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

Percentage Accurate: 85.2% → 90.5%

Time: 13.8s

Alternatives: 23

Speedup: 0.5×

• 50.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

   4. Applied rewrites 96.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 72.7%

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

   7. Applied rewrites 77.3%

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

4. Final simplification 95.0%

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

Alternative 2: 90.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 96.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 72.7%

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

   7. Applied rewrites 77.3%

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

Alternative 3: 90.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.7%

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

   4. Applied rewrites 96.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 72.7%

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

   7. Applied rewrites 77.3%

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

Alternative 4: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\\ t_2 := \mathsf{fma}\left(c, b, \left(i \cdot x\right) \cdot -4\right)\\ t_3 := \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ t_4 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_4 \leq -2 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 10^{-130}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* k j) (* b c)))
        (t_2 (fma c b (* (* i x) -4.0)))
        (t_3 (fma c b (* (* a t) -4.0)))
        (t_4 (* (* j 27.0) k)))
   (if (<= t_4 -2e+248)
     t_1
     (if (<= t_4 -4e-106)
       t_3
       (if (<= t_4 -1e-196)
         t_2
         (if (<= t_4 1e-130) t_3 (if (<= t_4 2e+150) t_2 t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (k * j), (b * c));
	double t_2 = fma(c, b, ((i * x) * -4.0));
	double t_3 = fma(c, b, ((a * t) * -4.0));
	double t_4 = (j * 27.0) * k;
	double tmp;
	if (t_4 <= -2e+248) {
		tmp = t_1;
	} else if (t_4 <= -4e-106) {
		tmp = t_3;
	} else if (t_4 <= -1e-196) {
		tmp = t_2;
	} else if (t_4 <= 1e-130) {
		tmp = t_3;
	} else if (t_4 <= 2e+150) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(k * j), Float64(b * c))
	t_2 = fma(c, b, Float64(Float64(i * x) * -4.0))
	t_3 = fma(c, b, Float64(Float64(a * t) * -4.0))
	t_4 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_4 <= -2e+248)
		tmp = t_1;
	elseif (t_4 <= -4e-106)
		tmp = t_3;
	elseif (t_4 <= -1e-196)
		tmp = t_2;
	elseif (t_4 <= 1e-130)
		tmp = t_3;
	elseif (t_4 <= 2e+150)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * b + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$4, -2e+248], t$95$1, If[LessEqual[t$95$4, -4e-106], t$95$3, If[LessEqual[t$95$4, -1e-196], t$95$2, If[LessEqual[t$95$4, 1e-130], t$95$3, If[LessEqual[t$95$4, 2e+150], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e248 or 1.99999999999999996e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.0%

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

   3. Taylor expanded in x around 0

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

      1. 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 86.3

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

   5. Applied rewrites 86.3%

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

   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 79.2%

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

   if -2.00000000000000009e248 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999976e-106 or -1e-196 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e-130

   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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 92.5%

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

   6. Applied rewrites 87.8%

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

   7. Taylor expanded in j around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. associate-+l+ N/A

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

      5. associate-*r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

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

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

      16. +-commutative N/A

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

      17. distribute-lft-out N/A

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

      18. lower-*.f64 N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 92.1

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

   9. Applied rewrites 92.1%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 57.7%

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

   if -3.99999999999999976e-106 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-196 or 1.0000000000000001e-130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999996e150

   1. Initial program 90.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 5.4

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

   5. Applied rewrites 5.4%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 72.5

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

   8. Applied rewrites 72.5%

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

   9. Taylor expanded in j around 0

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

   11. Applied rewrites 67.8%

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

   13. Applied rewrites 69.4%

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

Alternative 5: 33.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot a\right) \cdot t\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+248}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-196}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+233}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 a) t)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+248)
     (* (* k -27.0) j)
     (if (<= t_2 -4e-106)
       t_1
       (if (<= t_2 -1e-196)
         (* (* i x) -4.0)
         (if (<= t_2 2e-33)
           t_1
           (if (<= t_2 5e+233) (* b c) (* (* -27.0 j) k))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+248) {
		tmp = (k * -27.0) * j;
	} else if (t_2 <= -4e-106) {
		tmp = t_1;
	} else if (t_2 <= -1e-196) {
		tmp = (i * x) * -4.0;
	} else if (t_2 <= 2e-33) {
		tmp = t_1;
	} else if (t_2 <= 5e+233) {
		tmp = b * c;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-4.0d0) * a) * t
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+248)) then
        tmp = (k * (-27.0d0)) * j
    else if (t_2 <= (-4d-106)) then
        tmp = t_1
    else if (t_2 <= (-1d-196)) then
        tmp = (i * x) * (-4.0d0)
    else if (t_2 <= 2d-33) then
        tmp = t_1
    else if (t_2 <= 5d+233) then
        tmp = b * c
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * a) * t;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+248) {
		tmp = (k * -27.0) * j;
	} else if (t_2 <= -4e-106) {
		tmp = t_1;
	} else if (t_2 <= -1e-196) {
		tmp = (i * x) * -4.0;
	} else if (t_2 <= 2e-33) {
		tmp = t_1;
	} else if (t_2 <= 5e+233) {
		tmp = b * c;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * a) * t
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+248:
		tmp = (k * -27.0) * j
	elif t_2 <= -4e-106:
		tmp = t_1
	elif t_2 <= -1e-196:
		tmp = (i * x) * -4.0
	elif t_2 <= 2e-33:
		tmp = t_1
	elif t_2 <= 5e+233:
		tmp = b * c
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * a) * t)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+248)
		tmp = Float64(Float64(k * -27.0) * j);
	elseif (t_2 <= -4e-106)
		tmp = t_1;
	elseif (t_2 <= -1e-196)
		tmp = Float64(Float64(i * x) * -4.0);
	elseif (t_2 <= 2e-33)
		tmp = t_1;
	elseif (t_2 <= 5e+233)
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * a) * t;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+248)
		tmp = (k * -27.0) * j;
	elseif (t_2 <= -4e-106)
		tmp = t_1;
	elseif (t_2 <= -1e-196)
		tmp = (i * x) * -4.0;
	elseif (t_2 <= 2e-33)
		tmp = t_1;
	elseif (t_2 <= 5e+233)
		tmp = b * c;
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+248], N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$2, -4e-106], t$95$1, If[LessEqual[t$95$2, -1e-196], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$2, 2e-33], t$95$1, If[LessEqual[t$95$2, 5e+233], N[(b * c), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e248

   1. Initial program 77.7%

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

   3. Taylor expanded in 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 71.2

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

   5. Applied rewrites 71.2%

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

   7. Applied rewrites 71.2%

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

   if -2.00000000000000009e248 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999976e-106 or -1e-196 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e-33

   1. Initial program 89.8%

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

   3. Taylor expanded in 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 60.4

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

   5. Applied rewrites 60.4%

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

   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 28.4%

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

   9. Taylor expanded in t around inf

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 59.8

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

   11. Applied rewrites 59.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 37.2%

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]

   if -3.99999999999999976e-106 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-196

   1. Initial program 86.6%

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

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 86.7

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 86.7%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 78.9

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

   7. Applied rewrites 78.9%

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

   if 2.0000000000000001e-33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000009e233

   1. Initial program 91.6%

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

   3. Taylor expanded in 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 14.6

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

   5. Applied rewrites 14.6%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 74.9

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

   8. Applied rewrites 74.9%

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

   9. Taylor expanded in j around 0

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

   11. Applied rewrites 62.6%

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

   12. Taylor expanded in x around 0

       \[\leadsto b \cdot c \]
   13. Step-by-step derivation

   14. Applied rewrites 41.4%

       \[\leadsto b \cdot c \]

   if 5.00000000000000009e233 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 87.6

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

   5. Applied rewrites 87.6%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 33.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-27 \cdot j\right) \cdot k\\ t_2 := \left(-4 \cdot a\right) \cdot t\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-196}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+233}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -27.0 j) k)) (t_2 (* (* -4.0 a) t)) (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -2e+248)
     t_1
     (if (<= t_3 -4e-106)
       t_2
       (if (<= t_3 -1e-196)
         (* (* i x) -4.0)
         (if (<= t_3 2e-33) t_2 (if (<= t_3 5e+233) (* b c) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-27.0 * j) * k;
	double t_2 = (-4.0 * a) * t;
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -2e+248) {
		tmp = t_1;
	} else if (t_3 <= -4e-106) {
		tmp = t_2;
	} else if (t_3 <= -1e-196) {
		tmp = (i * x) * -4.0;
	} else if (t_3 <= 2e-33) {
		tmp = t_2;
	} else if (t_3 <= 5e+233) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((-27.0d0) * j) * k
    t_2 = ((-4.0d0) * a) * t
    t_3 = (j * 27.0d0) * k
    if (t_3 <= (-2d+248)) then
        tmp = t_1
    else if (t_3 <= (-4d-106)) then
        tmp = t_2
    else if (t_3 <= (-1d-196)) then
        tmp = (i * x) * (-4.0d0)
    else if (t_3 <= 2d-33) then
        tmp = t_2
    else if (t_3 <= 5d+233) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = (-27.0 * j) * k;
	double t_2 = (-4.0 * a) * t;
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -2e+248) {
		tmp = t_1;
	} else if (t_3 <= -4e-106) {
		tmp = t_2;
	} else if (t_3 <= -1e-196) {
		tmp = (i * x) * -4.0;
	} else if (t_3 <= 2e-33) {
		tmp = t_2;
	} else if (t_3 <= 5e+233) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 = (-27.0 * j) * k
	t_2 = (-4.0 * a) * t
	t_3 = (j * 27.0) * k
	tmp = 0
	if t_3 <= -2e+248:
		tmp = t_1
	elif t_3 <= -4e-106:
		tmp = t_2
	elif t_3 <= -1e-196:
		tmp = (i * x) * -4.0
	elif t_3 <= 2e-33:
		tmp = t_2
	elif t_3 <= 5e+233:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-27.0 * j) * k)
	t_2 = Float64(Float64(-4.0 * a) * t)
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -2e+248)
		tmp = t_1;
	elseif (t_3 <= -4e-106)
		tmp = t_2;
	elseif (t_3 <= -1e-196)
		tmp = Float64(Float64(i * x) * -4.0);
	elseif (t_3 <= 2e-33)
		tmp = t_2;
	elseif (t_3 <= 5e+233)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = (-27.0 * j) * k;
	t_2 = (-4.0 * a) * t;
	t_3 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_3 <= -2e+248)
		tmp = t_1;
	elseif (t_3 <= -4e-106)
		tmp = t_2;
	elseif (t_3 <= -1e-196)
		tmp = (i * x) * -4.0;
	elseif (t_3 <= 2e-33)
		tmp = t_2;
	elseif (t_3 <= 5e+233)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+248], t$95$1, If[LessEqual[t$95$3, -4e-106], t$95$2, If[LessEqual[t$95$3, -1e-196], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$3, 2e-33], t$95$2, If[LessEqual[t$95$3, 5e+233], N[(b * c), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e248 or 5.00000000000000009e233 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 78.6

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

   5. Applied rewrites 78.6%

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

   if -2.00000000000000009e248 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -3.99999999999999976e-106 or -1e-196 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e-33

   1. Initial program 89.8%

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

   3. Taylor expanded in 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 60.4

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

   5. Applied rewrites 60.4%

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

   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 28.4%

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

   9. Taylor expanded in t around inf

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 59.8

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

   11. Applied rewrites 59.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 37.2%

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]

   if -3.99999999999999976e-106 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-196

   1. Initial program 86.6%

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

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

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

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. metadata-eval 86.7

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. *-commutative N/A

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

   4. Applied rewrites 86.7%

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

   5. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 78.9

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

   7. Applied rewrites 78.9%

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

   if 2.0000000000000001e-33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000009e233

   1. Initial program 91.6%

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

   3. Taylor expanded in 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 14.6

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

   5. Applied rewrites 14.6%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 74.9

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

   8. Applied rewrites 74.9%

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

   9. Taylor expanded in j around 0

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

   11. Applied rewrites 62.6%

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

   12. Taylor expanded in x around 0

       \[\leadsto b \cdot c \]
   13. Step-by-step derivation

   14. Applied rewrites 41.4%

       \[\leadsto b \cdot c \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot x\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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)) (t_2 (* -4.0 (fma i x (* a t)))))
   (if (<= t_1 -1e+162)
     (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* y x) z) 18.0)) t (* c b)))
     (if (<= t_1 4e+45)
       (fma c b (fma (* 18.0 t) (* (* z y) x) t_2))
       (- (fma c b t_2) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = -4.0 * fma(i, x, (a * t));
	double tmp;
	if (t_1 <= -1e+162) {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((y * x) * z) * 18.0)), t, (c * b)));
	} else if (t_1 <= 4e+45) {
		tmp = fma(c, b, fma((18.0 * t), ((z * y) * x), t_2));
	} else {
		tmp = fma(c, b, t_2) - t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(-4.0 * fma(i, x, Float64(a * t)))
	tmp = 0.0
	if (t_1 <= -1e+162)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(y * x) * z) * 18.0)), t, Float64(c * b)));
	elseif (t_1 <= 4e+45)
		tmp = fma(c, b, fma(Float64(18.0 * t), Float64(Float64(z * y) * x), t_2));
	else
		tmp = Float64(fma(c, b, t_2) - t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+162], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+45], N[(c * b + N[(N[(18.0 * t), $MachinePrecision] * N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c * b + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999994e161

   1. Initial program 81.0%

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

   3. Taylor expanded in i around 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 94.5%

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

   7. Applied rewrites 97.2%

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

   if -9.9999999999999994e161 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999997e45

   1. Initial program 90.7%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 91.9%

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

   6. Applied rewrites 88.3%

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

   7. Taylor expanded in j around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. associate-+l+ N/A

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

      5. associate-*r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

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

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

      16. +-commutative N/A

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

      17. distribute-lft-out N/A

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

      18. lower-*.f64 N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 92.3

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

   9. Applied rewrites 92.3%

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

   if 3.9999999999999997e45 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.9%

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

   3. Taylor expanded in 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 90.0

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

   5. Applied rewrites 90.0%

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

Alternative 8: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* k j) (* b c))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+248)
     t_1
     (if (<= t_2 -1e+158)
       (* (* -4.0 a) t)
       (if (<= t_2 2e+150) (fma c b (* (* i x) -4.0)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (k * j), (b * c));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+248) {
		tmp = t_1;
	} else if (t_2 <= -1e+158) {
		tmp = (-4.0 * a) * t;
	} else if (t_2 <= 2e+150) {
		tmp = fma(c, b, ((i * x) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(k * j), Float64(b * c))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+248)
		tmp = t_1;
	elseif (t_2 <= -1e+158)
		tmp = Float64(Float64(-4.0 * a) * t);
	elseif (t_2 <= 2e+150)
		tmp = fma(c, b, Float64(Float64(i * x) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+248], t$95$1, If[LessEqual[t$95$2, -1e+158], N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, 2e+150], N[(c * b + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e248 or 1.99999999999999996e150 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.0%

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

   3. Taylor expanded in x around 0

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

      1. 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 86.3

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

   5. Applied rewrites 86.3%

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

   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 79.2%

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

   if -2.00000000000000009e248 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999953e157

   1. Initial program 91.7%

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

   3. Taylor expanded in 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 83.3

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

   5. Applied rewrites 83.3%

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

   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 20.7%

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

   9. Taylor expanded in t around inf

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 82.8

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

   11. Applied rewrites 82.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 66.3%

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]

   if -9.99999999999999953e157 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999996e150

   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. 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 3.9

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

   5. Applied rewrites 3.9%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 55.2

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

   8. Applied rewrites 55.2%

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

   9. Taylor expanded in j around 0

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

   11. Applied rewrites 52.8%

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

   13. Applied rewrites 53.4%

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

Alternative 9: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+248}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+233}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+248)
     (* (* k -27.0) j)
     (if (<= t_1 -1e+158)
       (* (* -4.0 a) t)
       (if (<= t_1 5e+233) (fma (* -4.0 i) x (* b c)) (* (* -27.0 j) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+248) {
		tmp = (k * -27.0) * j;
	} else if (t_1 <= -1e+158) {
		tmp = (-4.0 * a) * t;
	} else if (t_1 <= 5e+233) {
		tmp = fma((-4.0 * i), x, (b * c));
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+248)
		tmp = Float64(Float64(k * -27.0) * j);
	elseif (t_1 <= -1e+158)
		tmp = Float64(Float64(-4.0 * a) * t);
	elseif (t_1 <= 5e+233)
		tmp = fma(Float64(-4.0 * i), x, Float64(b * c));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+248], N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, -1e+158], N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 5e+233], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e248

   1. Initial program 77.7%

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

   3. Taylor expanded in 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 71.2

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

   5. Applied rewrites 71.2%

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

   7. Applied rewrites 71.2%

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

   if -2.00000000000000009e248 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999953e157

   1. Initial program 91.7%

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

   3. Taylor expanded in 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 83.3

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

   5. Applied rewrites 83.3%

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

   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 20.7%

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

   9. Taylor expanded in t around inf

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 82.8

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

   11. Applied rewrites 82.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 66.3%

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]

   if -9.99999999999999953e157 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000009e233

   1. Initial program 89.9%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 6.2

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

   5. Applied rewrites 6.2%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 57.3

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

   8. Applied rewrites 57.3%

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

   9. Taylor expanded in j around 0

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

   11. Applied rewrites 53.2%

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

   if 5.00000000000000009e233 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 87.6

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

   5. Applied rewrites 87.6%

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

Alternative 10: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+248}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+233}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+248)
     (* (* k -27.0) j)
     (if (<= t_1 -1e+158)
       (* (* -4.0 a) t)
       (if (<= t_1 5e+233) (fma c b (* (* i x) -4.0)) (* (* -27.0 j) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+248) {
		tmp = (k * -27.0) * j;
	} else if (t_1 <= -1e+158) {
		tmp = (-4.0 * a) * t;
	} else if (t_1 <= 5e+233) {
		tmp = fma(c, b, ((i * x) * -4.0));
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+248)
		tmp = Float64(Float64(k * -27.0) * j);
	elseif (t_1 <= -1e+158)
		tmp = Float64(Float64(-4.0 * a) * t);
	elseif (t_1 <= 5e+233)
		tmp = fma(c, b, Float64(Float64(i * x) * -4.0));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+248], N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, -1e+158], N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 5e+233], N[(c * b + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000009e248

   1. Initial program 77.7%

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

   3. Taylor expanded in 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 71.2

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

   5. Applied rewrites 71.2%

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

   7. Applied rewrites 71.2%

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

   if -2.00000000000000009e248 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999953e157

   1. Initial program 91.7%

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

   3. Taylor expanded in 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 83.3

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

   5. Applied rewrites 83.3%

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

   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 20.7%

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

   9. Taylor expanded in t around inf

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 82.8

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

   11. Applied rewrites 82.8%

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

   12. Taylor expanded in x around 0

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 66.3%

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]

   if -9.99999999999999953e157 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.00000000000000009e233

   1. Initial program 89.9%

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

   3. Taylor expanded in j around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 6.2

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

   5. Applied rewrites 6.2%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 57.3

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

   8. Applied rewrites 57.3%

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

   9. Taylor expanded in j around 0

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

   11. Applied rewrites 53.2%

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

   13. Applied rewrites 53.2%

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

   if 5.00000000000000009e233 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 87.6

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

   5. Applied rewrites 87.6%

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

Alternative 11: 84.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -2.45 \cdot 10^{+176} \lor \neg \left(i \leq 6 \cdot 10^{-31}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot x\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -2.45e+176) (not (<= i 6e-31)))
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
   (fma (* -27.0 j) k (fma (fma -4.0 a (* (* (* y x) z) 18.0)) t (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -2.45e+176) || !(i <= 6e-31)) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(-4.0, a, (((y * x) * z) * 18.0)), t, (c * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -2.45e+176) || !(i <= 6e-31))
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(-4.0, a, Float64(Float64(Float64(y * x) * z) * 18.0)), t, Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -2.45e+176], N[Not[LessEqual[i, 6e-31]], $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], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * a + N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.45e176 or 5.99999999999999962e-31 < i

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if -2.45e176 < i < 5.99999999999999962e-31

   1. Initial program 87.1%

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

   3. Taylor expanded in 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 90.6%

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

   7. Applied rewrites 91.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.45 \cdot 10^{+176} \lor \neg \left(i \leq 6 \cdot 10^{-31}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(y \cdot x\right) \cdot z\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+237} \lor \neg \left(y \leq 5.4 \cdot 10^{-34}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= y -1.3e+237) (not (<= y 5.4e-34)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((y <= -1.3e+237) || !(y <= 5.4e-34)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((y <= -1.3e+237) || !(y <= 5.4e-34))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[y, -1.3e+237], N[Not[LessEqual[y, 5.4e-34]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $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 < -1.30000000000000001e237 or 5.40000000000000034e-34 < y

   1. Initial program 82.7%

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

   3. Taylor expanded in 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 55.4

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

   5. Applied rewrites 55.4%

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

   if -1.30000000000000001e237 < y < 5.40000000000000034e-34

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-lft-out N/A

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

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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 85.9

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

   5. Applied rewrites 85.9%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+237} \lor \neg \left(y \leq 5.4 \cdot 10^{-34}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 79.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+205}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot y, x \cdot \left(t \cdot z\right), \left(a \cdot t\right) \cdot -4\right)\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -3.5e+205)
   (fma c b (fma (* 18.0 y) (* x (* t z)) (* (* a t) -4.0)))
   (if (<= y 5.4e-34)
     (- (fma c b (* -4.0 (fma i x (* a t)))) (* (* j 27.0) k))
     (* (fma -4.0 i (* (* (* z y) t) 18.0)) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -3.5e+205) {
		tmp = fma(c, b, fma((18.0 * y), (x * (t * z)), ((a * t) * -4.0)));
	} else if (y <= 5.4e-34) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t)))) - ((j * 27.0) * k);
	} else {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -3.5e+205)
		tmp = fma(c, b, fma(Float64(18.0 * y), Float64(x * Float64(t * z)), Float64(Float64(a * t) * -4.0)));
	elseif (y <= 5.4e-34)
		tmp = Float64(fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -3.5e+205], N[(c * b + N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-34], N[(N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4999999999999998e205

   1. Initial program 95.8%

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

      1. 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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 95.8%

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 87.9

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

   9. Applied rewrites 87.9%

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

   if -3.4999999999999998e205 < y < 5.40000000000000034e-34

   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. 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 85.8

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

   5. Applied rewrites 85.8%

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

   if 5.40000000000000034e-34 < y

   1. Initial program 79.8%

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

   3. Taylor expanded in 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 50.3

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

   5. Applied rewrites 50.3%

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

Alternative 14: 72.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;t \leq -2 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i \cdot -4, x, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot t, a, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j k) -27.0)))
   (if (<= t -2e+72)
     (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
     (if (<= t 1.4e+85)
       (fma c b (fma (* i -4.0) x t_1))
       (fma c b (fma (* -4.0 t) a t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * k) * -27.0;
	double tmp;
	if (t <= -2e+72) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= 1.4e+85) {
		tmp = fma(c, b, fma((i * -4.0), x, t_1));
	} else {
		tmp = fma(c, b, fma((-4.0 * t), a, t_1));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (t <= -2e+72)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 1.4e+85)
		tmp = fma(c, b, fma(Float64(i * -4.0), x, t_1));
	else
		tmp = fma(c, b, fma(Float64(-4.0 * t), a, t_1));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[t, -2e+72], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 1.4e+85], N[(c * b + N[(N[(i * -4.0), $MachinePrecision] * x + t$95$1), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(-4.0 * t), $MachinePrecision] * a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999989e72

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 76.6

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

   8. Applied rewrites 76.6%

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

   if -1.99999999999999989e72 < t < 1.4e85

   1. Initial program 90.7%

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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 90.7%

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

   6. Applied rewrites 94.5%

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

   7. Taylor expanded in j around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. associate-+l+ N/A

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

      5. associate-*r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

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

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

      16. +-commutative N/A

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

      17. distribute-lft-out N/A

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

      18. lower-*.f64 N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 73.7

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

   9. Applied rewrites 73.7%

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

   10. Taylor expanded in t around 0

       \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)}\right) \]
   11. Step-by-step derivation

       1. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right)\right) + -1 \cdot \left(27 \cdot \left(j \cdot k\right)\right)}\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-1 \cdot 4\right) \cdot \left(i \cdot x\right)} + -1 \cdot \left(27 \cdot \left(j \cdot k\right)\right)\right) \]

       3. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{-4} \cdot \left(i \cdot x\right) + -1 \cdot \left(27 \cdot \left(j \cdot k\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot i\right) \cdot x} + -1 \cdot \left(27 \cdot \left(j \cdot k\right)\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x + \color{blue}{\left(-1 \cdot 27\right) \cdot \left(j \cdot k\right)}\right) \]

       6. metadata-eval N/A

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

       7. lower-fma.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 N/A

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

       10. *-commutative N/A

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

       11. lower-*.f64 N/A

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

       12. lower-*.f64 77.7

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

   12. Applied rewrites 77.7%

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

   if 1.4e85 < t

   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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 94.1%

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

   6. Applied rewrites 82.7%

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

   7. Taylor expanded in j around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. associate-+l+ N/A

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

      5. associate-*r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

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

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

      16. +-commutative N/A

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

      17. distribute-lft-out N/A

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

      18. lower-*.f64 N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 86.5

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

   9. Applied rewrites 86.5%

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

   10. Taylor expanded in x around 0

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

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

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. metadata-eval N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 N/A

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

       7. *-commutative N/A

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

       8. lower-*.f64 N/A

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

       9. lower-*.f64 76.7

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

   12. Applied rewrites 76.7%

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

Alternative 15: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(x \cdot -4\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4 \cdot t, a, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2e+72)
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (if (<= t 1.4e+85)
     (fma c b (fma (* -27.0 j) k (* (* x -4.0) i)))
     (fma c b (fma (* -4.0 t) a (* (* j k) -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2e+72) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= 1.4e+85) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((x * -4.0) * i)));
	} else {
		tmp = fma(c, b, fma((-4.0 * t), a, ((j * k) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2e+72)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 1.4e+85)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(x * -4.0) * i)));
	else
		tmp = fma(c, b, fma(Float64(-4.0 * t), a, Float64(Float64(j * k) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2e+72], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 1.4e+85], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(x * -4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999989e72

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 76.6

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

   8. Applied rewrites 76.6%

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

   if -1.99999999999999989e72 < t < 1.4e85

   1. Initial program 90.7%

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

   3. Taylor expanded in 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 23.7

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

   5. Applied rewrites 23.7%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 77.6

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

   8. Applied rewrites 77.6%

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

   10. Applied rewrites 77.6%

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

   if 1.4e85 < t

   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

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

      3. associate--l- N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate--l+ N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

   4. Applied rewrites 94.1%

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

   6. Applied rewrites 82.7%

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

   7. Taylor expanded in j around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. associate-+l+ N/A

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

      5. associate-*r* N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

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

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

      16. +-commutative N/A

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

      17. distribute-lft-out N/A

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

      18. lower-*.f64 N/A

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

      19. lower-fma.f64 N/A

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

      20. lower-*.f64 86.5

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

   9. Applied rewrites 86.5%

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

   10. Taylor expanded in x around 0

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

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

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. metadata-eval N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 N/A

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

       7. *-commutative N/A

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

       8. lower-*.f64 N/A

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

       9. lower-*.f64 76.7

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

   12. Applied rewrites 76.7%

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

Alternative 16: 71.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(x \cdot -4\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2e+72)
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (if (<= t 2.6e-39)
     (fma c b (fma (* -27.0 j) k (* (* x -4.0) i)))
     (fma (* k -27.0) j (fma (* t a) -4.0 (* b c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2e+72) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= 2.6e-39) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((x * -4.0) * i)));
	} else {
		tmp = fma((k * -27.0), j, fma((t * a), -4.0, (b * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -2e+72)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 2.6e-39)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(x * -4.0) * i)));
	else
		tmp = fma(Float64(k * -27.0), j, fma(Float64(t * a), -4.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -2e+72], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.6e-39], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(x * -4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999989e72

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 76.6

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

   8. Applied rewrites 76.6%

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

   if -1.99999999999999989e72 < t < 2.6e-39

   1. Initial program 91.3%

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

   3. Taylor expanded in 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 23.2

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

   5. Applied rewrites 23.2%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 80.4

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

   8. Applied rewrites 80.4%

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

   10. Applied rewrites 80.5%

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

   if 2.6e-39 < t

   1. Initial program 89.3%

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

   3. Taylor expanded in 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 70.6

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

   5. Applied rewrites 70.6%

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

   7. Applied rewrites 72.0%

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

Alternative 17: 73.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(-27 \cdot j, k, \left(x \cdot -4\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -2e+72)
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (if (<= t 8.8e+85)
     (fma c b (fma (* -27.0 j) k (* (* x -4.0) i)))
     (* (fma (* z y) (* x 18.0) (* -4.0 a)) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -2e+72) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= 8.8e+85) {
		tmp = fma(c, b, fma((-27.0 * j), k, ((x * -4.0) * i)));
	} else {
		tmp = fma((z * y), (x * 18.0), (-4.0 * a)) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2e+72)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 8.8e+85)
		tmp = fma(c, b, fma(Float64(-27.0 * j), k, Float64(Float64(x * -4.0) * i)));
	else
		tmp = Float64(fma(Float64(z * y), Float64(x * 18.0), Float64(-4.0 * a)) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2e+72], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 8.8e+85], N[(c * b + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(x * -4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * N[(x * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999989e72

   1. Initial program 81.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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 18.8

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

   5. Applied rewrites 18.8%

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

   6. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 76.6

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

   8. Applied rewrites 76.6%

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

   if -1.99999999999999989e72 < t < 8.8000000000000007e85

   1. Initial program 90.7%

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

   3. Taylor expanded in 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 23.7

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

   5. Applied rewrites 23.7%

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

   6. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot x}, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      15. lower-*.f64 77.6

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, \color{blue}{b \cdot c}\right)\right) \]

   8. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 77.6%

       \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, \mathsf{fma}\left(-27 \cdot j, k, \left(x \cdot -4\right) \cdot i\right)\right) \]

   if 8.8000000000000007e85 < t

   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. 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 74.8

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   5. Applied rewrites 74.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

   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 23.8%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

       2. metadata-eval N/A

          \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

       3. +-commutative N/A

          \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       6. +-commutative N/A

          \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

       7. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

       8. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

       9. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       10. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       12. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       13. lower-*.f64 69.5

           \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   11. Applied rewrites 69.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]
   12. Step-by-step derivation

   13. Applied rewrites 69.5%

       \[\leadsto \mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+57} \lor \neg \left(t \leq 9 \cdot 10^{+64}\right):\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -3e+57) (not (<= t 9e+64)))
   (* (fma (* z y) (* x 18.0) (* -4.0 a)) t)
   (fma (* -4.0 i) x (* b c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3e+57) || !(t <= 9e+64)) {
		tmp = fma((z * y), (x * 18.0), (-4.0 * a)) * t;
	} else {
		tmp = fma((-4.0 * i), x, (b * c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3e+57) || !(t <= 9e+64))
		tmp = Float64(fma(Float64(z * y), Float64(x * 18.0), Float64(-4.0 * a)) * t);
	else
		tmp = fma(Float64(-4.0 * i), x, Float64(b * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3e+57], N[Not[LessEqual[t, 9e+64]], $MachinePrecision]], N[(N[(N[(z * y), $MachinePrecision] * N[(x * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e57 or 8.99999999999999946e64 < t

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. 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 68.0

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   5. Applied rewrites 68.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

   6. Taylor expanded in t around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 28.3%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

       2. metadata-eval N/A

          \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

       3. +-commutative N/A

          \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       6. +-commutative N/A

          \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

       7. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

       8. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

       9. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       10. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       12. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       13. lower-*.f64 71.7

           \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   11. Applied rewrites 71.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]
   12. Step-by-step derivation

   13. Applied rewrites 71.7%

       \[\leadsto \mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t \]

   if -3e57 < t < 8.99999999999999946e64

   1. Initial program 90.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      3. lower-*.f64 23.5

         \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

   5. Applied rewrites 23.5%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate--l+ N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot x}, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      15. lower-*.f64 78.4

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, \color{blue}{b \cdot c}\right)\right) \]

   8. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
   10. Step-by-step derivation

   11. Applied rewrites 60.5%

       \[\leadsto \mathsf{fma}\left(-4 \cdot i, \color{blue}{x}, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+57} \lor \neg \left(t \leq 9 \cdot 10^{+64}\right):\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+50} \lor \neg \left(x \leq 7 \cdot 10^{+15}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -7e+50) (not (<= x 7e+15)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma c b (* (* a t) -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -7e+50) || !(x <= 7e+15)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma(c, b, ((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])
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 <= -7e+50) || !(x <= 7e+15))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(c, b, Float64(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.
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, -7e+50], N[Not[LessEqual[x, 7e+15]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.00000000000000012e50 or 7e15 < x

   1. Initial program 78.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-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 73.3

          \[\leadsto \mathsf{fma}\left(-4, i, \left(\color{blue}{\left(z \cdot y\right)} \cdot t\right) \cdot 18\right) \cdot x \]

   5. Applied rewrites 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x} \]

   if -7.00000000000000012e50 < x < 7e15

   1. Initial program 95.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      3. associate--l- N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      4. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      6. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot c + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot c} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot b} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right) \cdot t - \mathsf{fma}\left(k, 27 \cdot j, i \cdot \left(4 \cdot x\right)\right)\right)} \]

   6. Applied rewrites 91.3%

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(18 \cdot y, x \cdot \left(t \cdot z\right), \left(t \cdot a\right) \cdot -4 - \mathsf{fma}\left(4 \cdot x, i, k \cdot \left(27 \cdot j\right)\right)\right)}\right) \]

   7. Taylor expanded in j around 0

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(i \cdot x\right)}\right) \]
   8. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(a \cdot t\right)\right)} + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(a \cdot t\right)\right) + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right) \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(-4 \cdot \left(a \cdot t\right) - \left(\mathsf{neg}\left(-4\right)\right) \cdot \left(i \cdot x\right)\right)}\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(-4 \cdot \left(a \cdot t\right) - \color{blue}{4} \cdot \left(i \cdot x\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(18 \cdot t, x \cdot \left(y \cdot z\right), -4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(\color{blue}{18 \cdot t}, x \cdot \left(y \cdot z\right), -4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(y \cdot z\right) \cdot x}, -4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(y \cdot z\right) \cdot x}, -4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(z \cdot y\right)} \cdot x, -4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \color{blue}{\left(z \cdot y\right)} \cdot x, -4 \cdot \left(a \cdot t\right) - 4 \cdot \left(i \cdot x\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, -4 \cdot \left(a \cdot t\right) - \color{blue}{\left(\mathsf{neg}\left(-4\right)\right)} \cdot \left(i \cdot x\right)\right)\right) \]

      15. fp-cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, \color{blue}{-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)}\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, \color{blue}{-4 \cdot \left(i \cdot x\right) + -4 \cdot \left(a \cdot t\right)}\right)\right) \]

      17. distribute-lft-out N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)}\right)\right) \]

      18. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, \color{blue}{-4 \cdot \left(i \cdot x + a \cdot t\right)}\right)\right) \]

      19. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, -4 \cdot \color{blue}{\mathsf{fma}\left(i, x, a \cdot t\right)}\right)\right) \]

      20. lower-*.f64 74.7

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, -4 \cdot \mathsf{fma}\left(i, x, \color{blue}{a \cdot t}\right)\right)\right) \]

   9. Applied rewrites 74.7%

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)}\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 59.0%

       \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot \color{blue}{-4}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+50} \lor \neg \left(x \leq 7 \cdot 10^{+15}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -3e+57)
   (* (fma (* (* y z) x) 18.0 (* -4.0 a)) t)
   (if (<= t 9e+64)
     (fma (* -4.0 i) x (* b c))
     (* (fma (* z y) (* x 18.0) (* -4.0 a)) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -3e+57) {
		tmp = fma(((y * z) * x), 18.0, (-4.0 * a)) * t;
	} else if (t <= 9e+64) {
		tmp = fma((-4.0 * i), x, (b * c));
	} else {
		tmp = fma((z * y), (x * 18.0), (-4.0 * a)) * t;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -3e+57)
		tmp = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= 9e+64)
		tmp = fma(Float64(-4.0 * i), x, Float64(b * c));
	else
		tmp = Float64(fma(Float64(z * y), Float64(x * 18.0), Float64(-4.0 * a)) * t);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -3e+57], N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 9e+64], N[(N[(-4.0 * i), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * N[(x * 18.0), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e57

   1. Initial program 81.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      3. lower-*.f64 19.6

         \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

   5. Applied rewrites 19.6%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

      2. metadata-eval N/A

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

      3. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

      12. lower-*.f64 76.1

          \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   8. Applied rewrites 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]

   if -3e57 < t < 8.99999999999999946e64

   1. Initial program 90.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

      3. lower-*.f64 23.5

         \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

   5. Applied rewrites 23.5%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate--l+ N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot x}, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      15. lower-*.f64 78.4

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, \color{blue}{b \cdot c}\right)\right) \]

   8. Applied rewrites 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
   10. Step-by-step derivation

   11. Applied rewrites 60.5%

       \[\leadsto \mathsf{fma}\left(-4 \cdot i, \color{blue}{x}, b \cdot c\right) \]

   if 8.99999999999999946e64 < t

   1. Initial program 89.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   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 72.8

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   5. Applied rewrites 72.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

   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 25.4%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

       2. metadata-eval N/A

          \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

       3. +-commutative N/A

          \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       6. +-commutative N/A

          \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

       7. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

       8. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

       9. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       10. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       12. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       13. lower-*.f64 67.0

           \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   11. Applied rewrites 67.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]
   12. Step-by-step derivation

   13. Applied rewrites 67.0%

       \[\leadsto \mathsf{fma}\left(z \cdot y, x \cdot 18, -4 \cdot a\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 34.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+90} \lor \neg \left(b \cdot c \leq 1.65 \cdot 10^{+172}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2.5e+90) (not (<= (* b c) 1.65e+172)))
   (* b c)
   (* (* -4.0 a) t)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.5e+90) || !((b * c) <= 1.65e+172)) {
		tmp = b * c;
	} else {
		tmp = (-4.0 * a) * t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-2.5d+90)) .or. (.not. ((b * c) <= 1.65d+172))) then
        tmp = b * c
    else
        tmp = ((-4.0d0) * a) * t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2.5e+90) || !((b * c) <= 1.65e+172)) {
		tmp = b * c;
	} else {
		tmp = (-4.0 * a) * t;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.5e+90) or not ((b * c) <= 1.65e+172):
		tmp = b * c
	else:
		tmp = (-4.0 * a) * t
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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) <= -2.5e+90) || !(Float64(b * c) <= 1.65e+172))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(-4.0 * a) * t);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.5e+90) || ~(((b * c) <= 1.65e+172)))
		tmp = b * c;
	else
		tmp = (-4.0 * a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.5e+90], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.65e+172]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.5000000000000002e90 or 1.64999999999999991e172 < (*.f64 b c)

   1. Initial program 85.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 13.9

         \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

   5. Applied rewrites 13.9%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate--l+ N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot x}, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      15. lower-*.f64 79.9

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, \color{blue}{b \cdot c}\right)\right) \]

   8. Applied rewrites 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
   10. Step-by-step derivation

   11. Applied rewrites 74.7%

       \[\leadsto \mathsf{fma}\left(-4 \cdot i, \color{blue}{x}, b \cdot c\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto b \cdot c \]
   13. Step-by-step derivation

   14. Applied rewrites 68.1%

       \[\leadsto b \cdot c \]

   if -2.5000000000000002e90 < (*.f64 b c) < 1.64999999999999991e172

   1. Initial program 89.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 57.4

          \[\leadsto \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \color{blue}{\left(k \cdot j\right)} \cdot 27 \]

   5. Applied rewrites 57.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27} \]

   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 28.3%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   10. Step-by-step derivation

       1. fp-cancel-sub-sign-inv N/A

          \[\leadsto t \cdot \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right)} \]

       2. metadata-eval N/A

          \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot a\right) \]

       3. +-commutative N/A

          \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

       4. *-commutative N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot t} \]

       6. +-commutative N/A

          \[\leadsto \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot a\right)} \cdot t \]

       7. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot 18} + -4 \cdot a\right) \cdot t \]

       8. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right)} \cdot t \]

       9. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       10. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot z\right) \cdot x}, 18, -4 \cdot a\right) \cdot t \]

       11. *-commutative N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       12. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(\color{blue}{\left(z \cdot y\right)} \cdot x, 18, -4 \cdot a\right) \cdot t \]

       13. lower-*.f64 51.5

           \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, \color{blue}{-4 \cdot a}\right) \cdot t \]

   11. Applied rewrites 51.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]

   12. Taylor expanded in x around 0

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 33.2%

       \[\leadsto \left(-4 \cdot a\right) \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+90} \lor \neg \left(b \cdot c \leq 1.65 \cdot 10^{+172}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 34.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -10500000 \lor \neg \left(b \cdot c \leq 1.4 \cdot 10^{+172}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -10500000.0) (not (<= (* b c) 1.4e+172)))
   (* b c)
   (* (* i x) -4.0)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -10500000.0) || !((b * c) <= 1.4e+172)) {
		tmp = b * c;
	} else {
		tmp = (i * x) * -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.
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 (((b * c) <= (-10500000.0d0)) .or. (.not. ((b * c) <= 1.4d+172))) then
        tmp = b * c
    else
        tmp = (i * x) * (-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;
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 (((b * c) <= -10500000.0) || !((b * c) <= 1.4e+172)) {
		tmp = b * c;
	} else {
		tmp = (i * x) * -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])
[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 ((b * c) <= -10500000.0) or not ((b * c) <= 1.4e+172):
		tmp = b * c
	else:
		tmp = (i * x) * -4.0
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -10500000.0) || !(Float64(b * c) <= 1.4e+172))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(i * x) * -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])){:}
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 (((b * c) <= -10500000.0) || ~(((b * c) <= 1.4e+172)))
		tmp = b * c;
	else
		tmp = (i * x) * -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.
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], -10500000.0], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.4e+172]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.05e7 or 1.4e172 < (*.f64 b c)

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in 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 15.7

         \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

   5. Applied rewrites 15.7%

      \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

      2. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

      3. metadata-eval N/A

         \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

      5. associate--l+ N/A

         \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot x}, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)}\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

      15. lower-*.f64 74.5

          \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, \color{blue}{b \cdot c}\right)\right) \]

   8. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
   10. Step-by-step derivation

   11. Applied rewrites 66.0%

       \[\leadsto \mathsf{fma}\left(-4 \cdot i, \color{blue}{x}, b \cdot c\right) \]

   12. Taylor expanded in x around 0

       \[\leadsto b \cdot c \]
   13. Step-by-step derivation

   14. Applied rewrites 57.6%

       \[\leadsto b \cdot c \]

   if -1.05e7 < (*.f64 b c) < 1.4e172

   1. Initial program 89.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   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

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(\mathsf{neg}\left(x \cdot 4\right)\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(x \cdot 4\right)\right) \cdot i + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(x \cdot 4\right), i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{x \cdot 4}\right), i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{4 \cdot x}\right), i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot x}, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot x}, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      10. metadata-eval 92.7

          \[\leadsto \mathsf{fma}\left(\color{blue}{-4} \cdot x, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      11. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c}\right) - \left(j \cdot 27\right) \cdot k \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      13. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right) \cdot t}\right) + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      15. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot x, i, \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) \cdot t} + b \cdot c\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, c \cdot b\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]

      3. lower-*.f64 28.2

         \[\leadsto \color{blue}{\left(i \cdot x\right)} \cdot -4 \]

   7. Applied rewrites 28.2%

      \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -10500000 \lor \neg \left(b \cdot c \leq 1.4 \cdot 10^{+172}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 24.1% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 88.4%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
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 20.7

      \[\leadsto \color{blue}{\left(-27 \cdot j\right)} \cdot k \]

5. Applied rewrites 20.7%

   \[\leadsto \color{blue}{\left(-27 \cdot j\right) \cdot k} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
7. Step-by-step derivation

   1. associate--r+ N/A

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right)} \]

   2. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right)} - 27 \cdot \left(j \cdot k\right) \]

   3. metadata-eval N/A

      \[\leadsto \left(b \cdot c + \color{blue}{-4} \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)} - 27 \cdot \left(j \cdot k\right) \]

   5. associate--l+ N/A

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

   6. *-commutative N/A

      \[\leadsto \color{blue}{\left(i \cdot x\right) \cdot -4} + \left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

   8. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot x}, -4, b \cdot c - 27 \cdot \left(j \cdot k\right)\right) \]

   9. fp-cancel-sub-sign-inv N/A

      \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + \color{blue}{-27} \cdot \left(j \cdot k\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{-27 \cdot \left(j \cdot k\right) + b \cdot c}\right) \]

   12. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \color{blue}{\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)}\right) \]

   13. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

   14. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, \color{blue}{k \cdot j}, b \cdot c\right)\right) \]

   15. lower-*.f64 60.0

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, \color{blue}{b \cdot c}\right)\right) \]

8. Applied rewrites 60.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, k \cdot j, b \cdot c\right)\right)} \]

9. Taylor expanded in j around 0

   \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
10. Step-by-step derivation

11. Applied rewrites 44.0%

    \[\leadsto \mathsf{fma}\left(-4 \cdot i, \color{blue}{x}, b \cdot c\right) \]

12. Taylor expanded in x around 0

    \[\leadsto b \cdot c \]
13. Step-by-step derivation

14. Applied rewrites 24.3%

    \[\leadsto b \cdot c \]
15. Add Preprocessing

Developer Target 1: 89.4% 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 2024320 
(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)))