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

Percentage Accurate: 85.6% → 89.5%

Time: 36.1s

Alternatives: 27

Speedup: 1.1×

• 50.5% 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: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-167}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.35e-167)
   (fma
    c
    b
    (-
     (* t (fma x (* 18.0 (* y z)) (* a -4.0)))
     (fma x (* 4.0 i) (* 27.0 (* j k)))))
   (if (<= x 8.2e-85)
     (-
      (fma
       (* t (* x (* 18.0 y)))
       z
       (fma t (* a -4.0) (fma b c (* -4.0 (* x i)))))
      (* k (* 27.0 j)))
     (fma x (fma (* y z) (* t 18.0) (* -4.0 i)) (fma k (* j -27.0) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.35e-167) {
		tmp = fma(c, b, ((t * fma(x, (18.0 * (y * z)), (a * -4.0))) - fma(x, (4.0 * i), (27.0 * (j * k)))));
	} else if (x <= 8.2e-85) {
		tmp = fma((t * (x * (18.0 * y))), z, fma(t, (a * -4.0), fma(b, c, (-4.0 * (x * i))))) - (k * (27.0 * j));
	} else {
		tmp = fma(x, fma((y * z), (t * 18.0), (-4.0 * i)), fma(k, (j * -27.0), (c * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.35e-167)
		tmp = fma(c, b, Float64(Float64(t * fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0))) - fma(x, Float64(4.0 * i), Float64(27.0 * Float64(j * k)))));
	elseif (x <= 8.2e-85)
		tmp = Float64(fma(Float64(t * Float64(x * Float64(18.0 * y))), z, fma(t, Float64(a * -4.0), fma(b, c, Float64(-4.0 * Float64(x * i))))) - Float64(k * Float64(27.0 * j)));
	else
		tmp = fma(x, fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)), fma(k, Float64(j * -27.0), Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.35e-167], N[(c * b + N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-85], N[(N[(N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + N[(t * N[(a * -4.0), $MachinePrecision] + N[(b * c + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e-167

   1. Initial program 81.4%

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

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 92.2%

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

   if -1.35e-167 < x < 8.19999999999999987e-85

   1. Initial program 97.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 97.3%

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

   if 8.19999999999999987e-85 < x

   1. Initial program 75.9%

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

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 82.9%

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

   5. Taylor expanded in a around 0

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

   7. Simplified 90.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-167}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right), z, \mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.9% accurate, 0.5× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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 94.4%

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

   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. Taylor expanded in t around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 60.5

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

   5. Simplified 60.5%

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

4. Final simplification 90.4%

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

Alternative 3: 54.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \end{array} \end{array} \]

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 (* k (* 27.0 j))))
   (if (<= t_1 -1e+136)
     (fma (* k -27.0) j (* c b))
     (if (<= t_1 -2e+35)
       (* y (* z (* x (* t 18.0))))
       (if (<= t_1 2e+87)
         (fma t (* a -4.0) (* c b))
         (fma (* x i) -4.0 (* (* j k) -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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e+136) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t_1 <= -2e+35) {
		tmp = y * (z * (x * (t * 18.0)));
	} else if (t_1 <= 2e+87) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else {
		tmp = fma((x * i), -4.0, ((j * k) * -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(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e+136)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t_1 <= -2e+35)
		tmp = Float64(y * Float64(z * Float64(x * Float64(t * 18.0))));
	elseif (t_1 <= 2e+87)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	else
		tmp = fma(Float64(x * i), -4.0, Float64(Float64(j * k) * -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[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+136], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+35], N[(y * N[(z * N[(x * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+87], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e136

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 72.9

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

   5. Simplified 72.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.1

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

   8. Simplified 73.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.1

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

   10. Applied egg-rr 73.1%

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

   if -1.00000000000000006e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999999e35

   1. Initial program 83.7%

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

   3. Taylor expanded in 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 44.7

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

   5. Simplified 44.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 48.5

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

   7. Applied egg-rr 48.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 48.8

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

   9. Applied egg-rr 48.8%

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

   if -1.9999999999999999e35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e87

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0

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

      1. 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 60.6

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

   5. Simplified 60.6%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 56.2

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

   8. Simplified 56.2%

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

   if 1.9999999999999999e87 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.8%

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

   3. Taylor expanded in i around 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 70.2

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

   5. Simplified 70.2%

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

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

      6. associate-*l* N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 70.1

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

   7. Applied egg-rr 70.1%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 2 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, t \cdot \left(a \cdot -4\right)\right)\\ \end{array} \end{array} \]

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 (* k (* 27.0 j))))
   (if (<= t_1 -1e+136)
     (fma (* k -27.0) j (* c b))
     (if (<= t_1 -2e+35)
       (* y (* z (* x (* t 18.0))))
       (if (<= t_1 5e+128)
         (fma t (* a -4.0) (* c b))
         (fma j (* k -27.0) (* t (* a -4.0))))))))

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 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e+136) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t_1 <= -2e+35) {
		tmp = y * (z * (x * (t * 18.0)));
	} else if (t_1 <= 5e+128) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else {
		tmp = fma(j, (k * -27.0), (t * (a * -4.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e+136)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t_1 <= -2e+35)
		tmp = Float64(y * Float64(z * Float64(x * Float64(t * 18.0))));
	elseif (t_1 <= 5e+128)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	else
		tmp = fma(j, Float64(k * -27.0), Float64(t * Float64(a * -4.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+136], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+35], N[(y * N[(z * N[(x * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+128], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e136

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 72.9

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

   5. Simplified 72.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.1

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

   8. Simplified 73.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.1

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

   10. Applied egg-rr 73.1%

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

   if -1.00000000000000006e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999999e35

   1. Initial program 83.7%

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

   3. Taylor expanded in 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 44.7

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

   5. Simplified 44.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 48.5

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

   7. Applied egg-rr 48.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 48.8

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

   9. Applied egg-rr 48.8%

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

   if -1.9999999999999999e35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5e128

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

      1. 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 60.3

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

   5. Simplified 60.3%

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

   6. 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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 55.5

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

   8. Simplified 55.5%

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

   if 5e128 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0

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

      1. 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 76.0

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

   5. Simplified 76.0%

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

   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. associate-*r* N/A

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

      8. *-commutative N/A

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

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

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

      10. *-lowering-*.f64 72.8

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

   8. Simplified 72.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 5 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, t \cdot \left(a \cdot -4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* 27.0 j))))
   (if (<= t_1 -1e+136)
     (fma (* k -27.0) j (* c b))
     (if (<= t_1 -2e+35)
       (* y (* z (* x (* t 18.0))))
       (if (<= t_1 4e+79)
         (fma t (* a -4.0) (* c b))
         (fma k (* j -27.0) (* c b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e+136) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t_1 <= -2e+35) {
		tmp = y * (z * (x * (t * 18.0)));
	} else if (t_1 <= 4e+79) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else {
		tmp = fma(k, (j * -27.0), (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e+136)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t_1 <= -2e+35)
		tmp = Float64(y * Float64(z * Float64(x * Float64(t * 18.0))));
	elseif (t_1 <= 4e+79)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	else
		tmp = fma(k, Float64(j * -27.0), Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+136], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+35], N[(y * N[(z * N[(x * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+79], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e136

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 72.9

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

   5. Simplified 72.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.1

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

   8. Simplified 73.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.1

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

   10. Applied egg-rr 73.1%

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

   if -1.00000000000000006e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999999e35

   1. Initial program 83.7%

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

   3. Taylor expanded in 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 44.7

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

   5. Simplified 44.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 48.5

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

   7. Applied egg-rr 48.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. *-lowering-*.f64 48.8

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

   9. Applied egg-rr 48.8%

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

   if -1.9999999999999999e35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999987e79

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

      1. 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 59.7

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

   5. Simplified 59.7%

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

   6. Taylor expanded in j around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 55.9

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

   8. Simplified 55.9%

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

   if 3.99999999999999987e79 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.9%

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

   3. Taylor expanded in 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 75.4

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

   5. Simplified 75.4%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 61.8

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

   8. Simplified 61.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+35}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* 27.0 j))))
   (if (<= t_1 -1e+136)
     (fma (* k -27.0) j (* c b))
     (if (<= t_1 -2e+35)
       (* 18.0 (* y (* z (* x t))))
       (if (<= t_1 4e+79)
         (fma t (* a -4.0) (* c b))
         (fma k (* j -27.0) (* c b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e+136) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t_1 <= -2e+35) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t_1 <= 4e+79) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else {
		tmp = fma(k, (j * -27.0), (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e+136)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t_1 <= -2e+35)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t_1 <= 4e+79)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	else
		tmp = fma(k, Float64(j * -27.0), Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+136], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+35], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+79], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e136

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. 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 72.9

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

   5. Simplified 72.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.1

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

   8. Simplified 73.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.1

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

   10. Applied egg-rr 73.1%

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

   if -1.00000000000000006e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999999e35

   1. Initial program 83.7%

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

   3. Taylor expanded in 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 44.7

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

   5. Simplified 44.7%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-lowering-*.f64 48.8

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

   7. Applied egg-rr 48.8%

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

   if -1.9999999999999999e35 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999987e79

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

      1. 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 59.7

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

   5. Simplified 59.7%

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

   6. Taylor expanded in j around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 55.9

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

   8. Simplified 55.9%

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

   if 3.99999999999999987e79 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.9%

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

   3. Taylor expanded in 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 75.4

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

   5. Simplified 75.4%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 61.8

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

   8. Simplified 61.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+35}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-61}:\\ \;\;\;\;\mathsf{fma}\left(c, b, 18 \cdot \left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.25e+91)
     t_1
     (if (<= t -7.4e-61)
       (fma c b (* 18.0 (* z (* x (* t y)))))
       (if (<= t -9.8e-145)
         (* x (fma (* y z) (* t 18.0) (* -4.0 i)))
         (if (<= t 2.3e-199)
           (fma (* k -27.0) j (* c b))
           (if (<= t 1.25e-116)
             (fma (* x i) -4.0 (* (* j k) -27.0))
             (if (<= t 2.5e+57) (fma i (* x -4.0) (* c b)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.25e+91) {
		tmp = t_1;
	} else if (t <= -7.4e-61) {
		tmp = fma(c, b, (18.0 * (z * (x * (t * y)))));
	} else if (t <= -9.8e-145) {
		tmp = x * fma((y * z), (t * 18.0), (-4.0 * i));
	} else if (t <= 2.3e-199) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t <= 1.25e-116) {
		tmp = fma((x * i), -4.0, ((j * k) * -27.0));
	} else if (t <= 2.5e+57) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.25e+91)
		tmp = t_1;
	elseif (t <= -7.4e-61)
		tmp = fma(c, b, Float64(18.0 * Float64(z * Float64(x * Float64(t * y)))));
	elseif (t <= -9.8e-145)
		tmp = Float64(x * fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)));
	elseif (t <= 2.3e-199)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t <= 1.25e-116)
		tmp = fma(Float64(x * i), -4.0, Float64(Float64(j * k) * -27.0));
	elseif (t <= 2.5e+57)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+91], t$95$1, If[LessEqual[t, -7.4e-61], N[(c * b + N[(18.0 * N[(z * N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e-145], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-199], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-116], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+57], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.2500000000000001e91 or 2.49999999999999986e57 < t

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 72.5

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

   5. Simplified 72.5%

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

   if -1.2500000000000001e91 < t < -7.3999999999999999e-61

   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. 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. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 87.1%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

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

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-lowering-*.f64 57.0

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

   7. Simplified 57.0%

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

   if -7.3999999999999999e-61 < t < -9.79999999999999934e-145

   1. Initial program 63.6%

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

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 68.2

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

   7. Simplified 68.2%

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

   if -9.79999999999999934e-145 < t < 2.3000000000000001e-199

   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 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 77.1

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

   5. Simplified 77.1%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.8

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

   8. Simplified 73.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.8

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

   10. Applied egg-rr 73.8%

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

   if 2.3000000000000001e-199 < t < 1.2500000000000001e-116

   1. Initial program 86.6%

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

   3. Taylor expanded in 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 78.6

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

   5. Simplified 78.6%

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

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

      6. associate-*l* N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 78.8

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

   7. Applied egg-rr 78.8%

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

   if 1.2500000000000001e-116 < t < 2.49999999999999986e57

   1. Initial program 87.9%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 63.4

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

   8. Simplified 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-61}:\\ \;\;\;\;\mathsf{fma}\left(c, b, 18 \cdot \left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right)\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -7e+77)
     t_1
     (if (<= t -5e-38)
       (fma t (* a -4.0) (* c b))
       (if (<= t -3.1e-145)
         (* x (fma (* y z) (* t 18.0) (* -4.0 i)))
         (if (<= t 2.4e-199)
           (fma (* k -27.0) j (* c b))
           (if (<= t 1.26e-116)
             (fma (* x i) -4.0 (* (* j k) -27.0))
             (if (<= t 6e+55) (fma i (* x -4.0) (* c b)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -7e+77) {
		tmp = t_1;
	} else if (t <= -5e-38) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else if (t <= -3.1e-145) {
		tmp = x * fma((y * z), (t * 18.0), (-4.0 * i));
	} else if (t <= 2.4e-199) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t <= 1.26e-116) {
		tmp = fma((x * i), -4.0, ((j * k) * -27.0));
	} else if (t <= 6e+55) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -7e+77)
		tmp = t_1;
	elseif (t <= -5e-38)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	elseif (t <= -3.1e-145)
		tmp = Float64(x * fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)));
	elseif (t <= 2.4e-199)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t <= 1.26e-116)
		tmp = fma(Float64(x * i), -4.0, Float64(Float64(j * k) * -27.0));
	elseif (t <= 6e+55)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+77], t$95$1, If[LessEqual[t, -5e-38], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e-145], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-199], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.26e-116], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+55], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.0000000000000003e77 or 6.00000000000000033e55 < t

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 71.8

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

   5. Simplified 71.8%

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

   if -7.0000000000000003e77 < t < -5.00000000000000033e-38

   1. Initial program 96.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 72.6

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

   5. Simplified 72.6%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 62.8

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

   8. Simplified 62.8%

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

   if -5.00000000000000033e-38 < t < -3.1e-145

   1. Initial program 67.6%

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

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 86.6%

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

   5. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

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

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

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

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

      10. *-commutative N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 66.5

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

   7. Simplified 66.5%

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

   if -3.1e-145 < t < 2.39999999999999996e-199

   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 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 77.1

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

   5. Simplified 77.1%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.8

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

   8. Simplified 73.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.8

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

   10. Applied egg-rr 73.8%

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

   if 2.39999999999999996e-199 < t < 1.2599999999999999e-116

   1. Initial program 86.6%

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

   3. Taylor expanded in 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 78.6

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

   5. Simplified 78.6%

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

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

      6. associate-*l* N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 78.8

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

   7. Applied egg-rr 78.8%

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

   if 1.2599999999999999e-116 < t < 6.00000000000000033e55

   1. Initial program 87.9%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 63.4

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

   8. Simplified 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -5.4e+77)
     t_1
     (if (<= t -1.1e-36)
       (fma t (* a -4.0) (* c b))
       (if (<= t -9.8e-145)
         (* x (fma -4.0 i (* t (* 18.0 (* y z)))))
         (if (<= t 2.4e-199)
           (fma (* k -27.0) j (* c b))
           (if (<= t 5.5e-116)
             (fma (* x i) -4.0 (* (* j k) -27.0))
             (if (<= t 4e+58) (fma i (* x -4.0) (* c b)) t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -5.4e+77) {
		tmp = t_1;
	} else if (t <= -1.1e-36) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else if (t <= -9.8e-145) {
		tmp = x * fma(-4.0, i, (t * (18.0 * (y * z))));
	} else if (t <= 2.4e-199) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t <= 5.5e-116) {
		tmp = fma((x * i), -4.0, ((j * k) * -27.0));
	} else if (t <= 4e+58) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -5.4e+77)
		tmp = t_1;
	elseif (t <= -1.1e-36)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	elseif (t <= -9.8e-145)
		tmp = Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))));
	elseif (t <= 2.4e-199)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t <= 5.5e-116)
		tmp = fma(Float64(x * i), -4.0, Float64(Float64(j * k) * -27.0));
	elseif (t <= 4e+58)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+77], t$95$1, If[LessEqual[t, -1.1e-36], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e-145], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-199], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-116], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+58], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.3999999999999997e77 or 3.99999999999999978e58 < t

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 71.8

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

   5. Simplified 71.8%

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

   if -5.3999999999999997e77 < t < -1.1e-36

   1. Initial program 96.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 72.6

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

   5. Simplified 72.6%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-lowering-*.f64 62.8

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

   8. Simplified 62.8%

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

   if -1.1e-36 < t < -9.79999999999999934e-145

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf

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

      1. *-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 66.5

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

   5. Simplified 66.5%

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

   if -9.79999999999999934e-145 < t < 2.39999999999999996e-199

   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 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 77.1

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

   5. Simplified 77.1%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 73.8

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

   8. Simplified 73.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 73.8

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

   10. Applied egg-rr 73.8%

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

   if 2.39999999999999996e-199 < t < 5.4999999999999998e-116

   1. Initial program 86.6%

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

   3. Taylor expanded in 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 78.6

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

   5. Simplified 78.6%

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

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

      6. associate-*l* N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 78.8

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

   7. Applied egg-rr 78.8%

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

   if 5.4999999999999998e-116 < t < 3.99999999999999978e58

   1. Initial program 87.9%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 63.4

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

   8. Simplified 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2.55 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 2.55e-39)
   (fma
    c
    b
    (-
     (* t (fma x (* 18.0 (* y z)) (* a -4.0)))
     (fma x (* 4.0 i) (* 27.0 (* j k)))))
   (fma x (fma (* y z) (* t 18.0) (* -4.0 i)) (fma k (* j -27.0) (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 2.55e-39) {
		tmp = fma(c, b, ((t * fma(x, (18.0 * (y * z)), (a * -4.0))) - fma(x, (4.0 * i), (27.0 * (j * k)))));
	} else {
		tmp = fma(x, fma((y * z), (t * 18.0), (-4.0 * i)), fma(k, (j * -27.0), (c * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 2.55e-39)
		tmp = fma(c, b, Float64(Float64(t * fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0))) - fma(x, Float64(4.0 * i), Float64(27.0 * Float64(j * k)))));
	else
		tmp = fma(x, fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)), fma(k, Float64(j * -27.0), Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 2.55e-39], N[(c * b + N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.54999999999999994e-39

   1. Initial program 87.9%

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

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 91.5%

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

   if 2.54999999999999994e-39 < 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. 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. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 80.0%

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

   5. Taylor expanded in a around 0

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

   7. Simplified 92.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.55 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \end{array} \]

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
         (fma
          -4.0
          (* x i)
          (fma t (fma -4.0 a (* 18.0 (* x (* y z)))) (* c b)))))
   (if (<= x -9.6e-47)
     t_1
     (if (<= x 8.5e-66)
       (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
       (if (<= x 5.5e+177)
         t_1
         (- (* x (fma -4.0 i (* t (* 18.0 (* y z))))) (* k (* 27.0 j))))))))

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), fma(t, fma(-4.0, a, (18.0 * (x * (y * z)))), (c * b)));
	double tmp;
	if (x <= -9.6e-47) {
		tmp = t_1;
	} else if (x <= 8.5e-66) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else if (x <= 5.5e+177) {
		tmp = t_1;
	} else {
		tmp = (x * fma(-4.0, i, (t * (18.0 * (y * z))))) - (k * (27.0 * j));
	}
	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), fma(t, fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))), Float64(c * b)))
	tmp = 0.0
	if (x <= -9.6e-47)
		tmp = t_1;
	elseif (x <= 8.5e-66)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	elseif (x <= 5.5e+177)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z))))) - Float64(k * Float64(27.0 * j)));
	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[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e-47], t$95$1, If[LessEqual[x, 8.5e-66], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+177], t$95$1, N[(N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5999999999999998e-47 or 8.49999999999999966e-66 < x < 5.49999999999999993e177

   1. Initial program 78.0%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 82.3%

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

   if -9.5999999999999998e-47 < x < 8.49999999999999966e-66

   1. Initial program 96.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 85.5

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

   5. Simplified 85.5%

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

   if 5.49999999999999993e177 < x

   1. Initial program 59.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]
   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 90.8

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

   5. Simplified 90.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) - k \cdot \left(27 \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-134}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1e-46)
   (fma -4.0 (* x i) (fma t (fma -4.0 a (* 18.0 (* x (* y z)))) (* c b)))
   (if (<= x 1.85e-134)
     (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
     (fma x (fma (* y z) (* t 18.0) (* -4.0 i)) (fma k (* j -27.0) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -1e-46) {
		tmp = fma(-4.0, (x * i), fma(t, fma(-4.0, a, (18.0 * (x * (y * z)))), (c * b)));
	} else if (x <= 1.85e-134) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = fma(x, fma((y * z), (t * 18.0), (-4.0 * i)), fma(k, (j * -27.0), (c * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1e-46)
		tmp = fma(-4.0, Float64(x * i), fma(t, fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))), Float64(c * b)));
	elseif (x <= 1.85e-134)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = fma(x, fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)), fma(k, Float64(j * -27.0), Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1e-46], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-134], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000002e-46

   1. Initial program 75.8%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 82.0%

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

   if -1.00000000000000002e-46 < x < 1.85e-134

   1. Initial program 96.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 85.9

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

   5. Simplified 85.9%

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

   if 1.85e-134 < x

   1. Initial program 78.6%

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

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

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

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

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

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in a around 0

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

   7. Simplified 90.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-134}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, t\_1\right)\right)\\ \end{array} \end{array} \]

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 (* k -27.0))))
   (if (<= x -1.3e-46)
     (fma -4.0 (* x i) (fma t (fma -4.0 a (* 18.0 (* x (* y z)))) (* c b)))
     (if (<= x 5.5e-135)
       (fma b c (fma -4.0 (* t a) t_1))
       (fma x (fma -4.0 i (* t (* 18.0 (* y z)))) (fma 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 tmp;
	if (x <= -1.3e-46) {
		tmp = fma(-4.0, (x * i), fma(t, fma(-4.0, a, (18.0 * (x * (y * z)))), (c * b)));
	} else if (x <= 5.5e-135) {
		tmp = fma(b, c, fma(-4.0, (t * a), t_1));
	} else {
		tmp = fma(x, fma(-4.0, i, (t * (18.0 * (y * z)))), fma(b, c, 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(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -1.3e-46)
		tmp = fma(-4.0, Float64(x * i), fma(t, fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))), Float64(c * b)));
	elseif (x <= 5.5e-135)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), t_1));
	else
		tmp = fma(x, fma(-4.0, i, Float64(t * Float64(18.0 * Float64(y * z)))), fma(b, c, 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e-46], N[(-4.0 * N[(x * i), $MachinePrecision] + N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-135], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(-4.0 * i + N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3000000000000001e-46

   1. Initial program 75.8%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 82.0%

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

   if -1.3000000000000001e-46 < x < 5.4999999999999999e-135

   1. Initial program 96.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 85.9

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

   5. Simplified 85.9%

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

   if 5.4999999999999999e-135 < x

   1. Initial program 78.6%

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

   3. Taylor expanded in a around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. associate--l+ N/A

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

   5. Simplified 88.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), c \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(b, c, j \cdot \left(k \cdot -27\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.25e+58)
     t_1
     (if (<= t 2.7e-199)
       (fma (* k -27.0) j (* c b))
       (if (<= t 4.5e-116)
         (fma (* x i) -4.0 (* (* j k) -27.0))
         (if (<= t 1.3e+55) (fma i (* x -4.0) (* c b)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.25e+58) {
		tmp = t_1;
	} else if (t <= 2.7e-199) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t <= 4.5e-116) {
		tmp = fma((x * i), -4.0, ((j * k) * -27.0));
	} else if (t <= 1.3e+55) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.25e+58)
		tmp = t_1;
	elseif (t <= 2.7e-199)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t <= 4.5e-116)
		tmp = fma(Float64(x * i), -4.0, Float64(Float64(j * k) * -27.0));
	elseif (t <= 1.3e+55)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+58], t$95$1, If[LessEqual[t, 2.7e-199], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-116], N[(N[(x * i), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+55], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.24999999999999996e58 or 1.3e55 < t

   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 t around inf

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

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

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

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

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

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

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

      8. *-lowering-*.f64 70.8

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

   5. Simplified 70.8%

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

   if -1.24999999999999996e58 < t < 2.69999999999999989e-199

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0

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

      1. 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 64.1

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

   5. Simplified 64.1%

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

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. *-lowering-*.f64 59.7

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

   8. Simplified 59.7%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

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

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

      5. *-lowering-*.f64 59.7

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

   10. Applied egg-rr 59.7%

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

   if 2.69999999999999989e-199 < t < 4.50000000000000012e-116

   1. Initial program 86.6%

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

   3. Taylor expanded in 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 78.6

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

   5. Simplified 78.6%

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

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

      6. associate-*l* N/A

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

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

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

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

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 78.8

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

   7. Applied egg-rr 78.8%

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

   if 4.50000000000000012e-116 < t < 1.3e55

   1. Initial program 87.9%

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

   3. Taylor expanded in j around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate-+r+ N/A

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-lowering-*.f64 63.4

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

   8. Simplified 63.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-199}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot i, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, t\_1\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), t\_1\right)\\ \end{array} \end{array} \]

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 k) -27.0)))
   (if (<= x -1.02e+117)
     (fma (fma -4.0 a (* 18.0 (* x (* y z)))) t t_1)
     (if (<= x 4.2e-68)
       (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
       (fma x (fma (* y z) (* t 18.0) (* -4.0 i)) 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 tmp;
	if (x <= -1.02e+117) {
		tmp = fma(fma(-4.0, a, (18.0 * (x * (y * z)))), t, t_1);
	} else if (x <= 4.2e-68) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = fma(x, fma((y * z), (t * 18.0), (-4.0 * i)), 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)
	tmp = 0.0
	if (x <= -1.02e+117)
		tmp = fma(fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))), t, t_1);
	elseif (x <= 4.2e-68)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = fma(x, fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)), 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 * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[x, -1.02e+117], N[(N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision], If[LessEqual[x, 4.2e-68], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e117

   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 t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      3. metadata-eval N/A

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) - \left(j \cdot 27\right) \cdot k \]

      4. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      6. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      7. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      8. *-lowering-*.f64 74.1

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} + \left(\mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right), t, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}, t, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right), t, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right), t, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right), t, \mathsf{neg}\left(\left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, \mathsf{neg}\left(\color{blue}{\left(27 \cdot j\right)} \cdot k\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, \mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      13. *-lowering-*.f64 74.1

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, -27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

   7. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, -27 \cdot \left(j \cdot k\right)\right)} \]

   if -1.02e117 < x < 4.20000000000000016e-68

   1. Initial program 93.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 81.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   if 4.20000000000000016e-68 < x

   1. Initial program 74.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. 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. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   7. Simplified 90.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \color{blue}{-27 \cdot \left(j \cdot k\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \color{blue}{-27 \cdot \left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 76.4

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), -27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

   10. Simplified 76.4%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \color{blue}{-27 \cdot \left(j \cdot k\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), t, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \left(j \cdot k\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \left(j \cdot k\right) \cdot -27\right)\\ \end{array} \end{array} \]

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
 (if (<= x -1.15e+117)
   (* t (fma -4.0 a (* 18.0 (* x (* y z)))))
   (if (<= x 3.6e-68)
     (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
     (fma x (fma (* y z) (* t 18.0) (* -4.0 i)) (* (* j k) -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 (x <= -1.15e+117) {
		tmp = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	} else if (x <= 3.6e-68) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = fma(x, fma((y * z), (t * 18.0), (-4.0 * i)), ((j * k) * -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 (x <= -1.15e+117)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (x <= 3.6e-68)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = fma(x, fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)), Float64(Float64(j * k) * -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[x, -1.15e+117], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-68], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.14999999999999994e117

   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 t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

      3. metadata-eval N/A

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

      4. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      8. *-lowering-*.f64 72.3

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.14999999999999994e117 < x < 3.60000000000000007e-68

   1. Initial program 93.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 81.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   if 3.60000000000000007e-68 < x

   1. Initial program 74.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. 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. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

   7. Simplified 90.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)\right)} \]

   8. Taylor expanded in k around inf

      \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \color{blue}{-27 \cdot \left(j \cdot k\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \color{blue}{-27 \cdot \left(j \cdot k\right)}\right) \]

      2. *-lowering-*.f64 76.4

         \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), -27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

   10. Simplified 76.4%

       \[\leadsto \mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right), \color{blue}{-27 \cdot \left(j \cdot k\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right), \left(j \cdot k\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* 27.0 j))))
   (if (<= t_1 -1e+136)
     (fma (* k -27.0) j (* c b))
     (if (<= t_1 4e+79)
       (fma t (* a -4.0) (* c b))
       (fma k (* j -27.0) (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (27.0 * j);
	double tmp;
	if (t_1 <= -1e+136) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (t_1 <= 4e+79) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else {
		tmp = fma(k, (j * -27.0), (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_1 <= -1e+136)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (t_1 <= 4e+79)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	else
		tmp = fma(k, Float64(j * -27.0), Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+136], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+79], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e136

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 72.9

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 72.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 73.1

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot -27\right) \cdot j} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{k \cdot -27}, j, b \cdot c\right) \]

      5. *-lowering-*.f64 73.1

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{b \cdot c}\right) \]

   10. Applied egg-rr 73.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

   if -1.00000000000000006e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999987e79

   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 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 57.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. 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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{-4 \cdot a}, b \cdot c\right) \]

      5. *-lowering-*.f64 52.8

         \[\leadsto \mathsf{fma}\left(t, -4 \cdot a, \color{blue}{b \cdot c}\right) \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

   if 3.99999999999999987e79 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 75.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 61.8

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 61.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma k (* j -27.0) (* c b))) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -1e+136)
     t_1
     (if (<= t_2 4e+79) (fma t (* a -4.0) (* c b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(k, (j * -27.0), (c * b));
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -1e+136) {
		tmp = t_1;
	} else if (t_2 <= 4e+79) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(k, Float64(j * -27.0), Float64(c * b))
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -1e+136)
		tmp = t_1;
	elseif (t_2 <= 4e+79)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+136], t$95$1, If[LessEqual[t$95$2, 4e+79], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000006e136 or 3.99999999999999987e79 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 74.2

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 67.3

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]

   if -1.00000000000000006e136 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.99999999999999987e79

   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 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 57.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 57.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. 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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{-4 \cdot a}, b \cdot c\right) \]

      5. *-lowering-*.f64 52.8

         \[\leadsto \mathsf{fma}\left(t, -4 \cdot a, \color{blue}{b \cdot c}\right) \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -1 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ t_2 := k \cdot \left(27 \cdot j\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma k (* j -27.0) (* c b))) (t_2 (* k (* 27.0 j))))
   (if (<= t_2 -2e+154)
     t_1
     (if (<= t_2 2e+37) (fma i (* x -4.0) (* c b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(k, (j * -27.0), (c * b));
	double t_2 = k * (27.0 * j);
	double tmp;
	if (t_2 <= -2e+154) {
		tmp = t_1;
	} else if (t_2 <= 2e+37) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(k, Float64(j * -27.0), Float64(c * b))
	t_2 = Float64(k * Float64(27.0 * j))
	tmp = 0.0
	if (t_2 <= -2e+154)
		tmp = t_1;
	elseif (t_2 <= 2e+37)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(27.0 * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+154], t$95$1, If[LessEqual[t$95$2, 2e+37], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000007e154 or 1.99999999999999991e37 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 76.3

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   6. 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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 66.2

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 66.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]

   if -2.00000000000000007e154 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999991e37

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \color{blue}{-4} \cdot \left(i \cdot x\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c}\right) \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), b \cdot c\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} + b \cdot c \]

      3. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(-4 \cdot x\right)} + b \cdot c \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i, -4 \cdot x, b \cdot c\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      7. *-lowering-*.f64 45.2

         \[\leadsto \mathsf{fma}\left(i, x \cdot -4, \color{blue}{b \cdot c}\right) \]

   8. Simplified 45.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(27 \cdot j\right) \leq -2 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \mathbf{elif}\;k \cdot \left(27 \cdot j\right) \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k, j \cdot -27, c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 68.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -1.42 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, t\_1\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (<= x -1.42e+119)
     (* t (fma -4.0 a (* 18.0 (* x (* y z)))))
     (if (<= x 6.2e-85)
       (fma b c (fma -4.0 (* t a) t_1))
       (if (<= x 3.3e+208)
         (fma b c (fma -4.0 (* x i) t_1))
         (* x (fma (* y z) (* t 18.0) (* -4.0 i))))))))

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 tmp;
	if (x <= -1.42e+119) {
		tmp = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	} else if (x <= 6.2e-85) {
		tmp = fma(b, c, fma(-4.0, (t * a), t_1));
	} else if (x <= 3.3e+208) {
		tmp = fma(b, c, fma(-4.0, (x * i), t_1));
	} else {
		tmp = x * fma((y * z), (t * 18.0), (-4.0 * i));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -1.42e+119)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (x <= 6.2e-85)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), t_1));
	elseif (x <= 3.3e+208)
		tmp = fma(b, c, fma(-4.0, Float64(x * i), t_1));
	else
		tmp = Float64(x * fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.42e+119], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-85], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+208], N[(b * c + N[(-4.0 * N[(x * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4199999999999999e119

   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 t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

      3. metadata-eval N/A

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

      4. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      8. *-lowering-*.f64 72.3

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.4199999999999999e119 < x < 6.2000000000000005e-85

   1. Initial program 93.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 80.6

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   if 6.2000000000000005e-85 < x < 3.3e208

   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 t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right)} \]

      3. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(i \cdot x\right)\right)\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)}\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(i \cdot x\right) + \left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x\right) + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, -27 \cdot \left(j \cdot k\right)\right)}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(j \cdot k\right) \cdot -27}\right)\right) \]

      12. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, \color{blue}{j \cdot \left(-27 \cdot k\right)}\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

      16. *-lowering-*.f64 70.9

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 70.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   if 3.3e208 < x

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 65.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)} \]

      6. associate-*r* N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)} + -4 \cdot i\right) \]

      7. *-commutative N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(y \cdot z\right) \cdot \left(18 \cdot t\right)} + -4 \cdot i\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(y \cdot z, 18 \cdot t, -4 \cdot i\right)} \]

      9. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(\color{blue}{y \cdot z}, 18 \cdot t, -4 \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, \color{blue}{t \cdot 18}, -4 \cdot i\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, \color{blue}{t \cdot 18}, -4 \cdot i\right) \]

      12. *-commutative N/A

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, \color{blue}{i \cdot -4}\right) \]

      13. *-lowering-*.f64 93.3

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, \color{blue}{i \cdot -4}\right) \]

   7. Simplified 93.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, x \cdot i, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot 18\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(y \cdot t\_1\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-217}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-37}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot t\_1\right)\\ \end{array} \end{array} \]

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 (* x (* t 18.0))))
   (if (<= x -5e+158)
     (* z (* y t_1))
     (if (<= x 2e-217)
       (fma t (* a -4.0) (* c b))
       (if (<= x 7.5e-37)
         (fma (* k -27.0) j (* c b))
         (if (<= x 2.05e+212) (fma i (* x -4.0) (* c b)) (* 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 = x * (t * 18.0);
	double tmp;
	if (x <= -5e+158) {
		tmp = z * (y * t_1);
	} else if (x <= 2e-217) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else if (x <= 7.5e-37) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (x <= 2.05e+212) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = 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(x * Float64(t * 18.0))
	tmp = 0.0
	if (x <= -5e+158)
		tmp = Float64(z * Float64(y * t_1));
	elseif (x <= 2e-217)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	elseif (x <= 7.5e-37)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (x <= 2.05e+212)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = Float64(y * Float64(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[(x * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+158], N[(z * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-217], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-37], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+212], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.9999999999999996e158

   1. Initial program 69.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 55.2

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      8. *-lowering-*.f64 55.1

         \[\leadsto \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 55.1%

      \[\leadsto \color{blue}{\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\left(t \cdot 18\right) \cdot x\right) \cdot y\right)} \cdot z \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(t \cdot 18\right) \cdot x\right) \cdot y\right)} \cdot z \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)} \cdot y\right) \cdot z \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)} \cdot y\right) \cdot z \]

      5. *-lowering-*.f64 59.6

         \[\leadsto \left(\left(x \cdot \color{blue}{\left(t \cdot 18\right)}\right) \cdot y\right) \cdot z \]

   9. Applied egg-rr 59.6%

      \[\leadsto \color{blue}{\left(\left(x \cdot \left(t \cdot 18\right)\right) \cdot y\right)} \cdot z \]

   if -4.9999999999999996e158 < x < 2.00000000000000016e-217

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 78.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{-4 \cdot a}, b \cdot c\right) \]

      5. *-lowering-*.f64 57.4

         \[\leadsto \mathsf{fma}\left(t, -4 \cdot a, \color{blue}{b \cdot c}\right) \]

   8. Simplified 57.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

   if 2.00000000000000016e-217 < x < 7.5000000000000004e-37

   1. Initial program 96.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 78.6

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 66.0

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot -27\right) \cdot j} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{k \cdot -27}, j, b \cdot c\right) \]

      5. *-lowering-*.f64 66.0

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{b \cdot c}\right) \]

   10. Applied egg-rr 66.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

   if 7.5000000000000004e-37 < x < 2.04999999999999995e212

   1. Initial program 80.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \color{blue}{-4} \cdot \left(i \cdot x\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c}\right) \]

   5. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), b \cdot c\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} + b \cdot c \]

      3. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(-4 \cdot x\right)} + b \cdot c \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i, -4 \cdot x, b \cdot c\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      7. *-lowering-*.f64 64.4

         \[\leadsto \mathsf{fma}\left(i, x \cdot -4, \color{blue}{b \cdot c}\right) \]

   8. Simplified 64.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]

   if 2.04999999999999995e212 < x

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 59.8

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      8. *-lowering-*.f64 58.7

         \[\leadsto \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\left(t \cdot 18\right) \cdot x\right) \cdot y\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right) \cdot y} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right) \cdot y} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right)} \cdot y \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)}\right) \cdot y \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)}\right) \cdot y \]

      8. *-lowering-*.f64 65.9

         \[\leadsto \left(z \cdot \left(x \cdot \color{blue}{\left(t \cdot 18\right)}\right)\right) \cdot y \]

   9. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-217}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-37}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 49.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-218}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= x -8.8e+158)
   (* z (* (* t 18.0) (* x y)))
   (if (<= x 8e-218)
     (fma t (* a -4.0) (* c b))
     (if (<= x 5.6e-34)
       (fma (* k -27.0) j (* c b))
       (if (<= x 9e+217)
         (fma i (* x -4.0) (* c b))
         (* y (* z (* x (* t 18.0)))))))))

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 (x <= -8.8e+158) {
		tmp = z * ((t * 18.0) * (x * y));
	} else if (x <= 8e-218) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else if (x <= 5.6e-34) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (x <= 9e+217) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = y * (z * (x * (t * 18.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -8.8e+158)
		tmp = Float64(z * Float64(Float64(t * 18.0) * Float64(x * y)));
	elseif (x <= 8e-218)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	elseif (x <= 5.6e-34)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (x <= 9e+217)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = Float64(y * Float64(z * Float64(x * Float64(t * 18.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -8.8e+158], N[(z * N[(N[(t * 18.0), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-218], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e-34], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+217], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(x * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.8000000000000005e158

   1. Initial program 69.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 55.2

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      8. *-lowering-*.f64 55.1

         \[\leadsto \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 55.1%

      \[\leadsto \color{blue}{\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]

   if -8.8000000000000005e158 < x < 8.0000000000000003e-218

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 78.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{-4 \cdot a}, b \cdot c\right) \]

      5. *-lowering-*.f64 57.4

         \[\leadsto \mathsf{fma}\left(t, -4 \cdot a, \color{blue}{b \cdot c}\right) \]

   8. Simplified 57.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

   if 8.0000000000000003e-218 < x < 5.59999999999999994e-34

   1. Initial program 96.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 78.6

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 66.0

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot -27\right) \cdot j} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{k \cdot -27}, j, b \cdot c\right) \]

      5. *-lowering-*.f64 66.0

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{b \cdot c}\right) \]

   10. Applied egg-rr 66.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

   if 5.59999999999999994e-34 < x < 8.99999999999999976e217

   1. Initial program 80.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \color{blue}{-4} \cdot \left(i \cdot x\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c}\right) \]

   5. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), b \cdot c\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} + b \cdot c \]

      3. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(-4 \cdot x\right)} + b \cdot c \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i, -4 \cdot x, b \cdot c\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      7. *-lowering-*.f64 64.4

         \[\leadsto \mathsf{fma}\left(i, x \cdot -4, \color{blue}{b \cdot c}\right) \]

   8. Simplified 64.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]

   if 8.99999999999999976e217 < x

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 59.8

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      8. *-lowering-*.f64 58.7

         \[\leadsto \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\left(t \cdot 18\right) \cdot x\right) \cdot y\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right) \cdot y} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right) \cdot y} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right)} \cdot y \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)}\right) \cdot y \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)}\right) \cdot y \]

      8. *-lowering-*.f64 65.9

         \[\leadsto \left(z \cdot \left(x \cdot \color{blue}{\left(t \cdot 18\right)}\right)\right) \cdot y \]

   9. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-218}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+217}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 49.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+158}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-218}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+213}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= x -9.5e+158)
   (* 18.0 (* z (* x (* t y))))
   (if (<= x 8.4e-218)
     (fma t (* a -4.0) (* c b))
     (if (<= x 1.25e-34)
       (fma (* k -27.0) j (* c b))
       (if (<= x 9.5e+213)
         (fma i (* x -4.0) (* c b))
         (* y (* z (* x (* t 18.0)))))))))

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 (x <= -9.5e+158) {
		tmp = 18.0 * (z * (x * (t * y)));
	} else if (x <= 8.4e-218) {
		tmp = fma(t, (a * -4.0), (c * b));
	} else if (x <= 1.25e-34) {
		tmp = fma((k * -27.0), j, (c * b));
	} else if (x <= 9.5e+213) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = y * (z * (x * (t * 18.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -9.5e+158)
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(t * y))));
	elseif (x <= 8.4e-218)
		tmp = fma(t, Float64(a * -4.0), Float64(c * b));
	elseif (x <= 1.25e-34)
		tmp = fma(Float64(k * -27.0), j, Float64(c * b));
	elseif (x <= 9.5e+213)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = Float64(y * Float64(z * Float64(x * Float64(t * 18.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -9.5e+158], N[(18.0 * N[(z * N[(x * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.4e-218], N[(t * N[(a * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-34], N[(N[(k * -27.0), $MachinePrecision] * j + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+213], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * N[(x * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.49999999999999913e158

   1. Initial program 69.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. 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. associate-*l* N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) \cdot z} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(18 \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(t \cdot \left(x \cdot y\right)\right) \cdot 18\right)} \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) \cdot 18} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right) \cdot 18} \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)} \cdot 18 \]

      9. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot t\right)}\right) \cdot 18 \]

      10. associate-*l* N/A

          \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(y \cdot t\right)\right)}\right) \cdot 18 \]

      11. *-commutative N/A

          \[\leadsto \left(z \cdot \left(x \cdot \color{blue}{\left(t \cdot y\right)}\right)\right) \cdot 18 \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot y\right)\right)}\right) \cdot 18 \]

      13. *-lowering-*.f64 57.4

          \[\leadsto \left(z \cdot \left(x \cdot \color{blue}{\left(t \cdot y\right)}\right)\right) \cdot 18 \]

   7. Simplified 57.4%

      \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right) \cdot 18} \]

   if -9.49999999999999913e158 < x < 8.39999999999999976e-218

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 78.4

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{-4 \cdot a}, b \cdot c\right) \]

      5. *-lowering-*.f64 57.4

         \[\leadsto \mathsf{fma}\left(t, -4 \cdot a, \color{blue}{b \cdot c}\right) \]

   8. Simplified 57.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -4 \cdot a, b \cdot c\right)} \]

   if 8.39999999999999976e-218 < x < 1.2500000000000001e-34

   1. Initial program 96.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 78.6

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   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. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} + b \cdot c \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{k \cdot \left(-27 \cdot j\right)} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k, -27 \cdot j, b \cdot c\right)} \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(k, \color{blue}{j \cdot -27}, b \cdot c\right) \]

      6. *-lowering-*.f64 66.0

         \[\leadsto \mathsf{fma}\left(k, j \cdot -27, \color{blue}{b \cdot c}\right) \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k, j \cdot -27, b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto k \cdot \color{blue}{\left(-27 \cdot j\right)} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(k \cdot -27\right) \cdot j} + b \cdot c \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{k \cdot -27}, j, b \cdot c\right) \]

      5. *-lowering-*.f64 66.0

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, \color{blue}{b \cdot c}\right) \]

   10. Applied egg-rr 66.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)} \]

   if 1.2500000000000001e-34 < x < 9.49999999999999993e213

   1. Initial program 80.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \color{blue}{-4} \cdot \left(i \cdot x\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c}\right) \]

   5. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), b \cdot c\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} + b \cdot c \]

      3. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(-4 \cdot x\right)} + b \cdot c \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i, -4 \cdot x, b \cdot c\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      7. *-lowering-*.f64 64.4

         \[\leadsto \mathsf{fma}\left(i, x \cdot -4, \color{blue}{b \cdot c}\right) \]

   8. Simplified 64.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]

   if 9.49999999999999993e213 < x

   1. Initial program 53.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 59.8

         \[\leadsto 18 \cdot \left(t \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   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. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(\color{blue}{\left(t \cdot 18\right)} \cdot \left(x \cdot y\right)\right) \cdot z \]

      8. *-lowering-*.f64 58.7

         \[\leadsto \left(\left(t \cdot 18\right) \cdot \color{blue}{\left(x \cdot y\right)}\right) \cdot z \]

   7. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right) \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(t \cdot 18\right) \cdot \left(x \cdot y\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\left(t \cdot 18\right) \cdot x\right) \cdot y\right)} \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right) \cdot y} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right) \cdot y} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(t \cdot 18\right) \cdot x\right)\right)} \cdot y \]

      6. *-commutative N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)}\right) \cdot y \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot \left(t \cdot 18\right)\right)}\right) \cdot y \]

      8. *-lowering-*.f64 65.9

         \[\leadsto \left(z \cdot \left(x \cdot \color{blue}{\left(t \cdot 18\right)}\right)\right) \cdot y \]

   9. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+158}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(t \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-218}:\\ \;\;\;\;\mathsf{fma}\left(t, a \cdot -4, c \cdot b\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, c \cdot b\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+213}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x \cdot \left(t \cdot 18\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 67.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -8.6e+118)
   (* t (fma -4.0 a (* 18.0 (* x (* y z)))))
   (if (<= x 2.1e-64)
     (fma b c (fma -4.0 (* t a) (* j (* k -27.0))))
     (* x (fma (* y z) (* t 18.0) (* -4.0 i))))))

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 <= -8.6e+118) {
		tmp = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	} else if (x <= 2.1e-64) {
		tmp = fma(b, c, fma(-4.0, (t * a), (j * (k * -27.0))));
	} else {
		tmp = x * fma((y * z), (t * 18.0), (-4.0 * i));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -8.6e+118)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (x <= 2.1e-64)
		tmp = fma(b, c, fma(-4.0, Float64(t * a), Float64(j * Float64(k * -27.0))));
	else
		tmp = Float64(x * fma(Float64(y * z), Float64(t * 18.0), Float64(-4.0 * i)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -8.6e+118], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-64], N[(b * c + N[(-4.0 * N[(t * a), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.6000000000000006e118

   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 t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

      3. metadata-eval N/A

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

      4. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, \color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      8. *-lowering-*.f64 72.3

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -8.6000000000000006e118 < x < 2.10000000000000011e-64

   1. Initial program 92.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 81.0

          \[\leadsto \mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \color{blue}{\left(k \cdot -27\right)}\right)\right) \]

   5. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, a \cdot t, j \cdot \left(k \cdot -27\right)\right)\right)} \]

   if 2.10000000000000011e-64 < x

   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

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) - \mathsf{fma}\left(x, 4 \cdot i, 27 \cdot \left(j \cdot k\right)\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)} \]

      6. associate-*r* N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot z\right)} + -4 \cdot i\right) \]

      7. *-commutative N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(y \cdot z\right) \cdot \left(18 \cdot t\right)} + -4 \cdot i\right) \]

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(y \cdot z, 18 \cdot t, -4 \cdot i\right)} \]

      9. *-lowering-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(\color{blue}{y \cdot z}, 18 \cdot t, -4 \cdot i\right) \]

      10. *-commutative N/A

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, \color{blue}{t \cdot 18}, -4 \cdot i\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, \color{blue}{t \cdot 18}, -4 \cdot i\right) \]

      12. *-commutative N/A

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, \color{blue}{i \cdot -4}\right) \]

      13. *-lowering-*.f64 63.7

          \[\leadsto x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, \color{blue}{i \cdot -4}\right) \]

   7. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, i \cdot -4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(b, c, \mathsf{fma}\left(-4, t \cdot a, j \cdot \left(k \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(y \cdot z, t \cdot 18, -4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 34.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot b \leq -7.4 \cdot 10^{+186}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* c b) -7.4e+186)
   (* c b)
   (if (<= (* c b) 3.4e+89) (* -4.0 (* t a)) (* c b))))

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 ((c * b) <= -7.4e+186) {
		tmp = c * b;
	} else if ((c * b) <= 3.4e+89) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((c * b) <= (-7.4d+186)) then
        tmp = c * b
    else if ((c * b) <= 3.4d+89) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c * b) <= -7.4e+186) {
		tmp = c * b;
	} else if ((c * b) <= 3.4e+89) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c * b) <= -7.4e+186:
		tmp = c * b
	elif (c * b) <= 3.4e+89:
		tmp = -4.0 * (t * a)
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(c * b) <= -7.4e+186)
		tmp = Float64(c * b);
	elseif (Float64(c * b) <= 3.4e+89)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c * b) <= -7.4e+186)
		tmp = c * b;
	elseif ((c * b) <= 3.4e+89)
		tmp = -4.0 * (t * a);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(c * b), $MachinePrecision], -7.4e+186], N[(c * b), $MachinePrecision], If[LessEqual[N[(c * b), $MachinePrecision], 3.4e+89], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -7.4e186 or 3.4000000000000002e89 < (*.f64 b c)

   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 b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 59.1

         \[\leadsto \color{blue}{b \cdot c} \]

   5. Simplified 59.1%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -7.4e186 < (*.f64 b c) < 3.4000000000000002e89

   1. Initial program 89.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 30.5

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

   5. Simplified 30.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot b \leq -7.4 \cdot 10^{+186}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \cdot b \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 43.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

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 (<= t 1.6e+68) (fma i (* x -4.0) (* c b)) (* -4.0 (* t a))))

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 (t <= 1.6e+68) {
		tmp = fma(i, (x * -4.0), (c * b));
	} else {
		tmp = -4.0 * (t * a);
	}
	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 (t <= 1.6e+68)
		tmp = fma(i, Float64(x * -4.0), Float64(c * b));
	else
		tmp = Float64(-4.0 * Float64(t * a));
	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[t, 1.6e+68], N[(i * N[(x * -4.0), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.59999999999999997e68

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)} \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) + \color{blue}{-4} \cdot \left(i \cdot x\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i \cdot x, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right)}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)}\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(\left(\mathsf{neg}\left(4 \cdot \left(a \cdot t\right)\right)\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + b \cdot c}\right) \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x \cdot i, \mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right), b \cdot c\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + b \cdot c} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + b \cdot c \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{i \cdot \left(x \cdot -4\right)} + b \cdot c \]

      3. *-commutative N/A

         \[\leadsto i \cdot \color{blue}{\left(-4 \cdot x\right)} + b \cdot c \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i, -4 \cdot x, b \cdot c\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, \color{blue}{x \cdot -4}, b \cdot c\right) \]

      7. *-lowering-*.f64 44.1

         \[\leadsto \mathsf{fma}\left(i, x \cdot -4, \color{blue}{b \cdot c}\right) \]

   8. Simplified 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i, x \cdot -4, b \cdot c\right)} \]

   if 1.59999999999999997e68 < t

   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 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 62.9

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

   5. Simplified 62.9%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(i, x \cdot -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 24.0% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = c * b
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(c * b)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = c * b;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

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 24.9

      \[\leadsto \color{blue}{b \cdot c} \]

5. Simplified 24.9%

   \[\leadsto \color{blue}{b \cdot c} \]

6. Final simplification 24.9%

   \[\leadsto c \cdot b \]
7. 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 2024198 
(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)))