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

Percentage Accurate: 86.0% → 92.9%

Time: 14.8s

Alternatives: 20

Speedup: 0.9×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-146} \lor \neg \left(t \leq 1.36 \cdot 10^{+72}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, t\_1\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 x) i))))
   (if (or (<= t -2.7e-146) (not (<= t 1.36e+72)))
     (fma (* -27.0 j) k (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t t_1))
     (-
      (fma y (* (* 18.0 x) (* t z)) (fma (* -4.0 a) t t_1))
      (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((-4.0 * x) * i));
	double tmp;
	if ((t <= -2.7e-146) || !(t <= 1.36e+72)) {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, t_1));
	} else {
		tmp = fma(y, ((18.0 * x) * (t * z)), fma((-4.0 * a), t, t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * x) * i))
	tmp = 0.0
	if ((t <= -2.7e-146) || !(t <= 1.36e+72))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, t_1));
	else
		tmp = Float64(fma(y, Float64(Float64(18.0 * x) * Float64(t * z)), fma(Float64(-4.0 * a), t, t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2.7e-146], N[Not[LessEqual[t, 1.36e+72]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(18.0 * x), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999995e-146 or 1.3599999999999999e72 < t

   1. Initial program 88.9%

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

   4. Applied rewrites 94.6%

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

   if -2.69999999999999995e-146 < t < 1.3599999999999999e72

   1. Initial program 88.2%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

   4. Applied rewrites 95.7%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-146} \lor \neg \left(t \leq 1.36 \cdot 10^{+72}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(18 \cdot x\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.9%

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

   4. Applied rewrites 96.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

Alternative 3: 92.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{-145} \lor \neg \left(t \leq 6.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, t\_1\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 x) i))))
   (if (or (<= t -1.95e-145) (not (<= t 6.5e+71)))
     (fma (* -27.0 j) k (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t t_1))
     (-
      (fma x (* (* y 18.0) (* t z)) (fma (* -4.0 a) t t_1))
      (* (* j 27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((-4.0 * x) * i));
	double tmp;
	if ((t <= -1.95e-145) || !(t <= 6.5e+71)) {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, t_1));
	} else {
		tmp = fma(x, ((y * 18.0) * (t * z)), fma((-4.0 * a), t, t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * x) * i))
	tmp = 0.0
	if ((t <= -1.95e-145) || !(t <= 6.5e+71))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, t_1));
	else
		tmp = Float64(fma(x, Float64(Float64(y * 18.0) * Float64(t * z)), fma(Float64(-4.0 * a), t, t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -1.95e-145], N[Not[LessEqual[t, 6.5e+71]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.95000000000000015e-145 or 6.49999999999999954e71 < t

   1. Initial program 88.9%

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

   4. Applied rewrites 94.6%

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

   if -1.95000000000000015e-145 < t < 6.49999999999999954e71

   1. Initial program 88.2%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. associate-*l* N/A

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

   4. Applied rewrites 95.7%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-145} \lor \neg \left(t \leq 6.5 \cdot 10^{+71}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \left(y \cdot 18\right) \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+132} \lor \neg \left(b \cdot c \leq 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -4e+132) (not (<= (* b c) 1e+36)))
   (fma (* -27.0 j) k (fma (* i x) -4.0 (* b c)))
   (fma (* -27.0 j) k (* (fma i x (* a t)) -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 tmp;
	if (((b * c) <= -4e+132) || !((b * c) <= 1e+36)) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, (b * c)));
	} else {
		tmp = fma((-27.0 * j), k, (fma(i, x, (a * t)) * -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)
	tmp = 0.0
	if ((Float64(b * c) <= -4e+132) || !(Float64(b * c) <= 1e+36))
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, Float64(b * c)));
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(fma(i, x, Float64(a * t)) * -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_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -4e+132], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+36]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.99999999999999996e132 or 1.00000000000000004e36 < (*.f64 b c)

   1. Initial program 86.3%

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

   4. Applied rewrites 91.6%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 79.6

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

   7. Applied rewrites 79.6%

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

   if -3.99999999999999996e132 < (*.f64 b c) < 1.00000000000000004e36

   1. Initial program 90.0%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

   4. Applied rewrites 89.0%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-out N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 77.1

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

   7. Applied rewrites 77.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 75.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+132} \lor \neg \left(b \cdot c \leq 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+132} \lor \neg \left(b \cdot c \leq 4 \cdot 10^{+146}\right):\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -4e+132) (not (<= (* b c) 4e+146)))
   (fma (* k j) -27.0 (* b c))
   (fma (* -27.0 j) k (* (fma i x (* a t)) -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 tmp;
	if (((b * c) <= -4e+132) || !((b * c) <= 4e+146)) {
		tmp = fma((k * j), -27.0, (b * c));
	} else {
		tmp = fma((-27.0 * j), k, (fma(i, x, (a * t)) * -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)
	tmp = 0.0
	if ((Float64(b * c) <= -4e+132) || !(Float64(b * c) <= 4e+146))
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(fma(i, x, Float64(a * t)) * -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_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -4e+132], N[Not[LessEqual[N[(b * c), $MachinePrecision], 4e+146]], $MachinePrecision]], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.99999999999999996e132 or 3.99999999999999973e146 < (*.f64 b c)

   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 x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.0%

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

   if -3.99999999999999996e132 < (*.f64 b c) < 3.99999999999999973e146

   1. Initial program 90.1%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

   4. Applied rewrites 89.8%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-out N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 77.8

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

   7. Applied rewrites 77.8%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 74.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+132} \lor \neg \left(b \cdot c \leq 4 \cdot 10^{+146}\right):\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(t, \mathsf{fma}\left(\left(x \cdot 18\right) \cdot y, z, a \cdot -4\right), b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -1.08e+129)
   (fma (* k -27.0) j (fma t (fma (* (* x 18.0) y) z (* a -4.0)) (* b c)))
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -1.08e+129) {
		tmp = fma((k * -27.0), j, fma(t, fma(((x * 18.0) * y), z, (a * -4.0)), (b * c)));
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -1.08e+129)
		tmp = fma(Float64(k * -27.0), j, fma(t, fma(Float64(Float64(x * 18.0) * y), z, Float64(a * -4.0)), Float64(b * c)));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -1.08e+129], N[(N[(k * -27.0), $MachinePrecision] * j + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08e129

   1. Initial program 82.1%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 80.2%

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

   7. Applied rewrites 86.9%

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

   if -1.08e129 < y

   1. Initial program 90.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 81.7

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

   5. Applied rewrites 81.7%

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

Alternative 7: 82.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4, \mathsf{fma}\left(i, x, t \cdot a\right), b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2.5e+23)
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (fma (* -27.0 j) k (fma -4.0 (fma i x (* t a)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2.5e+23) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else {
		tmp = fma((-27.0 * j), k, fma(-4.0, fma(i, x, (t * a)), (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -2.5e+23)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(-4.0, fma(i, x, Float64(t * a)), Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -2.5e+23], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5e23

   1. Initial program 80.9%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 92.0%

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

   if -2.5e23 < t

   1. Initial program 90.5%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-out N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 84.0

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

   7. Applied rewrites 84.0%

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

Alternative 8: 46.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot x\right) \cdot i\\ \mathbf{if}\;x \leq -2 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;\left(y \cdot \left(\left(x \cdot 18\right) \cdot t\right)\right) \cdot z\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{elif}\;x \leq 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* -4.0 x) i)))
   (if (<= x -2e+227)
     t_1
     (if (<= x -1.8e+51)
       (* (* y (* (* x 18.0) t)) z)
       (if (<= x -7.8e-47)
         (fma (* k j) -27.0 (* b c))
         (if (<= x 1e+46) (fma (* -4.0 a) t (* (* k j) -27.0)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * x) * i;
	double tmp;
	if (x <= -2e+227) {
		tmp = t_1;
	} else if (x <= -1.8e+51) {
		tmp = (y * ((x * 18.0) * t)) * z;
	} else if (x <= -7.8e-47) {
		tmp = fma((k * j), -27.0, (b * c));
	} else if (x <= 1e+46) {
		tmp = fma((-4.0 * a), t, ((k * j) * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * x) * i)
	tmp = 0.0
	if (x <= -2e+227)
		tmp = t_1;
	elseif (x <= -1.8e+51)
		tmp = Float64(Float64(y * Float64(Float64(x * 18.0) * t)) * z);
	elseif (x <= -7.8e-47)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	elseif (x <= 1e+46)
		tmp = fma(Float64(-4.0 * a), t, Float64(Float64(k * j) * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[x, -2e+227], t$95$1, If[LessEqual[x, -1.8e+51], N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -7.8e-47], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+46], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.0000000000000002e227 or 9.9999999999999999e45 < x

   1. Initial program 81.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.1

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

   5. Applied rewrites 59.1%

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

   if -2.0000000000000002e227 < x < -1.80000000000000005e51

   1. Initial program 74.1%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 71.7%

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

   7. Applied rewrites 71.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 51.2%

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

   12. Applied rewrites 63.6%

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

   if -1.80000000000000005e51 < x < -7.79999999999999956e-47

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.9%

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

   if -7.79999999999999956e-47 < x < 9.9999999999999999e45

   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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 77.4

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 55.5%

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

Alternative 9: 58.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{elif}\;x \leq 4.55 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)))
   (if (<= x -1.95e+48)
     t_1
     (if (<= x -7.8e-47)
       (fma (* k j) -27.0 (* b c))
       (if (<= x 4.55e+18) (fma (* -4.0 a) t (* (* k j) -27.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	double tmp;
	if (x <= -1.95e+48) {
		tmp = t_1;
	} else if (x <= -7.8e-47) {
		tmp = fma((k * j), -27.0, (b * c));
	} else if (x <= 4.55e+18) {
		tmp = fma((-4.0 * a), t, ((k * j) * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x)
	tmp = 0.0
	if (x <= -1.95e+48)
		tmp = t_1;
	elseif (x <= -7.8e-47)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	elseif (x <= 4.55e+18)
		tmp = fma(Float64(-4.0 * a), t, Float64(Float64(k * j) * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.95e+48], t$95$1, If[LessEqual[x, -7.8e-47], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.55e+18], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95e48 or 4.55e18 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.5

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

   5. Applied rewrites 74.5%

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

   if -1.95e48 < x < -7.79999999999999956e-47

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.9%

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

   if -7.79999999999999956e-47 < x < 4.55e18

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 79.0

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.0%

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

Alternative 10: 36.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+159} \lor \neg \left(t\_1 \leq 1000000000000\right):\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -1e+159) (not (<= t_1 1000000000000.0)))
     (* (* -27.0 j) k)
     (* (* t a) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+159) || !(t_1 <= 1000000000000.0)) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (t * a) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-1d+159)) .or. (.not. (t_1 <= 1000000000000.0d0))) then
        tmp = ((-27.0d0) * j) * k
    else
        tmp = (t * a) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -1e+159) || !(t_1 <= 1000000000000.0)) {
		tmp = (-27.0 * j) * k;
	} else {
		tmp = (t * a) * -4.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -1e+159) or not (t_1 <= 1000000000000.0):
		tmp = (-27.0 * j) * k
	else:
		tmp = (t * a) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -1e+159) || !(t_1 <= 1000000000000.0))
		tmp = Float64(Float64(-27.0 * j) * k);
	else
		tmp = Float64(Float64(t * a) * -4.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -1e+159) || ~((t_1 <= 1000000000000.0)))
		tmp = (-27.0 * j) * k;
	else
		tmp = (t * a) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+159], N[Not[LessEqual[t$95$1, 1000000000000.0]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999993e158 or 1e12 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 92.0%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 53.8

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

   5. Applied rewrites 53.8%

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

   if -9.9999999999999993e158 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e12

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 26.9%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+159} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 1000000000000\right):\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+266}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -4.8e+266)
   (* x (* (* y z) (* 18.0 t)))
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -4.8e+266) {
		tmp = x * ((y * z) * (18.0 * t));
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -4.8e+266)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(18.0 * t)));
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -4.8e+266], N[(x * N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000003e266

   1. Initial program 75.6%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 88.1%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 69.6%

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

   12. Applied rewrites 87.5%

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

   if -4.80000000000000003e266 < y

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 81.0

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

   5. Applied rewrites 81.0%

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

Alternative 12: 72.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67} \lor \neg \left(t \leq 1.1 \cdot 10^{+100}\right):\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(\left(x \cdot y\right) \cdot -18, z, 4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.8e+67) (not (<= t 1.1e+100)))
   (* (- t) (fma (* (* x y) -18.0) z (* 4.0 a)))
   (fma (* -27.0 j) k (fma (* i x) -4.0 (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.8e+67) || !(t <= 1.1e+100)) {
		tmp = -t * fma(((x * y) * -18.0), z, (4.0 * a));
	} else {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3.8e+67) || !(t <= 1.1e+100))
		tmp = Float64(Float64(-t) * fma(Float64(Float64(x * y) * -18.0), z, Float64(4.0 * a)));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.8e+67], N[Not[LessEqual[t, 1.1e+100]], $MachinePrecision]], N[((-t) * N[(N[(N[(x * y), $MachinePrecision] * -18.0), $MachinePrecision] * z + N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8000000000000002e67 or 1.1e100 < t

   1. Initial program 86.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 61.0

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 50.2%

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

   9. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

          \[\leadsto -1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot a\right)\right) \]

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

          \[\leadsto -1 \cdot \left(t \cdot \color{blue}{\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + 4 \cdot a\right)}\right) \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + 4 \cdot a\right)} \]

       4. +-commutative N/A

          \[\leadsto \left(-1 \cdot t\right) \cdot \color{blue}{\left(4 \cdot a + -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

       5. metadata-eval N/A

          \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{\left(-1 \cdot -4\right)} \cdot a + -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

       6. associate-*r* N/A

          \[\leadsto \left(-1 \cdot t\right) \cdot \left(\color{blue}{-1 \cdot \left(-4 \cdot a\right)} + -18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

       7. metadata-eval N/A

          \[\leadsto \left(-1 \cdot t\right) \cdot \left(-1 \cdot \left(-4 \cdot a\right) + \color{blue}{\left(-1 \cdot 18\right)} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

       8. associate-*r* N/A

          \[\leadsto \left(-1 \cdot t\right) \cdot \left(-1 \cdot \left(-4 \cdot a\right) + \color{blue}{-1 \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

       9. distribute-lft-in N/A

          \[\leadsto \left(-1 \cdot t\right) \cdot \color{blue}{\left(-1 \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

       10. lower-*.f64 N/A

           \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-1 \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

       11. mul-1-neg N/A

           \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot \left(-1 \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) \]

       12. lower-neg.f64 N/A

           \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(-1 \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) \]

       13. distribute-lft-in N/A

           \[\leadsto \left(-t\right) \cdot \color{blue}{\left(-1 \cdot \left(-4 \cdot a\right) + -1 \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

       14. associate-*r* N/A

           \[\leadsto \left(-t\right) \cdot \left(\color{blue}{\left(-1 \cdot -4\right) \cdot a} + -1 \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) \]

       15. metadata-eval N/A

           \[\leadsto \left(-t\right) \cdot \left(\color{blue}{4} \cdot a + -1 \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) \]

       16. associate-*r* N/A

           \[\leadsto \left(-t\right) \cdot \left(4 \cdot a + \color{blue}{\left(-1 \cdot 18\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}\right) \]

       17. metadata-eval N/A

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

   11. Applied rewrites 80.7%

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

   if -3.8000000000000002e67 < t < 1.1e100

   1. Initial program 89.7%

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

   4. Applied rewrites 91.5%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 77.1

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

   7. Applied rewrites 77.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+67} \lor \neg \left(t \leq 1.1 \cdot 10^{+100}\right):\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(\left(x \cdot y\right) \cdot -18, z, 4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+102} \lor \neg \left(x \leq 8 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -5.6e+102) (not (<= x 8e+45)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* -27.0 j) k (fma (* t a) -4.0 (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -5.6e+102) || !(x <= 8e+45)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((-27.0 * j), k, fma((t * a), -4.0, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -5.6e+102) || !(x <= 8e+45))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(t * a), -4.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -5.6e+102], N[Not[LessEqual[x, 8e+45]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000037e102 or 7.9999999999999994e45 < x

   1. Initial program 79.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if -5.60000000000000037e102 < x < 7.9999999999999994e45

   1. Initial program 94.6%

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

   4. Applied rewrites 95.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 76.0

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

   7. Applied rewrites 76.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+102} \lor \neg \left(x \leq 8 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 77.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+266}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4, \mathsf{fma}\left(i, x, t \cdot a\right), b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -4.8e+266)
   (* x (* (* y z) (* 18.0 t)))
   (fma (* -27.0 j) k (fma -4.0 (fma i x (* t a)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -4.8e+266) {
		tmp = x * ((y * z) * (18.0 * t));
	} else {
		tmp = fma((-27.0 * j), k, fma(-4.0, fma(i, x, (t * a)), (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -4.8e+266)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(18.0 * t)));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(-4.0, fma(i, x, Float64(t * a)), Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -4.8e+266], N[(x * N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000003e266

   1. Initial program 75.6%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 81.8%

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

   7. Applied rewrites 88.1%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 69.6%

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

   12. Applied rewrites 87.5%

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

   if -4.80000000000000003e266 < y

   1. Initial program 89.5%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. associate-*l* N/A

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-out N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 81.0

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

   7. Applied rewrites 81.0%

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

Alternative 15: 47.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot x\right) \cdot i\\ \mathbf{if}\;x \leq -2 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;\left(y \cdot \left(\left(x \cdot 18\right) \cdot t\right)\right) \cdot z\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 x) i)))
   (if (<= x -2e+227)
     t_1
     (if (<= x -1.8e+51)
       (* (* y (* (* x 18.0) t)) z)
       (if (<= x 9.2e+53) (fma (* k j) -27.0 (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * x) * i;
	double tmp;
	if (x <= -2e+227) {
		tmp = t_1;
	} else if (x <= -1.8e+51) {
		tmp = (y * ((x * 18.0) * t)) * z;
	} else if (x <= 9.2e+53) {
		tmp = fma((k * j), -27.0, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * x) * i)
	tmp = 0.0
	if (x <= -2e+227)
		tmp = t_1;
	elseif (x <= -1.8e+51)
		tmp = Float64(Float64(y * Float64(Float64(x * 18.0) * t)) * z);
	elseif (x <= 9.2e+53)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[x, -2e+227], t$95$1, If[LessEqual[x, -1.8e+51], N[(N[(y * N[(N[(x * 18.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 9.2e+53], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0000000000000002e227 or 9.20000000000000079e53 < x

   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. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -2.0000000000000002e227 < x < -1.80000000000000005e51

   1. Initial program 74.1%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 71.7%

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

   7. Applied rewrites 71.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 51.2%

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

   12. Applied rewrites 63.6%

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

   if -1.80000000000000005e51 < x < 9.20000000000000079e53

   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. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.0%

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

Alternative 16: 46.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot x\right) \cdot i\\ \mathbf{if}\;x \leq -9 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 x) i)))
   (if (<= x -9e+226)
     t_1
     (if (<= x -1.8e+51)
       (* x (* (* y z) (* 18.0 t)))
       (if (<= x 9.2e+53) (fma (* k j) -27.0 (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * x) * i;
	double tmp;
	if (x <= -9e+226) {
		tmp = t_1;
	} else if (x <= -1.8e+51) {
		tmp = x * ((y * z) * (18.0 * t));
	} else if (x <= 9.2e+53) {
		tmp = fma((k * j), -27.0, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * x) * i)
	tmp = 0.0
	if (x <= -9e+226)
		tmp = t_1;
	elseif (x <= -1.8e+51)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(18.0 * t)));
	elseif (x <= 9.2e+53)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[x, -9e+226], t$95$1, If[LessEqual[x, -1.8e+51], N[(x * N[(N[(y * z), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+53], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999978e226 or 9.20000000000000079e53 < x

   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. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -8.99999999999999978e226 < x < -1.80000000000000005e51

   1. Initial program 74.1%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 71.7%

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

   7. Applied rewrites 71.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 51.2%

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

   12. Applied rewrites 58.7%

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

   if -1.80000000000000005e51 < x < 9.20000000000000079e53

   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. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.0%

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

Alternative 17: 47.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot x\right) \cdot i\\ \mathbf{if}\;x \leq -9 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 x) i)))
   (if (<= x -9e+226)
     t_1
     (if (<= x -4.8e+100)
       (* (* (* (* y z) x) t) 18.0)
       (if (<= x 9.2e+53) (fma (* k j) -27.0 (* b c)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * x) * i;
	double tmp;
	if (x <= -9e+226) {
		tmp = t_1;
	} else if (x <= -4.8e+100) {
		tmp = (((y * z) * x) * t) * 18.0;
	} else if (x <= 9.2e+53) {
		tmp = fma((k * j), -27.0, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * x) * i)
	tmp = 0.0
	if (x <= -9e+226)
		tmp = t_1;
	elseif (x <= -4.8e+100)
		tmp = Float64(Float64(Float64(Float64(y * z) * x) * t) * 18.0);
	elseif (x <= 9.2e+53)
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[x, -9e+226], t$95$1, If[LessEqual[x, -4.8e+100], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[x, 9.2e+53], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999978e226 or 9.20000000000000079e53 < x

   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. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -8.99999999999999978e226 < x < -4.80000000000000023e100

   1. Initial program 73.7%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. metadata-eval N/A

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

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

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 67.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 54.4%

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

   if -4.80000000000000023e100 < x < 9.20000000000000079e53

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 52.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+226}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -3.35 \cdot 10^{-22} \lor \neg \left(i \leq 1.4 \cdot 10^{+88}\right):\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -3.35e-22) (not (<= i 1.4e+88)))
   (* (* -4.0 x) i)
   (fma (* k j) -27.0 (* b c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -3.35e-22) || !(i <= 1.4e+88)) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = fma((k * j), -27.0, (b * c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -3.35e-22) || !(i <= 1.4e+88))
		tmp = Float64(Float64(-4.0 * x) * i);
	else
		tmp = fma(Float64(k * j), -27.0, Float64(b * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -3.35e-22], N[Not[LessEqual[i, 1.4e+88]], $MachinePrecision]], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.34999999999999996e-22 or 1.39999999999999994e88 < i

   1. Initial program 83.4%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 50.0

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

   5. Applied rewrites 50.0%

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

   if -3.34999999999999996e-22 < i < 1.39999999999999994e88

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.35 \cdot 10^{-22} \lor \neg \left(i \leq 1.4 \cdot 10^{+88}\right):\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -3.35 \cdot 10^{-22} \lor \neg \left(i \leq 0.0037\right):\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -3.35e-22) (not (<= i 0.0037)))
   (* (* -4.0 x) i)
   (* (* -27.0 j) k)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -3.35e-22) || !(i <= 0.0037)) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 ((i <= (-3.35d-22)) .or. (.not. (i <= 0.0037d0))) then
        tmp = ((-4.0d0) * x) * i
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((i <= -3.35e-22) || !(i <= 0.0037)) {
		tmp = (-4.0 * x) * i;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -3.35e-22) or not (i <= 0.0037):
		tmp = (-4.0 * x) * i
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -3.35e-22) || !(i <= 0.0037))
		tmp = Float64(Float64(-4.0 * x) * i);
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -3.35e-22) || ~((i <= 0.0037)))
		tmp = (-4.0 * x) * i;
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -3.35e-22], N[Not[LessEqual[i, 0.0037]], $MachinePrecision]], N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.34999999999999996e-22 or 0.0037000000000000002 < i

   1. Initial program 85.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 46.6

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

   5. Applied rewrites 46.6%

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

   if -3.34999999999999996e-22 < i < 0.0037000000000000002

   1. Initial program 92.4%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 34.2

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

   5. Applied rewrites 34.2%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.35 \cdot 10^{-22} \lor \neg \left(i \leq 0.0037\right):\\ \;\;\;\;\left(-4 \cdot x\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \left(t \cdot a\right) \cdot -4 \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (t * a) * -4.0;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (t * a) * (-4.0d0)
end function

Java

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

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return (t * a) * -4.0

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(t * a) * -4.0)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (t * a) * -4.0;
end

Wolfram

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

Derivation

1. Initial program 88.6%

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

3. Taylor expanded in x around 0

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

   1. associate--r+ N/A

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

   2. lower--.f64 N/A

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

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

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

   4. metadata-eval N/A

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

   5. +-commutative N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 57.5

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

5. Applied rewrites 57.5%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 22.2%

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

Developer Target 1: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024339 
(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)))