
	} else if (x <= 2.15e+111) {
		tmp = fma(fma(x, t_1, (a * -4.0)), t, (b * c));
	} else {
		tmp = (x * fma(-4.0, i, (t * t_1))) - t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(y * z))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -4.3e+99)
		tmp = Float64(Float64(x * fma(18.0, Float64(z * Float64(y * t)), Float64(i * -4.0))) - t_2);
	elseif (x <= 0.23)
		tmp = fma(b, c, fma(-4.0, fma(a, t, Float64(x * i)), Float64(j * Float64(k * -27.0))));
	elseif (x <= 2.15e+111)
		tmp = fma(fma(x, t_1, Float64(a * -4.0)), t, Float64(b * c));
	else
		tmp = Float64(Float64(x * fma(-4.0, i, Float64(t * t_1))) - t_2);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -4.3e+99], N[(N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, 0.23], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+111], N[(N[(x * t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-4.0 * i + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.3000000000000001e99

   1. Initial program 75.7%

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. accelerator-lowering-fma.f64 N/A

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

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

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

   4. Applied egg-rr 75.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 91.5

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

   7. Simplified 91.5%

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

   if -4.3000000000000001e99 < x < 0.23000000000000001

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 N/A

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

      18. *-commutative N/A

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

      19. *-lowering-*.f64 82.7

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

   5. Simplified 82.7%

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

   if 0.23000000000000001 < x < 2.14999999999999997e111

   1. Initial program 76.4%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 88.2

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

   7. Simplified 88.2%

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

   if 2.14999999999999997e111 < x

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 90.6

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

   5. Simplified 90.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 0.23:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot z\right)\\ t_2 := x \cdot \mathsf{fma}\left(-4, i, t \cdot t\_1\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 0.0075:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, t\_1, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* y z)))
        (t_2 (- (* x (fma -4.0 i (* t t_1))) (* (* j 27.0) k))))
   (if (<= x -1.02e+102)
     t_2
     (if (<= x 0.0075)
       (fma b c (fma -4.0 (fma a t (* x i)) (* j (* k -27.0))))
       (if (<= x 1.8e+112) (fma (fma x t_1 (* a -4.0)) t (* b c)) t_2)))))

C

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 = 18.0 * (y * z);
	double t_2 = (x * fma(-4.0, i, (t * t_1))) - ((j * 27.0) * k);
	double tmp;
	if (x <= -1.02e+102) {
		tmp = t_2;
	} else if (x <= 0.0075) {
		tmp = fma(b, c, fma(-4.0, fma(a, t, (x * i)), (j * (k * -27.0))));
	} else if (x <= 1.8e+112) {
		tmp = fma(fma(x, t_1, (a * -4.0)), t, (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(y * z))
	t_2 = Float64(Float64(x * fma(-4.0, i, Float64(t * t_1))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (x <= -1.02e+102)
		tmp = t_2;
	elseif (x <= 0.0075)
		tmp = fma(b, c, fma(-4.0, fma(a, t, Float64(x * i)), Float64(j * Float64(k * -27.0))));
	elseif (x <= 1.8e+112)
		tmp = fma(fma(x, t_1, Float64(a * -4.0)), t, Float64(b * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(-4.0 * i + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+102], t$95$2, If[LessEqual[x, 0.0075], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+112], N[(N[(x * t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.01999999999999999e102 or 1.8e112 < x

   1. Initial program 74.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 90.9

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

   5. Simplified 90.9%

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

   if -1.01999999999999999e102 < x < 0.0074999999999999997

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 N/A

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

      18. *-commutative N/A

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

      19. *-lowering-*.f64 82.7

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

   5. Simplified 82.7%

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

   if 0.0074999999999999997 < x < 1.8e112

   1. Initial program 76.4%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 88.2

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

   7. Simplified 88.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 0.0075:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right) - t\_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z, a \cdot -4\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -1e+123)
     (- (* x (fma 18.0 (* z (* y t)) (* i -4.0))) t_1)
     (if (<= x 6.8e+81)
       (fma t (fma (* (* x 18.0) y) z (* a -4.0)) (fma b c (* j (* k -27.0))))
       (- (* x (fma -4.0 i (* t (* 18.0 (* y z))))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -1e+123) {
		tmp = (x * fma(18.0, (z * (y * t)), (i * -4.0))) - t_1;
	} else if (x <= 6.8e+81) {
		tmp = fma(t, fma(((x * 18.0) * y), z, (a * -4.0)), fma(b, c, (j * (k * -27.0))));
	} else {
		tmp = (x * fma(-4.0, i, (t * (18.0 * (y * z))))) - t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -1e+123)
		tmp = Float64(Float64(x * fma(18.0, Float64(z * Float64(y * t)), Float64(i * -4.0))) - t_1);
	elseif (x <= 6.8e+81)
		tmp = fma(t, fma(Float64(Float64(x * 18.0) * y), z, Float64(a * -4.0)), fma(b, c, Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z))))) - t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[x, -1e+123], N[(N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 6.8e+81], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999978e122

   1. Initial program 74.4%

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. accelerator-lowering-fma.f64 N/A

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

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

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

   4. Applied egg-rr 74.4%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 91.0

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

   7. Simplified 91.0%

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

   if -9.99999999999999978e122 < x < 6.80000000000000005e81

   1. Initial program 90.7%

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

   3. Taylor expanded in i around 0

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

      1. associate--r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 85.1%

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 87.5

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

   7. Applied egg-rr 87.5%

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

   if 6.80000000000000005e81 < x

   1. Initial program 71.3%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 87.5

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

   5. Simplified 87.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z, a \cdot -4\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right) - t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -2.4e+122)
     (- (* x (fma 18.0 (* z (* y t)) (* i -4.0))) t_1)
     (if (<= x 5.2e+112)
       (fma t (fma -4.0 a (* 18.0 (* x (* y z)))) (fma b c (* j (* k -27.0))))
       (- (* x (fma -4.0 i (* t (* 18.0 (* y z))))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -2.4e+122) {
		tmp = (x * fma(18.0, (z * (y * t)), (i * -4.0))) - t_1;
	} else if (x <= 5.2e+112) {
		tmp = fma(t, fma(-4.0, a, (18.0 * (x * (y * z)))), fma(b, c, (j * (k * -27.0))));
	} else {
		tmp = (x * fma(-4.0, i, (t * (18.0 * (y * z))))) - t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -2.4e+122)
		tmp = Float64(Float64(x * fma(18.0, Float64(z * Float64(y * t)), Float64(i * -4.0))) - t_1);
	elseif (x <= 5.2e+112)
		tmp = fma(t, fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))), fma(b, c, Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z))))) - t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[x, -2.4e+122], N[(N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 5.2e+112], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4000000000000002e122

   1. Initial program 74.4%

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. accelerator-lowering-fma.f64 N/A

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

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

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

   4. Applied egg-rr 74.4%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 91.0

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

   7. Simplified 91.0%

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

   if -2.4000000000000002e122 < x < 5.2000000000000001e112

   1. Initial program 89.7%

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

   3. Taylor expanded in i around 0

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

      1. associate--r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 84.8%

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

   if 5.2000000000000001e112 < x

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 90.6

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

   5. Simplified 90.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+202}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+202)
     (fma j (* k -27.0) (* -4.0 (* t a)))
     (if (<= t_1 1e+193)
       (fma b c (* -4.0 (fma a t (* x i))))
       (fma (* x i) -4.0 (* k (* j -27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+202) {
		tmp = fma(j, (k * -27.0), (-4.0 * (t * a)));
	} else if (t_1 <= 1e+193) {
		tmp = fma(b, c, (-4.0 * fma(a, t, (x * i))));
	} else {
		tmp = fma((x * i), -4.0, (k * (j * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+202)
		tmp = fma(j, Float64(k * -27.0), Float64(-4.0 * Float64(t * a)));
	elseif (t_1 <= 1e+193)
		tmp = fma(b, c, Float64(-4.0 * fma(a, t, Float64(x * i))));
	else
		tmp = fma(Float64(x * i), -4.0, Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+202], N[(j * N[(k * -27.0), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+193], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999999e202

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 74.5

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

   5. Simplified 74.5%

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

   6. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 74.9

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

   8. Simplified 74.9%

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

   if -4.9999999999999999e202 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000007e193

   1. Initial program 85.5%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 N/A

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

      18. *-commutative N/A

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

      19. *-lowering-*.f64 71.8

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

   5. Simplified 71.8%

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

   6. Taylor expanded in j around 0

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

      1. *-lowering-*.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 67.1

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

   8. Simplified 67.1%

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

   if 1.00000000000000007e193 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.0%

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

   3. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 81.6

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

   5. Simplified 81.6%

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 N/A

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

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

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

      9. *-lowering-*.f64 N/A

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

      10. metadata-eval 81.6

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

   7. Applied egg-rr 81.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+202}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot z\right)\\ t_2 := x \cdot \mathsf{fma}\left(-4, i, t \cdot t\_1\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 0.022:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, t\_1, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* y z))) (t_2 (* x (fma -4.0 i (* t t_1)))))
   (if (<= x -6e+99)
     t_2
     (if (<= x 0.022)
       (fma (* t -4.0) a (fma j (* k -27.0) (* b c)))
       (if (<= x 1.5e+111) (fma (fma x t_1 (* a -4.0)) t (* b c)) t_2)))))

C

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 = 18.0 * (y * z);
	double t_2 = x * fma(-4.0, i, (t * t_1));
	double tmp;
	if (x <= -6e+99) {
		tmp = t_2;
	} else if (x <= 0.022) {
		tmp = fma((t * -4.0), a, fma(j, (k * -27.0), (b * c)));
	} else if (x <= 1.5e+111) {
		tmp = fma(fma(x, t_1, (a * -4.0)), t, (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(y * z))
	t_2 = Float64(x * fma(-4.0, i, Float64(t * t_1)))
	tmp = 0.0
	if (x <= -6e+99)
		tmp = t_2;
	elseif (x <= 0.022)
		tmp = fma(Float64(t * -4.0), a, fma(j, Float64(k * -27.0), Float64(b * c)));
	elseif (x <= 1.5e+111)
		tmp = fma(fma(x, t_1, Float64(a * -4.0)), t, Float64(b * c));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+99], t$95$2, If[LessEqual[x, 0.022], N[(N[(t * -4.0), $MachinePrecision] * a + N[(j * N[(k * -27.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+111], N[(N[(x * t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.00000000000000029e99 or 1.5e111 < x

   1. Initial program 74.5%

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

   3. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 83.8

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

   5. Simplified 83.8%

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

   if -6.00000000000000029e99 < x < 0.021999999999999999

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. distribute-neg-in N/A

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 74.3

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

   5. Simplified 74.3%

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 77.0

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

   7. Applied egg-rr 77.0%

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

   if 0.021999999999999999 < x < 1.5e111

   1. Initial program 76.4%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 88.2

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

   7. Simplified 88.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.022:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+202}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e+202)
     (* (* j k) -27.0)
     (if (<= t_1 2e+162) (fma -4.0 (* x i) (* b c)) (* k (* j -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e+202) {
		tmp = (j * k) * -27.0;
	} else if (t_1 <= 2e+162) {
		tmp = fma(-4.0, (x * i), (b * c));
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e+202)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (t_1 <= 2e+162)
		tmp = fma(-4.0, Float64(x * i), Float64(b * c));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+202], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+162], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999999e202

   1. Initial program 74.4%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

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

      7. metadata-eval N/A

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

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

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

      9. metadata-eval N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. *-lowering-*.f64 N/A

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

      18. *-commutative N/A

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

      19. *-lowering-*.f64 83.8

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

   5. Simplified 83.8%

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

   6. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 68.5

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

   8. Simplified 68.5%

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

   if -4.9999999999999999e202 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e162

   1. Initial program 85.0%

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. accelerator-lowering-fma.f64 N/A

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

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

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 54.2

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

   7. Simplified 54.2%

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

   8. Taylor expanded in j around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 50.3

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

   10. Simplified 50.3%

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

   if 1.9999999999999999e162 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 88.1%

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

      1. associate--l+ N/A

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

      2. sub-neg N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. accelerator-lowering-fma.f64 N/A

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

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

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

      15. *-lowering-*.f64 N/A

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

      16. metadata-eval N/A

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

   4. Applied egg-rr 85.2%

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

   5. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 63.0

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

   7. Simplified 63.0%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+202}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot 18\right) \cdot z, y, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* x 18.0) z) y (* a -4.0)) t (* b c))))
   (if (<= t -2e+100)
     t_1
     (if (<= t 4.7e+45)
       (fma b c (fma -4.0 (fma a t (* x i)) (* j (* k -27.0))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(fma(((x * 18.0) * z), y, (a * -4.0)), t, (b * c));
	double tmp;
	if (t <= -2e+100) {
		tmp = t_1;
	} else if (t <= 4.7e+45) {
		tmp = fma(b, c, fma(-4.0, fma(a, t, (x * i)), (j * (k * -27.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(x * 18.0) * z), y, Float64(a * -4.0)), t, Float64(b * c))
	tmp = 0.0
	if (t <= -2e+100)
		tmp = t_1;
	elseif (t <= 4.7e+45)
		tmp = fma(b, c, fma(-4.0, fma(a, t, Float64(x * i)), Float64(j * Float64(k * -27.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+100], t$95$1, If[LessEqual[t, 4.7e+45], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000003e100 or 4.70000000000000002e45 < t

   1. Initial program 82.4%

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

      1. associate--l- N/A

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

      2. associate--l+ N/A

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

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

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. associate-*l* N/A

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

      8. associate-*l* N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

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

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

      13. *-lowering-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. --lowering--.f64 N/A

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

      16. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 89.7%

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

   5. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 80.0

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

   7. Simplified 80.0%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 82.8

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

   9. Applied egg-rr 82.8%

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

   if -2.00000000000000003e100 < t < 4.70000000000000002e45

   1. Initial program 85.4%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. distribute-neg-in N/A

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

      5. distribute-lft-out N/A

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

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

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t + i \cdot x, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{\mathsf{fma}\left(a, t, i \cdot x\right)}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      19. *-lowering-*.f64 84.0

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 56.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1e+136)
   (* x (fma -4.0 i (* t (* 18.0 (* y z)))))
   (if (<= y -1.22e-175)
     (fma b c (* -4.0 (fma a t (* x i))))
     (if (<= y 2.3e-85)
       (fma (* x i) -4.0 (* k (* j -27.0)))
       (* t (fma -4.0 a (* z (* 18.0 (* x y)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1e+136) {
		tmp = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	} else if (y <= -1.22e-175) {
		tmp = fma(b, c, (-4.0 * fma(a, t, (x * i))));
	} else if (y <= 2.3e-85) {
		tmp = fma((x * i), -4.0, (k * (j * -27.0)));
	} else {
		tmp = t * fma(-4.0, a, (z * (18.0 * (x * y))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1e+136)
		tmp = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))));
	elseif (y <= -1.22e-175)
		tmp = fma(b, c, Float64(-4.0 * fma(a, t, Float64(x * i))));
	elseif (y <= 2.3e-85)
		tmp = fma(Float64(x * i), -4.0, Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(t * fma(-4.0, a, Float64(z * Float64(18.0 * Float64(x * y)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1e+136], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.22e-175], N[(b * c + N[(-4.0 * N[(a * t + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-85], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * a + N[(z * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.00000000000000006e136

   1. Initial program 76.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      4. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \]

      7. associate-*l* N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      10. *-lowering-*.f64 59.6

          \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\color{blue}{\left(y \cdot z\right)} \cdot 18\right)\right) \]

   5. Simplified 59.6%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right)} \]

   if -1.00000000000000006e136 < y < -1.2200000000000001e-175

   1. Initial program 79.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      5. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(b, c, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t + i \cdot x, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{\mathsf{fma}\left(a, t, i \cdot x\right)}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      19. *-lowering-*.f64 70.8

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\mathsf{fma}\left(a, t, i \cdot x\right)}\right) \]

      3. *-lowering-*.f64 66.3

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(a, t, \color{blue}{i \cdot x}\right)\right) \]

   8. Simplified 66.3%

      \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)}\right) \]

   if -1.2200000000000001e-175 < y < 2.3e-85

   1. Initial program 96.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      3. *-lowering-*.f64 58.9

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot i\right) \cdot -4} + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot i, -4, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot i}, -4, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, \mathsf{neg}\left(\color{blue}{k \cdot \left(j \cdot 27\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, \color{blue}{k \cdot \left(\mathsf{neg}\left(j \cdot 27\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, \color{blue}{k \cdot \left(\mathsf{neg}\left(j \cdot 27\right)\right)}\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, k \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, k \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)}\right) \]

      10. metadata-eval 58.9

          \[\leadsto \mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot \color{blue}{-27}\right)\right) \]

   7. Applied egg-rr 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)} \]

   if 2.3e-85 < y

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot \left(\left(x \cdot 18\right) \cdot y\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \color{blue}{\left(18 \cdot y\right)}\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{t \cdot \left(\mathsf{neg}\left(a \cdot 4\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{\mathsf{fma}\left(t, \mathsf{neg}\left(a \cdot 4\right), b \cdot c - \left(x \cdot 4\right) \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot \color{blue}{-4}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right) \cdot z}\right) \]

      5. *-commutative N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{z \cdot \left(18 \cdot \left(x \cdot y\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)}\right) \]

      8. *-lowering-*.f64 52.3

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, z \cdot \left(18 \cdot \color{blue}{\left(x \cdot y\right)}\right)\right) \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \mathsf{fma}\left(a, t, x \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -4e+174) t_1 (if (<= t_2 5e+122) (* b c) t_1))))

C

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 * k) * -27.0;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+174) {
		tmp = t_1;
	} else if (t_2 <= 5e+122) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (j * k) * (-27.0d0)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-4d+174)) then
        tmp = t_1
    else if (t_2 <= 5d+122) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * k) * -27.0;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+174) {
		tmp = t_1;
	} else if (t_2 <= 5e+122) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * k) * -27.0
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -4e+174:
		tmp = t_1
	elif t_2 <= 5e+122:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -4e+174)
		tmp = t_1;
	elseif (t_2 <= 5e+122)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * k) * -27.0;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -4e+174)
		tmp = t_1;
	elseif (t_2 <= 5e+122)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+174], t$95$1, If[LessEqual[t$95$2, 5e+122], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.00000000000000028e174 or 4.99999999999999989e122 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      5. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(b, c, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t + i \cdot x, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{\mathsf{fma}\left(a, t, i \cdot x\right)}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      19. *-lowering-*.f64 83.5

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-lowering-*.f64 61.1

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

   8. Simplified 61.1%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -4.00000000000000028e174 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e122

   1. Initial program 84.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 28.5

         \[\leadsto \color{blue}{b \cdot c} \]

   5. Simplified 28.5%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+174}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+122}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -2600000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-189}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= c -2600000.0)
     (* b c)
     (if (<= c -1.2e-189)
       (* k (* j -27.0))
       (if (<= c 3.1e-137)
         t_1
         (if (<= c 5.4e+38)
           (* -4.0 (* t a))
           (if (<= c 9e+151) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (c <= -2600000.0) {
		tmp = b * c;
	} else if (c <= -1.2e-189) {
		tmp = k * (j * -27.0);
	} else if (c <= 3.1e-137) {
		tmp = t_1;
	} else if (c <= 5.4e+38) {
		tmp = -4.0 * (t * a);
	} else if (c <= 9e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (-4.0d0) * (x * i)
    if (c <= (-2600000.0d0)) then
        tmp = b * c
    else if (c <= (-1.2d-189)) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 3.1d-137) then
        tmp = t_1
    else if (c <= 5.4d+38) then
        tmp = (-4.0d0) * (t * a)
    else if (c <= 9d+151) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = -4.0 * (x * i);
	double tmp;
	if (c <= -2600000.0) {
		tmp = b * c;
	} else if (c <= -1.2e-189) {
		tmp = k * (j * -27.0);
	} else if (c <= 3.1e-137) {
		tmp = t_1;
	} else if (c <= 5.4e+38) {
		tmp = -4.0 * (t * a);
	} else if (c <= 9e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if c <= -2600000.0:
		tmp = b * c
	elif c <= -1.2e-189:
		tmp = k * (j * -27.0)
	elif c <= 3.1e-137:
		tmp = t_1
	elif c <= 5.4e+38:
		tmp = -4.0 * (t * a)
	elif c <= 9e+151:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (c <= -2600000.0)
		tmp = Float64(b * c);
	elseif (c <= -1.2e-189)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 3.1e-137)
		tmp = t_1;
	elseif (c <= 5.4e+38)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (c <= 9e+151)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (c <= -2600000.0)
		tmp = b * c;
	elseif (c <= -1.2e-189)
		tmp = k * (j * -27.0);
	elseif (c <= 3.1e-137)
		tmp = t_1;
	elseif (c <= 5.4e+38)
		tmp = -4.0 * (t * a);
	elseif (c <= 9e+151)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2600000.0], N[(b * c), $MachinePrecision], If[LessEqual[c, -1.2e-189], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.1e-137], t$95$1, If[LessEqual[c, 5.4e+38], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e+151], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.6e6 or 8.9999999999999997e151 < c

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 50.2

         \[\leadsto \color{blue}{b \cdot c} \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -2.6e6 < c < -1.1999999999999999e-189

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot \left(\left(x \cdot 18\right) \cdot y\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \color{blue}{\left(18 \cdot y\right)}\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{t \cdot \left(\mathsf{neg}\left(a \cdot 4\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{\mathsf{fma}\left(t, \mathsf{neg}\left(a \cdot 4\right), b \cdot c - \left(x \cdot 4\right) \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot \color{blue}{-4}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} \]

      4. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(j \cdot -27\right)} \]

      5. *-lowering-*.f64 37.7

         \[\leadsto k \cdot \color{blue}{\left(j \cdot -27\right)} \]

   7. Simplified 37.7%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   if -1.1999999999999999e-189 < c < 3.09999999999999978e-137 or 5.39999999999999992e38 < c < 8.9999999999999997e151

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

      3. *-lowering-*.f64 38.0

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   5. Simplified 38.0%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]

   if 3.09999999999999978e-137 < c < 5.39999999999999992e38

   1. Initial program 75.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

      2. *-lowering-*.f64 33.7

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

   5. Simplified 33.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2600000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-189}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-137}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+151}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -180000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-192}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= c -180000000.0)
     (* b c)
     (if (<= c -2.7e-192)
       (* (* j k) -27.0)
       (if (<= c 9.8e-138)
         t_1
         (if (<= c 5.8e+38)
           (* -4.0 (* t a))
           (if (<= c 5e+151) t_1 (* b c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (c <= -180000000.0) {
		tmp = b * c;
	} else if (c <= -2.7e-192) {
		tmp = (j * k) * -27.0;
	} else if (c <= 9.8e-138) {
		tmp = t_1;
	} else if (c <= 5.8e+38) {
		tmp = -4.0 * (t * a);
	} else if (c <= 5e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (-4.0d0) * (x * i)
    if (c <= (-180000000.0d0)) then
        tmp = b * c
    else if (c <= (-2.7d-192)) then
        tmp = (j * k) * (-27.0d0)
    else if (c <= 9.8d-138) then
        tmp = t_1
    else if (c <= 5.8d+38) then
        tmp = (-4.0d0) * (t * a)
    else if (c <= 5d+151) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = -4.0 * (x * i);
	double tmp;
	if (c <= -180000000.0) {
		tmp = b * c;
	} else if (c <= -2.7e-192) {
		tmp = (j * k) * -27.0;
	} else if (c <= 9.8e-138) {
		tmp = t_1;
	} else if (c <= 5.8e+38) {
		tmp = -4.0 * (t * a);
	} else if (c <= 5e+151) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if c <= -180000000.0:
		tmp = b * c
	elif c <= -2.7e-192:
		tmp = (j * k) * -27.0
	elif c <= 9.8e-138:
		tmp = t_1
	elif c <= 5.8e+38:
		tmp = -4.0 * (t * a)
	elif c <= 5e+151:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (c <= -180000000.0)
		tmp = Float64(b * c);
	elseif (c <= -2.7e-192)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (c <= 9.8e-138)
		tmp = t_1;
	elseif (c <= 5.8e+38)
		tmp = Float64(-4.0 * Float64(t * a));
	elseif (c <= 5e+151)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (c <= -180000000.0)
		tmp = b * c;
	elseif (c <= -2.7e-192)
		tmp = (j * k) * -27.0;
	elseif (c <= 9.8e-138)
		tmp = t_1;
	elseif (c <= 5.8e+38)
		tmp = -4.0 * (t * a);
	elseif (c <= 5e+151)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -180000000.0], N[(b * c), $MachinePrecision], If[LessEqual[c, -2.7e-192], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[c, 9.8e-138], t$95$1, If[LessEqual[c, 5.8e+38], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e+151], t$95$1, N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.8e8 or 5.0000000000000002e151 < c

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 50.2

         \[\leadsto \color{blue}{b \cdot c} \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.8e8 < c < -2.69999999999999991e-192

   1. Initial program 89.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{neg}\left(\color{blue}{\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + 27 \cdot \left(j \cdot k\right)\right)}\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      5. distribute-lft-out N/A

         \[\leadsto \mathsf{fma}\left(b, c, \left(\mathsf{neg}\left(\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t + i \cdot x, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      11. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{\mathsf{fma}\left(a, t, i \cdot x\right)}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, \color{blue}{x \cdot i}\right), -27 \cdot \left(j \cdot k\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      19. *-lowering-*.f64 87.1

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 87.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \mathsf{fma}\left(a, t, x \cdot i\right), j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

      2. *-lowering-*.f64 36.2

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

   8. Simplified 36.2%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -2.69999999999999991e-192 < c < 9.80000000000000033e-138 or 5.80000000000000013e38 < c < 5.0000000000000002e151

   1. Initial program 86.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

      3. *-lowering-*.f64 39.1

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} \]

   5. Simplified 39.1%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} \]

   if 9.80000000000000033e-138 < c < 5.80000000000000013e38

   1. Initial program 76.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

      2. *-lowering-*.f64 32.6

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

   5. Simplified 32.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -180000000:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-192}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-138}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+151}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2.7e+63)
   (* z (* (* x y) (* 18.0 t)))
   (if (<= y -1.7e-139)
     (fma (* a -4.0) t (* b c))
     (if (<= y 1.22e+40)
       (fma j (* k -27.0) (* -4.0 (* t a)))
       (* (* x y) (* z (* 18.0 t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2.7e+63) {
		tmp = z * ((x * y) * (18.0 * t));
	} else if (y <= -1.7e-139) {
		tmp = fma((a * -4.0), t, (b * c));
	} else if (y <= 1.22e+40) {
		tmp = fma(j, (k * -27.0), (-4.0 * (t * a)));
	} else {
		tmp = (x * y) * (z * (18.0 * t));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2.7e+63)
		tmp = Float64(z * Float64(Float64(x * y) * Float64(18.0 * t)));
	elseif (y <= -1.7e-139)
		tmp = fma(Float64(a * -4.0), t, Float64(b * c));
	elseif (y <= 1.22e+40)
		tmp = fma(j, Float64(k * -27.0), Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(x * y) * Float64(z * Float64(18.0 * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2.7e+63], N[(z * N[(N[(x * y), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-139], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+40], N[(j * N[(k * -27.0), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.70000000000000017e63

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 45.7

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 45.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \cdot z \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 48.8

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 48.8%

      \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

   if -2.70000000000000017e63 < y < -1.69999999999999999e-139

   1. Initial program 79.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, \color{blue}{18 \cdot \left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \color{blue}{\left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot \color{blue}{-4}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

   4. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 73.6

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   7. Simplified 73.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 59.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   10. Simplified 59.5%

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   if -1.69999999999999999e-139 < y < 1.22000000000000004e40

   1. Initial program 90.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 60.0

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(a \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} + -4 \cdot \left(a \cdot t\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + -4 \cdot \left(a \cdot t\right) \]

      3. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + -4 \cdot \left(a \cdot t\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, -4 \cdot \left(a \cdot t\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(a \cdot t\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(a \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right) \]

      8. *-lowering-*.f64 42.7

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]

   8. Simplified 42.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, -4 \cdot \left(a \cdot t\right)\right)} \]

   if 1.22000000000000004e40 < y

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 46.3

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 46.3%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \cdot z \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 51.0

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 51.0%

      \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right) \cdot \left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right) \cdot \left(x \cdot y\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right)} \cdot \left(x \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot \left(x \cdot y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot \left(x \cdot y\right) \]

      7. *-lowering-*.f64 47.8

         \[\leadsto \left(z \cdot \left(t \cdot 18\right)\right) \cdot \color{blue}{\left(x \cdot y\right)} \]

   9. Applied egg-rr 47.8%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 18\right)\right) \cdot \left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* t (* 18.0 (* y z)))))))
   (if (<= x -4.2e+101)
     t_1
     (if (<= x 1.4e+41) (fma (* t -4.0) a (fma j (* k -27.0) (* b c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	double tmp;
	if (x <= -4.2e+101) {
		tmp = t_1;
	} else if (x <= 1.4e+41) {
		tmp = fma((t * -4.0), a, fma(j, (k * -27.0), (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (x <= -4.2e+101)
		tmp = t_1;
	elseif (x <= 1.4e+41)
		tmp = fma(Float64(t * -4.0), a, fma(j, Float64(k * -27.0), Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+101], t$95$1, If[LessEqual[x, 1.4e+41], N[(N[(t * -4.0), $MachinePrecision] * a + N[(j * N[(k * -27.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e101 or 1.4e41 < x

   1. Initial program 73.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      4. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \]

      7. associate-*l* N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      10. *-lowering-*.f64 80.3

          \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\color{blue}{\left(y \cdot z\right)} \cdot 18\right)\right) \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right)} \]

   if -4.2e101 < x < 1.4e41

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 74.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + j \cdot \left(k \cdot -27\right)\right) + b \cdot c} \]

      2. associate-+l+ N/A

         \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + \left(j \cdot \left(k \cdot -27\right) + b \cdot c\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + \left(j \cdot \left(k \cdot -27\right) + b \cdot c\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + \left(j \cdot \left(k \cdot -27\right) + b \cdot c\right) \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(t \cdot -4\right) \cdot a} + \left(j \cdot \left(k \cdot -27\right) + b \cdot c\right) \]

      6. +-commutative N/A

         \[\leadsto \left(t \cdot -4\right) \cdot a + \color{blue}{\left(b \cdot c + j \cdot \left(k \cdot -27\right)\right)} \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot -4, a, b \cdot c + j \cdot \left(k \cdot -27\right)\right)} \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot -4}, a, b \cdot c + j \cdot \left(k \cdot -27\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(t \cdot -4, a, \color{blue}{j \cdot \left(k \cdot -27\right) + b \cdot c}\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot -4, a, \color{blue}{\mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)}\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, b \cdot c\right)\right) \]

      12. *-lowering-*.f64 77.0

          \[\leadsto \mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, \color{blue}{b \cdot c}\right)\right) \]

   7. Applied egg-rr 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(j, k \cdot -27, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, t \cdot \left(a \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* t (* 18.0 (* y z)))))))
   (if (<= x -5.4e+99)
     t_1
     (if (<= x 2.1e+41) (fma b c (fma (* j k) -27.0 (* t (* a -4.0)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	double tmp;
	if (x <= -5.4e+99) {
		tmp = t_1;
	} else if (x <= 2.1e+41) {
		tmp = fma(b, c, fma((j * k), -27.0, (t * (a * -4.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (x <= -5.4e+99)
		tmp = t_1;
	elseif (x <= 2.1e+41)
		tmp = fma(b, c, fma(Float64(j * k), -27.0, Float64(t * Float64(a * -4.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+99], t$95$1, If[LessEqual[x, 2.1e+41], N[(b * c + N[(N[(j * k), $MachinePrecision] * -27.0 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999978e99 or 2.1e41 < x

   1. Initial program 73.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      4. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \]

      7. associate-*l* N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      10. *-lowering-*.f64 80.3

          \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\color{blue}{\left(y \cdot z\right)} \cdot 18\right)\right) \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right)} \]

   if -5.39999999999999978e99 < x < 2.1e41

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 74.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{j \cdot \left(k \cdot -27\right) + -4 \cdot \left(a \cdot t\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(j \cdot k\right) \cdot -27} + -4 \cdot \left(a \cdot t\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(j \cdot k, -27, -4 \cdot \left(a \cdot t\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(\color{blue}{j \cdot k}, -27, -4 \cdot \left(a \cdot t\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, \color{blue}{\left(-4 \cdot a\right) \cdot t}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, \color{blue}{t \cdot \left(-4 \cdot a\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, \color{blue}{t \cdot \left(-4 \cdot a\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, t \cdot \color{blue}{\left(a \cdot -4\right)}\right)\right) \]

      9. *-lowering-*.f64 74.3

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, t \cdot \color{blue}{\left(a \cdot -4\right)}\right)\right) \]

   7. Applied egg-rr 74.3%

      \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(j \cdot k, -27, t \cdot \left(a \cdot -4\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(j \cdot k, -27, t \cdot \left(a \cdot -4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 71.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* t (* 18.0 (* y z)))))))
   (if (<= x -2.7e+102)
     t_1
     (if (<= x 6e+38) (fma b c (fma -4.0 (* t a) (* j (* k -27.0)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	double tmp;
	if (x <= -2.7e+102) {
		tmp = t_1;
	} else if (x <= 6e+38) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (x <= -2.7e+102)
		tmp = t_1;
	elseif (x <= 6e+38)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+102], t$95$1, If[LessEqual[x, 6e+38], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e102 or 6.0000000000000002e38 < x

   1. Initial program 73.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 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. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      3. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      4. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 18}\right) \]

      7. associate-*l* N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right) \]

      10. *-lowering-*.f64 80.3

          \[\leadsto x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\color{blue}{\left(y \cdot z\right)} \cdot 18\right)\right) \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(\left(y \cdot z\right) \cdot 18\right)\right)} \]

   if -2.7000000000000001e102 < x < 6.0000000000000002e38

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 74.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-172}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2e+63)
   (* z (* (* x y) (* 18.0 t)))
   (if (<= y -8.2e-172)
     (fma (* a -4.0) t (* b c))
     (if (<= y 1.9e+46)
       (- (* b c) (* 27.0 (* j k)))
       (* (* x y) (* z (* 18.0 t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2e+63) {
		tmp = z * ((x * y) * (18.0 * t));
	} else if (y <= -8.2e-172) {
		tmp = fma((a * -4.0), t, (b * c));
	} else if (y <= 1.9e+46) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = (x * y) * (z * (18.0 * t));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2e+63)
		tmp = Float64(z * Float64(Float64(x * y) * Float64(18.0 * t)));
	elseif (y <= -8.2e-172)
		tmp = fma(Float64(a * -4.0), t, Float64(b * c));
	elseif (y <= 1.9e+46)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(x * y) * Float64(z * Float64(18.0 * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2e+63], N[(z * N[(N[(x * y), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-172], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+46], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.00000000000000012e63

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 45.7

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 45.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \cdot z \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 48.8

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 48.8%

      \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

   if -2.00000000000000012e63 < y < -8.2e-172

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, \color{blue}{18 \cdot \left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \color{blue}{\left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot \color{blue}{-4}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

   4. Applied egg-rr 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.6

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   7. Simplified 72.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 60.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   10. Simplified 60.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   if -8.2e-172 < y < 1.9e46

   1. Initial program 89.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 42.2

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 42.2%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{b \cdot c - \left(j \cdot 27\right) \cdot k} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative N/A

         \[\leadsto b \cdot c - \color{blue}{k \cdot \left(j \cdot 27\right)} \]

      4. associate-*r* N/A

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      6. *-lowering-*.f64 42.2

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   7. Applied egg-rr 42.2%

      \[\leadsto \color{blue}{b \cdot c - \left(k \cdot j\right) \cdot 27} \]

   if 1.9e46 < y

   1. Initial program 84.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 45.4

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \cdot z \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 50.2

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 50.2%

      \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right) \cdot \left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right) \cdot \left(x \cdot y\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right)} \cdot \left(x \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot \left(x \cdot y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot \left(x \cdot y\right) \]

      7. *-lowering-*.f64 46.9

         \[\leadsto \left(z \cdot \left(t \cdot 18\right)\right) \cdot \color{blue}{\left(x \cdot y\right)} \]

   9. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 18\right)\right) \cdot \left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-172}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-174}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2.7e+63)
   (* 18.0 (* z (* t (* x y))))
   (if (<= y -2.3e-174)
     (fma (* a -4.0) t (* b c))
     (if (<= y 1.3e+43)
       (- (* b c) (* 27.0 (* j k)))
       (* (* x y) (* z (* 18.0 t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2.7e+63) {
		tmp = 18.0 * (z * (t * (x * y)));
	} else if (y <= -2.3e-174) {
		tmp = fma((a * -4.0), t, (b * c));
	} else if (y <= 1.3e+43) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = (x * y) * (z * (18.0 * t));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2.7e+63)
		tmp = Float64(18.0 * Float64(z * Float64(t * Float64(x * y))));
	elseif (y <= -2.3e-174)
		tmp = fma(Float64(a * -4.0), t, Float64(b * c));
	elseif (y <= 1.3e+43)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(x * y) * Float64(z * Float64(18.0 * t)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2.7e+63], N[(18.0 * N[(z * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-174], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+43], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.70000000000000017e63

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 45.7

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 45.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot y\right)\right)} \cdot z\right) \]

      5. *-lowering-*.f64 48.7

         \[\leadsto 18 \cdot \left(\left(t \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z\right) \]

   7. Applied egg-rr 48.7%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)} \]

   if -2.70000000000000017e63 < y < -2.2999999999999999e-174

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, \color{blue}{18 \cdot \left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \color{blue}{\left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot \color{blue}{-4}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

   4. Applied egg-rr 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.6

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   7. Simplified 72.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 60.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   10. Simplified 60.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   if -2.2999999999999999e-174 < y < 1.3000000000000001e43

   1. Initial program 89.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 42.6

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{b \cdot c - \left(j \cdot 27\right) \cdot k} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative N/A

         \[\leadsto b \cdot c - \color{blue}{k \cdot \left(j \cdot 27\right)} \]

      4. associate-*r* N/A

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      6. *-lowering-*.f64 42.6

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   7. Applied egg-rr 42.6%

      \[\leadsto \color{blue}{b \cdot c - \left(k \cdot j\right) \cdot 27} \]

   if 1.3000000000000001e43 < y

   1. Initial program 85.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 46.3

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 46.3%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \cdot z \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 51.0

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 51.0%

      \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right) \cdot \left(x \cdot y\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right) \cdot \left(x \cdot y\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(18 \cdot t\right)\right)} \cdot \left(x \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot \left(x \cdot y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot \left(x \cdot y\right) \]

      7. *-lowering-*.f64 47.8

         \[\leadsto \left(z \cdot \left(t \cdot 18\right)\right) \cdot \color{blue}{\left(x \cdot y\right)} \]

   9. Applied egg-rr 47.8%

      \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot 18\right)\right) \cdot \left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-174}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+43}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 46.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-174}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* z (* t (* x y))))))
   (if (<= y -8.6e+62)
     t_1
     (if (<= y -1.45e-174)
       (fma (* a -4.0) t (* b c))
       (if (<= y 3.25e+40) (- (* b c) (* 27.0 (* j k))) t_1)))))

C

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 = 18.0 * (z * (t * (x * y)));
	double tmp;
	if (y <= -8.6e+62) {
		tmp = t_1;
	} else if (y <= -1.45e-174) {
		tmp = fma((a * -4.0), t, (b * c));
	} else if (y <= 3.25e+40) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(z * Float64(t * Float64(x * y))))
	tmp = 0.0
	if (y <= -8.6e+62)
		tmp = t_1;
	elseif (y <= -1.45e-174)
		tmp = fma(Float64(a * -4.0), t, Float64(b * c));
	elseif (y <= 3.25e+40)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(z * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+62], t$95$1, If[LessEqual[y, -1.45e-174], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.25e+40], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5999999999999994e62 or 3.2500000000000001e40 < y

   1. Initial program 80.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 46.0

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 46.0%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(\color{blue}{\left(t \cdot \left(x \cdot y\right)\right)} \cdot z\right) \]

      5. *-lowering-*.f64 50.0

         \[\leadsto 18 \cdot \left(\left(t \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z\right) \]

   7. Applied egg-rr 50.0%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot z\right)} \]

   if -8.5999999999999994e62 < y < -1.45000000000000005e-174

   1. Initial program 81.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, \color{blue}{18 \cdot \left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \color{blue}{\left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot \color{blue}{-4}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

   4. Applied egg-rr 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.6

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   7. Simplified 72.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 60.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   10. Simplified 60.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   if -1.45000000000000005e-174 < y < 3.2500000000000001e40

   1. Initial program 89.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 42.6

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{b \cdot c - \left(j \cdot 27\right) \cdot k} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative N/A

         \[\leadsto b \cdot c - \color{blue}{k \cdot \left(j \cdot 27\right)} \]

      4. associate-*r* N/A

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right) \cdot 27} \]

      6. *-lowering-*.f64 42.6

         \[\leadsto b \cdot c - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   7. Applied egg-rr 42.6%

      \[\leadsto \color{blue}{b \cdot c - \left(k \cdot j\right) \cdot 27} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+62}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-174}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 51.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 4 \leq 4 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* a -4.0) t (* b c))))
   (if (<= (* a 4.0) -2e+35)
     t_1
     (if (<= (* a 4.0) 4e+110) (fma -4.0 (* x i) (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((a * -4.0), t, (b * c));
	double tmp;
	if ((a * 4.0) <= -2e+35) {
		tmp = t_1;
	} else if ((a * 4.0) <= 4e+110) {
		tmp = fma(-4.0, (x * i), (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(a * -4.0), t, Float64(b * c))
	tmp = 0.0
	if (Float64(a * 4.0) <= -2e+35)
		tmp = t_1;
	elseif (Float64(a * 4.0) <= 4e+110)
		tmp = fma(-4.0, Float64(x * i), Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 4.0), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(a * 4.0), $MachinePrecision], 4e+110], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -1.9999999999999999e35 or 4.0000000000000001e110 < (*.f64 a #s(literal 4 binary64))

   1. Initial program 78.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, \color{blue}{18 \cdot \left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \color{blue}{\left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot \color{blue}{-4}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

   4. Applied egg-rr 84.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 74.3

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   7. Simplified 74.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 62.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   10. Simplified 62.5%

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   if -1.9999999999999999e35 < (*.f64 a #s(literal 4 binary64)) < 4.0000000000000001e110

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot \left(\left(x \cdot 18\right) \cdot y\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \color{blue}{\left(18 \cdot y\right)}\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{t \cdot \left(\mathsf{neg}\left(a \cdot 4\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{\mathsf{fma}\left(t, \mathsf{neg}\left(a \cdot 4\right), b \cdot c - \left(x \cdot 4\right) \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot \color{blue}{-4}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \color{blue}{-27} \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, -4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)}\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right)\right) \]

      12. *-lowering-*.f64 70.6

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right)\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)\right)} \]

   8. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   9. Step-by-step derivation

      1. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right) \]

      3. *-lowering-*.f64 53.2

         \[\leadsto \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right) \]

   10. Simplified 53.2%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{elif}\;a \cdot 4 \leq 4 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 51.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 4 \leq 4 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma b c (* -4.0 (* t a)))))
   (if (<= (* a 4.0) -2e+35)
     t_1
     (if (<= (* a 4.0) 4e+110) (fma -4.0 (* x i) (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(b, c, (-4.0 * (t * a)));
	double tmp;
	if ((a * 4.0) <= -2e+35) {
		tmp = t_1;
	} else if ((a * 4.0) <= 4e+110) {
		tmp = fma(-4.0, (x * i), (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(b, c, Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(a * 4.0) <= -2e+35)
		tmp = t_1;
	elseif (Float64(a * 4.0) <= 4e+110)
		tmp = fma(-4.0, Float64(x * i), Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 4.0), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(a * 4.0), $MachinePrecision], 4e+110], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 4 binary64)) < -1.9999999999999999e35 or 4.0000000000000001e110 < (*.f64 a #s(literal 4 binary64))

   1. Initial program 78.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 68.9

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 68.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right) \]

      4. *-lowering-*.f64 60.3

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]

   8. Simplified 60.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right)\right)} \]

   if -1.9999999999999999e35 < (*.f64 a #s(literal 4 binary64)) < 4.0000000000000001e110

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot \left(\left(x \cdot 18\right) \cdot y\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \color{blue}{\left(18 \cdot y\right)}\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{t \cdot \left(\mathsf{neg}\left(a \cdot 4\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{\mathsf{fma}\left(t, \mathsf{neg}\left(a \cdot 4\right), b \cdot c - \left(x \cdot 4\right) \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot \color{blue}{-4}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \color{blue}{-27} \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, -4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)}\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right)\right) \]

      12. *-lowering-*.f64 70.6

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right)\right) \]

   7. Simplified 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)\right)} \]

   8. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   9. Step-by-step derivation

      1. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right) \]

      3. *-lowering-*.f64 53.2

         \[\leadsto \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right) \]

   10. Simplified 53.2%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 4 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;a \cdot 4 \leq 4 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{if}\;i \leq -2.05 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-208}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;i \leq 0.033:\\ \;\;\;\;\mathsf{fma}\left(c, b, k \cdot \left(j \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -4.0 (* x i) (* b c))))
   (if (<= i -2.05e+26)
     t_1
     (if (<= i -3.5e-208)
       (fma b c (* -4.0 (* t a)))
       (if (<= i 0.033) (fma c b (* k (* j -27.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, (x * i), (b * c));
	double tmp;
	if (i <= -2.05e+26) {
		tmp = t_1;
	} else if (i <= -3.5e-208) {
		tmp = fma(b, c, (-4.0 * (t * a)));
	} else if (i <= 0.033) {
		tmp = fma(c, b, (k * (j * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-4.0, Float64(x * i), Float64(b * c))
	tmp = 0.0
	if (i <= -2.05e+26)
		tmp = t_1;
	elseif (i <= -3.5e-208)
		tmp = fma(b, c, Float64(-4.0 * Float64(t * a)));
	elseif (i <= 0.033)
		tmp = fma(c, b, Float64(k * Float64(j * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.05e+26], t$95$1, If[LessEqual[i, -3.5e-208], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.033], N[(c * b + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.04999999999999992e26 or 0.033000000000000002 < i

   1. Initial program 81.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot \left(\left(x \cdot 18\right) \cdot y\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \color{blue}{\left(18 \cdot y\right)}\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{t \cdot \left(\mathsf{neg}\left(a \cdot 4\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{\mathsf{fma}\left(t, \mathsf{neg}\left(a \cdot 4\right), b \cdot c - \left(x \cdot 4\right) \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot \color{blue}{-4}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \color{blue}{-27} \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, -4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)}\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right)\right) \]

      12. *-lowering-*.f64 72.0

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right)\right) \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)\right)} \]

   8. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   9. Step-by-step derivation

      1. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right) \]

      3. *-lowering-*.f64 64.1

         \[\leadsto \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right) \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]

   if -2.04999999999999992e26 < i < -3.49999999999999991e-208

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 64.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right) \]

      4. *-lowering-*.f64 52.7

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right)\right)} \]

   if -3.49999999999999991e-208 < i < 0.033000000000000002

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 52.5

         \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 52.5%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\color{blue}{k \cdot \left(j \cdot 27\right)}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{k \cdot \left(\mathsf{neg}\left(j \cdot 27\right)\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{k \cdot \left(\mathsf{neg}\left(j \cdot 27\right)\right)}\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(c, b, k \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, k \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)}\right) \]

      9. metadata-eval 52.6

         \[\leadsto \mathsf{fma}\left(c, b, k \cdot \left(j \cdot \color{blue}{-27}\right)\right) \]

   7. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, k \cdot \left(j \cdot -27\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-208}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;i \leq 0.033:\\ \;\;\;\;\mathsf{fma}\left(c, b, k \cdot \left(j \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{if}\;i \leq -9.2 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;i \leq 0.8:\\ \;\;\;\;\mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -4.0 (* x i) (* b c))))
   (if (<= i -9.2e+25)
     t_1
     (if (<= i -2.3e-208)
       (fma b c (* -4.0 (* t a)))
       (if (<= i 0.8) (fma b c (* j (* k -27.0))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, (x * i), (b * c));
	double tmp;
	if (i <= -9.2e+25) {
		tmp = t_1;
	} else if (i <= -2.3e-208) {
		tmp = fma(b, c, (-4.0 * (t * a)));
	} else if (i <= 0.8) {
		tmp = fma(b, c, (j * (k * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-4.0, Float64(x * i), Float64(b * c))
	tmp = 0.0
	if (i <= -9.2e+25)
		tmp = t_1;
	elseif (i <= -2.3e-208)
		tmp = fma(b, c, Float64(-4.0 * Float64(t * a)));
	elseif (i <= 0.8)
		tmp = fma(b, c, Float64(j * Float64(k * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.2e+25], t$95$1, If[LessEqual[i, -2.3e-208], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.8], N[(b * c + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.1999999999999992e25 or 0.80000000000000004 < i

   1. Initial program 81.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. sub-neg N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right) \cdot z} + \left(\left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot y\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot \left(\left(x \cdot 18\right) \cdot y\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)}, z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \color{blue}{\left(18 \cdot y\right)}\right), z, \left(\mathsf{neg}\left(\left(a \cdot 4\right) \cdot t\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(a \cdot 4\right)}\right)\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{t \cdot \left(\mathsf{neg}\left(a \cdot 4\right)\right)} + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \color{blue}{\mathsf{fma}\left(t, \mathsf{neg}\left(a \cdot 4\right), b \cdot c - \left(x \cdot 4\right) \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot \color{blue}{-4}, b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) + \color{blue}{-27} \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, -4 \cdot \left(i \cdot x\right) + b \cdot c\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot -27}, -4 \cdot \left(i \cdot x\right) + b \cdot c\right) \]

      10. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)}\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right)\right) \]

      12. *-lowering-*.f64 72.0

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right)\right) \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)\right)} \]

   8. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   9. Step-by-step derivation

      1. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{i \cdot x}, b \cdot c\right) \]

      3. *-lowering-*.f64 64.1

         \[\leadsto \mathsf{fma}\left(-4, i \cdot x, \color{blue}{b \cdot c}\right) \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, b \cdot c\right)} \]

   if -9.1999999999999992e25 < i < -2.29999999999999997e-208

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 64.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(a \cdot t\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right) \]

      4. *-lowering-*.f64 52.7

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right)\right)} \]

   if -2.29999999999999997e-208 < i < 0.80000000000000004

   1. Initial program 88.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(a \cdot t\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      15. *-lowering-*.f64 65.7

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 65.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot c + -27 \cdot \left(j \cdot k\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -27 \cdot \left(j \cdot k\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(j \cdot k\right) \cdot -27}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{j \cdot \left(k \cdot -27\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, j \cdot \color{blue}{\left(k \cdot -27\right)}\right) \]

      8. *-lowering-*.f64 52.5

         \[\leadsto \mathsf{fma}\left(b, c, j \cdot \color{blue}{\left(k \cdot -27\right)}\right) \]

   8. Simplified 52.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-208}:\\ \;\;\;\;\mathsf{fma}\left(b, c, -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;i \leq 0.8:\\ \;\;\;\;\mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 44.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2.1e+63)
   (* z (* (* x y) (* 18.0 t)))
   (if (<= y -2.3e-135)
     (fma (* a -4.0) t (* b c))
     (fma (* x i) -4.0 (* k (* j -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -2.1e+63) {
		tmp = z * ((x * y) * (18.0 * t));
	} else if (y <= -2.3e-135) {
		tmp = fma((a * -4.0), t, (b * c));
	} else {
		tmp = fma((x * i), -4.0, (k * (j * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2.1e+63)
		tmp = Float64(z * Float64(Float64(x * y) * Float64(18.0 * t)));
	elseif (y <= -2.3e-135)
		tmp = fma(Float64(a * -4.0), t, Float64(b * c));
	else
		tmp = fma(Float64(x * i), -4.0, Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2.1e+63], N[(z * N[(N[(x * y), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-135], N[(N[(a * -4.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000002e63

   1. Initial program 75.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. *-lowering-*.f64 45.7

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 45.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right)} \cdot z \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(18 \cdot t\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 48.8

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 48.8%

      \[\leadsto \color{blue}{\left(\left(18 \cdot t\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

   if -2.1000000000000002e63 < y < -2.2999999999999999e-135

   1. Initial program 77.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + \left(\mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \mathsf{neg}\left(a \cdot 4\right)\right)}, t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, \color{blue}{18 \cdot \left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \color{blue}{\left(y \cdot z\right)}, \mathsf{neg}\left(a \cdot 4\right)\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(4\right)\right)}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot \color{blue}{-4}\right), t, b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

   4. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 74.0

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   7. Simplified 74.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), t, \color{blue}{b \cdot c}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 58.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   10. Simplified 58.9%

       \[\leadsto \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, b \cdot c\right) \]

   if -2.2999999999999999e-135 < y

   1. Initial program 88.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      3. *-lowering-*.f64 47.1

         \[\leadsto -4 \cdot \color{blue}{\left(x \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{-4 \cdot \left(x \cdot i\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot i\right) \cdot -4} + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot i, -4, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{x \cdot i}, -4, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, \mathsf{neg}\left(\color{blue}{k \cdot \left(j \cdot 27\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, \color{blue}{k \cdot \left(\mathsf{neg}\left(j \cdot 27\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, \color{blue}{k \cdot \left(\mathsf{neg}\left(j \cdot 27\right)\right)}\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, k \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)}\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot i, -4, k \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(27\right)\right)\right)}\right) \]

      10. metadata-eval 47.1

          \[\leadsto \mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot \color{blue}{-27}\right)\right) \]

   7. Applied egg-rr 47.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot -4, t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, k \cdot \left(j \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 24.3% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 84.1%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 24.1

      \[\leadsto \color{blue}{b \cdot c} \]

5. Simplified 24.1%

   \[\leadsto \color{blue}{b \cdot c} \]
6. Add Preprocessing

Developer Target 1: 89.6% 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 2024199 
(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)))