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

Percentage Accurate: 85.3% → 91.7%

Time: 34.4s

Alternatives: 22

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: 85.3% 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: 91.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.0%

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

   3. Simplified 95.3%

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

      1. associate-*r* 97.0%

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

      2. distribute-rgt-out-- 97.0%

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

      3. associate-+l- 97.0%

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

      4. associate-*r* 95.3%

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

      5. *-commutative 95.3%

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

      6. *-commutative 95.3%

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

      7. associate-*l* 95.3%

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

      8. fma-neg 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in t around 0 95.3%

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

      1. fma-def 95.3%

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

      2. cancel-sign-sub-inv 95.3%

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

      3. metadata-eval 95.3%

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

      4. *-commutative 95.3%

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

   9. Simplified 95.3%

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

   10. Taylor expanded in t around 0 95.3%

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

       1. fma-def 95.3%

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

       2. associate-*r* 97.0%

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

   12. Simplified 97.0%

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

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

   1. Initial program 0.0%

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

   3. Simplified 33.3%

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

      1. associate-*r* 29.6%

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

      2. distribute-rgt-out-- 0.0%

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

      3. associate-+l- 0.0%

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

      4. associate-*r* 3.7%

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

      5. *-commutative 3.7%

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

      6. *-commutative 3.7%

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

      7. associate-*l* 3.7%

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

      8. fma-neg 7.4%

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

   6. Applied egg-rr 7.4%

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

   7. Taylor expanded in t around 0 33.3%

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

      1. fma-def 44.4%

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

      2. cancel-sign-sub-inv 44.4%

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

      3. metadata-eval 44.4%

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

      4. *-commutative 44.4%

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

   9. Simplified 44.4%

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

   10. Taylor expanded in x around -inf 74.1%

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

       1. associate-*r* 74.1%

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

       2. neg-mul-1 74.1%

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

       3. cancel-sign-sub-inv 74.1%

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

       4. *-commutative 74.1%

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

       5. associate-*r* 74.2%

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

       6. metadata-eval 74.2%

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

   12. Simplified 74.2%

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

   13. Taylor expanded in t around 0 74.1%

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

       1. *-commutative 74.1%

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

       2. associate-*r* 74.2%

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

       3. *-commutative 74.2%

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

       4. associate-*r* 74.2%

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

       5. associate-*l* 74.2%

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

   15. Simplified 74.2%

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

4. Final simplification 94.6%

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

Alternative 2: 91.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i))
	return tmp

Julia

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

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.0%

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

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

   1. Initial program 0.0%

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

   3. Simplified 33.3%

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

      1. associate-*r* 29.6%

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

      2. distribute-rgt-out-- 0.0%

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

      3. associate-+l- 0.0%

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

      4. associate-*r* 3.7%

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

      5. *-commutative 3.7%

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

      6. *-commutative 3.7%

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

      7. associate-*l* 3.7%

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

      8. fma-neg 7.4%

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

   6. Applied egg-rr 7.4%

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

   7. Taylor expanded in t around 0 33.3%

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

      1. fma-def 44.4%

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

      2. cancel-sign-sub-inv 44.4%

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

      3. metadata-eval 44.4%

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

      4. *-commutative 44.4%

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

   9. Simplified 44.4%

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

   10. Taylor expanded in x around -inf 74.1%

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

       1. associate-*r* 74.1%

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

       2. neg-mul-1 74.1%

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

       3. cancel-sign-sub-inv 74.1%

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

       4. *-commutative 74.1%

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

       5. associate-*r* 74.2%

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

       6. metadata-eval 74.2%

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

   12. Simplified 74.2%

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

   13. Taylor expanded in t around 0 74.1%

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

       1. *-commutative 74.1%

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

       2. associate-*r* 74.2%

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

       3. *-commutative 74.2%

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

       4. associate-*r* 74.2%

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

       5. associate-*l* 74.2%

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

   15. Simplified 74.2%

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

4. Final simplification 94.5%

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

Alternative 3: 56.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t\_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+50}:\\ \;\;\;\;t\_2 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-257}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-299}:\\ \;\;\;\;b \cdot c + t\_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(t \cdot \left(z \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* 18.0 (* t (* x (* y z))))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* -4.0 (* t a)))))
   (if (<= x -6.8e+160)
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
     (if (<= x -1.05e+50)
       (+ t_2 (* -4.0 (* x i)))
       (if (<= x -1.4e+33)
         t_1
         (if (<= x -4.4e-257)
           t_3
           (if (<= x 1.3e-299)
             (+ (* b c) t_2)
             (if (<= x 2.1e-163)
               t_3
               (if (<= x 3.5e+14)
                 t_1
                 (if (<= x 4.5e+57)
                   t_3
                   (* x (- (* y (* t (* z (- -18.0)))) (* 4.0 i)))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (18.0 * (t * (x * (y * z))));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (-4.0 * (t * a));
	double tmp;
	if (x <= -6.8e+160) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -1.05e+50) {
		tmp = t_2 + (-4.0 * (x * i));
	} else if (x <= -1.4e+33) {
		tmp = t_1;
	} else if (x <= -4.4e-257) {
		tmp = t_3;
	} else if (x <= 1.3e-299) {
		tmp = (b * c) + t_2;
	} else if (x <= 2.1e-163) {
		tmp = t_3;
	} else if (x <= 3.5e+14) {
		tmp = t_1;
	} else if (x <= 4.5e+57) {
		tmp = t_3;
	} else {
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = (b * c) + (18.0d0 * (t * (x * (y * z))))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + ((-4.0d0) * (t * a))
    if (x <= (-6.8d+160)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= (-1.05d+50)) then
        tmp = t_2 + ((-4.0d0) * (x * i))
    else if (x <= (-1.4d+33)) then
        tmp = t_1
    else if (x <= (-4.4d-257)) then
        tmp = t_3
    else if (x <= 1.3d-299) then
        tmp = (b * c) + t_2
    else if (x <= 2.1d-163) then
        tmp = t_3
    else if (x <= 3.5d+14) then
        tmp = t_1
    else if (x <= 4.5d+57) then
        tmp = t_3
    else
        tmp = x * ((y * (t * (z * -(-18.0d0)))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = (b * c) + (18.0 * (t * (x * (y * z))));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (-4.0 * (t * a));
	double tmp;
	if (x <= -6.8e+160) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -1.05e+50) {
		tmp = t_2 + (-4.0 * (x * i));
	} else if (x <= -1.4e+33) {
		tmp = t_1;
	} else if (x <= -4.4e-257) {
		tmp = t_3;
	} else if (x <= 1.3e-299) {
		tmp = (b * c) + t_2;
	} else if (x <= 2.1e-163) {
		tmp = t_3;
	} else if (x <= 3.5e+14) {
		tmp = t_1;
	} else if (x <= 4.5e+57) {
		tmp = t_3;
	} else {
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (18.0 * (t * (x * (y * z))))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (-4.0 * (t * a))
	tmp = 0
	if x <= -6.8e+160:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= -1.05e+50:
		tmp = t_2 + (-4.0 * (x * i))
	elif x <= -1.4e+33:
		tmp = t_1
	elif x <= -4.4e-257:
		tmp = t_3
	elif x <= 1.3e-299:
		tmp = (b * c) + t_2
	elif x <= 2.1e-163:
		tmp = t_3
	elif x <= 3.5e+14:
		tmp = t_1
	elif x <= 4.5e+57:
		tmp = t_3
	else:
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -6.8e+160)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= -1.05e+50)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(x * i)));
	elseif (x <= -1.4e+33)
		tmp = t_1;
	elseif (x <= -4.4e-257)
		tmp = t_3;
	elseif (x <= 1.3e-299)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (x <= 2.1e-163)
		tmp = t_3;
	elseif (x <= 3.5e+14)
		tmp = t_1;
	elseif (x <= 4.5e+57)
		tmp = t_3;
	else
		tmp = Float64(x * Float64(Float64(y * Float64(t * Float64(z * Float64(-(-18.0))))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (18.0 * (t * (x * (y * z))));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -6.8e+160)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= -1.05e+50)
		tmp = t_2 + (-4.0 * (x * i));
	elseif (x <= -1.4e+33)
		tmp = t_1;
	elseif (x <= -4.4e-257)
		tmp = t_3;
	elseif (x <= 1.3e-299)
		tmp = (b * c) + t_2;
	elseif (x <= 2.1e-163)
		tmp = t_3;
	elseif (x <= 3.5e+14)
		tmp = t_1;
	elseif (x <= 4.5e+57)
		tmp = t_3;
	else
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+160], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e+50], N[(t$95$2 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e+33], t$95$1, If[LessEqual[x, -4.4e-257], t$95$3, If[LessEqual[x, 1.3e-299], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, 2.1e-163], t$95$3, If[LessEqual[x, 3.5e+14], t$95$1, If[LessEqual[x, 4.5e+57], t$95$3, N[(x * N[(N[(y * N[(t * N[(z * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.80000000000000061e160

   1. Initial program 73.2%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 85.5%

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

   if -6.80000000000000061e160 < x < -1.05e50

   1. Initial program 73.1%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in i around inf 66.3%

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

      1. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -1.05e50 < x < -1.4e33 or 2.09999999999999998e-163 < x < 3.5e14

   1. Initial program 92.9%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in j around 0 89.9%

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

   6. Taylor expanded in a around 0 75.7%

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

   7. Taylor expanded in i around 0 65.1%

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

   if -1.4e33 < x < -4.39999999999999975e-257 or 1.2999999999999999e-299 < x < 2.09999999999999998e-163 or 3.5e14 < x < 4.49999999999999996e57

   1. Initial program 95.8%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around inf 73.6%

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

   if -4.39999999999999975e-257 < x < 1.2999999999999999e-299

   1. Initial program 92.1%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in b around inf 77.6%

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

   if 4.49999999999999996e57 < x

   1. Initial program 80.3%

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

   3. Simplified 86.3%

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

      1. associate-*r* 83.3%

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

      2. distribute-rgt-out-- 80.3%

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

      3. associate-+l- 80.3%

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

      4. associate-*r* 83.2%

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

      5. *-commutative 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. fma-neg 83.2%

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

   6. Applied egg-rr 83.2%

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

   7. Taylor expanded in t around 0 86.2%

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

      1. fma-def 87.8%

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

      2. cancel-sign-sub-inv 87.8%

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

      3. metadata-eval 87.8%

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

      4. *-commutative 87.8%

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

   9. Simplified 87.8%

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

   10. Taylor expanded in x around -inf 80.6%

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

       1. associate-*r* 80.6%

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

       2. neg-mul-1 80.6%

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

       3. cancel-sign-sub-inv 80.6%

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

       4. *-commutative 80.6%

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

       5. associate-*r* 80.6%

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

       6. metadata-eval 80.6%

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

   12. Simplified 80.6%

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

   13. Taylor expanded in t around 0 80.6%

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

       1. *-commutative 80.6%

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

       2. associate-*r* 80.6%

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

       3. *-commutative 80.6%

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

       4. associate-*r* 80.6%

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

       5. associate-*l* 78.1%

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

   15. Simplified 78.1%

       \[\leadsto \left(-x\right) \cdot \left(\color{blue}{y \cdot \left(t \cdot \left(z \cdot -18\right)\right)} + 4 \cdot i\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-299}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-163}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(t \cdot \left(z \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ t_4 := b \cdot c + t\_3\\ t_5 := t\_3 + t\_1\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+50}:\\ \;\;\;\;t\_3 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-259}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-300}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x \leq 235000:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+57}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a)))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_3 (* j (* k -27.0)))
        (t_4 (+ (* b c) t_3))
        (t_5 (+ t_3 t_1)))
   (if (<= x -9.5e+160)
     t_2
     (if (<= x -1e+50)
       (+ t_3 (* -4.0 (* x i)))
       (if (<= x -9.2e+45)
         t_2
         (if (<= x -6e-259)
           t_5
           (if (<= x 1.7e-300)
             t_4
             (if (<= x 4.6e-164)
               t_5
               (if (<= x 235000.0)
                 (+ (* b c) t_1)
                 (if (<= x 4.3e+57) t_4 t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_3 = j * (k * -27.0);
	double t_4 = (b * c) + t_3;
	double t_5 = t_3 + t_1;
	double tmp;
	if (x <= -9.5e+160) {
		tmp = t_2;
	} else if (x <= -1e+50) {
		tmp = t_3 + (-4.0 * (x * i));
	} else if (x <= -9.2e+45) {
		tmp = t_2;
	} else if (x <= -6e-259) {
		tmp = t_5;
	} else if (x <= 1.7e-300) {
		tmp = t_4;
	} else if (x <= 4.6e-164) {
		tmp = t_5;
	} else if (x <= 235000.0) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.3e+57) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * a)
    t_2 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_3 = j * (k * (-27.0d0))
    t_4 = (b * c) + t_3
    t_5 = t_3 + t_1
    if (x <= (-9.5d+160)) then
        tmp = t_2
    else if (x <= (-1d+50)) then
        tmp = t_3 + ((-4.0d0) * (x * i))
    else if (x <= (-9.2d+45)) then
        tmp = t_2
    else if (x <= (-6d-259)) then
        tmp = t_5
    else if (x <= 1.7d-300) then
        tmp = t_4
    else if (x <= 4.6d-164) then
        tmp = t_5
    else if (x <= 235000.0d0) then
        tmp = (b * c) + t_1
    else if (x <= 4.3d+57) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (t * a);
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_3 = j * (k * -27.0);
	double t_4 = (b * c) + t_3;
	double t_5 = t_3 + t_1;
	double tmp;
	if (x <= -9.5e+160) {
		tmp = t_2;
	} else if (x <= -1e+50) {
		tmp = t_3 + (-4.0 * (x * i));
	} else if (x <= -9.2e+45) {
		tmp = t_2;
	} else if (x <= -6e-259) {
		tmp = t_5;
	} else if (x <= 1.7e-300) {
		tmp = t_4;
	} else if (x <= 4.6e-164) {
		tmp = t_5;
	} else if (x <= 235000.0) {
		tmp = (b * c) + t_1;
	} else if (x <= 4.3e+57) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_3 = j * (k * -27.0)
	t_4 = (b * c) + t_3
	t_5 = t_3 + t_1
	tmp = 0
	if x <= -9.5e+160:
		tmp = t_2
	elif x <= -1e+50:
		tmp = t_3 + (-4.0 * (x * i))
	elif x <= -9.2e+45:
		tmp = t_2
	elif x <= -6e-259:
		tmp = t_5
	elif x <= 1.7e-300:
		tmp = t_4
	elif x <= 4.6e-164:
		tmp = t_5
	elif x <= 235000.0:
		tmp = (b * c) + t_1
	elif x <= 4.3e+57:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_3 = Float64(j * Float64(k * -27.0))
	t_4 = Float64(Float64(b * c) + t_3)
	t_5 = Float64(t_3 + t_1)
	tmp = 0.0
	if (x <= -9.5e+160)
		tmp = t_2;
	elseif (x <= -1e+50)
		tmp = Float64(t_3 + Float64(-4.0 * Float64(x * i)));
	elseif (x <= -9.2e+45)
		tmp = t_2;
	elseif (x <= -6e-259)
		tmp = t_5;
	elseif (x <= 1.7e-300)
		tmp = t_4;
	elseif (x <= 4.6e-164)
		tmp = t_5;
	elseif (x <= 235000.0)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 4.3e+57)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_3 = j * (k * -27.0);
	t_4 = (b * c) + t_3;
	t_5 = t_3 + t_1;
	tmp = 0.0;
	if (x <= -9.5e+160)
		tmp = t_2;
	elseif (x <= -1e+50)
		tmp = t_3 + (-4.0 * (x * i));
	elseif (x <= -9.2e+45)
		tmp = t_2;
	elseif (x <= -6e-259)
		tmp = t_5;
	elseif (x <= 1.7e-300)
		tmp = t_4;
	elseif (x <= 4.6e-164)
		tmp = t_5;
	elseif (x <= 235000.0)
		tmp = (b * c) + t_1;
	elseif (x <= 4.3e+57)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 + t$95$1), $MachinePrecision]}, If[LessEqual[x, -9.5e+160], t$95$2, If[LessEqual[x, -1e+50], N[(t$95$3 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e+45], t$95$2, If[LessEqual[x, -6e-259], t$95$5, If[LessEqual[x, 1.7e-300], t$95$4, If[LessEqual[x, 4.6e-164], t$95$5, If[LessEqual[x, 235000.0], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 4.3e+57], t$95$4, t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.5000000000000006e160 or -1.0000000000000001e50 < x < -9.20000000000000049e45 or 4.30000000000000033e57 < x

   1. Initial program 78.9%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around inf 82.6%

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

   if -9.5000000000000006e160 < x < -1.0000000000000001e50

   1. Initial program 73.1%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in i around inf 66.3%

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

      1. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -9.20000000000000049e45 < x < -6.0000000000000004e-259 or 1.70000000000000009e-300 < x < 4.59999999999999971e-164

   1. Initial program 95.5%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in a around inf 72.3%

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

   if -6.0000000000000004e-259 < x < 1.70000000000000009e-300 or 235000 < x < 4.30000000000000033e57

   1. Initial program 89.8%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 75.0%

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

   if 4.59999999999999971e-164 < x < 235000

   1. Initial program 95.7%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in j around 0 87.7%

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

   6. Taylor expanded in x around 0 56.2%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-259}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-300}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 235000:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+57}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ t_4 := t\_3 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;t\_3 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-252}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-300}:\\ \;\;\;\;b \cdot c + t\_3\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-163}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* 18.0 (* t (* x (* y z))))))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (t_3 (* j (* k -27.0)))
        (t_4 (+ t_3 (* -4.0 (* t a)))))
   (if (<= x -5.4e+160)
     t_2
     (if (<= x -1.2e+50)
       (+ t_3 (* -4.0 (* x i)))
       (if (<= x -7.2e+41)
         t_1
         (if (<= x -2e-252)
           t_4
           (if (<= x 5.8e-300)
             (+ (* b c) t_3)
             (if (<= x 4.3e-163)
               t_4
               (if (<= x 1.85e+16) t_1 (if (<= x 1.1e+57) t_4 t_2))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (18.0 * (t * (x * (y * z))));
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_3 = j * (k * -27.0);
	double t_4 = t_3 + (-4.0 * (t * a));
	double tmp;
	if (x <= -5.4e+160) {
		tmp = t_2;
	} else if (x <= -1.2e+50) {
		tmp = t_3 + (-4.0 * (x * i));
	} else if (x <= -7.2e+41) {
		tmp = t_1;
	} else if (x <= -2e-252) {
		tmp = t_4;
	} else if (x <= 5.8e-300) {
		tmp = (b * c) + t_3;
	} else if (x <= 4.3e-163) {
		tmp = t_4;
	} else if (x <= 1.85e+16) {
		tmp = t_1;
	} else if (x <= 1.1e+57) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b * c) + (18.0d0 * (t * (x * (y * z))))
    t_2 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_3 = j * (k * (-27.0d0))
    t_4 = t_3 + ((-4.0d0) * (t * a))
    if (x <= (-5.4d+160)) then
        tmp = t_2
    else if (x <= (-1.2d+50)) then
        tmp = t_3 + ((-4.0d0) * (x * i))
    else if (x <= (-7.2d+41)) then
        tmp = t_1
    else if (x <= (-2d-252)) then
        tmp = t_4
    else if (x <= 5.8d-300) then
        tmp = (b * c) + t_3
    else if (x <= 4.3d-163) then
        tmp = t_4
    else if (x <= 1.85d+16) then
        tmp = t_1
    else if (x <= 1.1d+57) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (18.0 * (t * (x * (y * z))));
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double t_3 = j * (k * -27.0);
	double t_4 = t_3 + (-4.0 * (t * a));
	double tmp;
	if (x <= -5.4e+160) {
		tmp = t_2;
	} else if (x <= -1.2e+50) {
		tmp = t_3 + (-4.0 * (x * i));
	} else if (x <= -7.2e+41) {
		tmp = t_1;
	} else if (x <= -2e-252) {
		tmp = t_4;
	} else if (x <= 5.8e-300) {
		tmp = (b * c) + t_3;
	} else if (x <= 4.3e-163) {
		tmp = t_4;
	} else if (x <= 1.85e+16) {
		tmp = t_1;
	} else if (x <= 1.1e+57) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (18.0 * (t * (x * (y * z))))
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_3 = j * (k * -27.0)
	t_4 = t_3 + (-4.0 * (t * a))
	tmp = 0
	if x <= -5.4e+160:
		tmp = t_2
	elif x <= -1.2e+50:
		tmp = t_3 + (-4.0 * (x * i))
	elif x <= -7.2e+41:
		tmp = t_1
	elif x <= -2e-252:
		tmp = t_4
	elif x <= 5.8e-300:
		tmp = (b * c) + t_3
	elif x <= 4.3e-163:
		tmp = t_4
	elif x <= 1.85e+16:
		tmp = t_1
	elif x <= 1.1e+57:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_3 = Float64(j * Float64(k * -27.0))
	t_4 = Float64(t_3 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (x <= -5.4e+160)
		tmp = t_2;
	elseif (x <= -1.2e+50)
		tmp = Float64(t_3 + Float64(-4.0 * Float64(x * i)));
	elseif (x <= -7.2e+41)
		tmp = t_1;
	elseif (x <= -2e-252)
		tmp = t_4;
	elseif (x <= 5.8e-300)
		tmp = Float64(Float64(b * c) + t_3);
	elseif (x <= 4.3e-163)
		tmp = t_4;
	elseif (x <= 1.85e+16)
		tmp = t_1;
	elseif (x <= 1.1e+57)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (18.0 * (t * (x * (y * z))));
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	t_3 = j * (k * -27.0);
	t_4 = t_3 + (-4.0 * (t * a));
	tmp = 0.0;
	if (x <= -5.4e+160)
		tmp = t_2;
	elseif (x <= -1.2e+50)
		tmp = t_3 + (-4.0 * (x * i));
	elseif (x <= -7.2e+41)
		tmp = t_1;
	elseif (x <= -2e-252)
		tmp = t_4;
	elseif (x <= 5.8e-300)
		tmp = (b * c) + t_3;
	elseif (x <= 4.3e-163)
		tmp = t_4;
	elseif (x <= 1.85e+16)
		tmp = t_1;
	elseif (x <= 1.1e+57)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+160], t$95$2, If[LessEqual[x, -1.2e+50], N[(t$95$3 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e+41], t$95$1, If[LessEqual[x, -2e-252], t$95$4, If[LessEqual[x, 5.8e-300], N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[x, 4.3e-163], t$95$4, If[LessEqual[x, 1.85e+16], t$95$1, If[LessEqual[x, 1.1e+57], t$95$4, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.4e160 or 1.1e57 < x

   1. Initial program 78.2%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in x around inf 82.0%

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

   if -5.4e160 < x < -1.2000000000000001e50

   1. Initial program 73.1%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in i around inf 66.3%

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

      1. *-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -1.2000000000000001e50 < x < -7.20000000000000051e41 or 4.30000000000000009e-163 < x < 1.85e16

   1. Initial program 92.9%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in j around 0 89.9%

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

   6. Taylor expanded in a around 0 75.7%

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

   7. Taylor expanded in i around 0 65.1%

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

   if -7.20000000000000051e41 < x < -1.99999999999999989e-252 or 5.79999999999999985e-300 < x < 4.30000000000000009e-163 or 1.85e16 < x < 1.1e57

   1. Initial program 95.8%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around inf 73.6%

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

   if -1.99999999999999989e-252 < x < 5.79999999999999985e-300

   1. Initial program 92.1%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in b around inf 77.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+41}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-300}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-163}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+57}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ t_3 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+217}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+275}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (+ (* j (* k -27.0)) (* 18.0 (* t (* z (* x y))))))
        (t_3 (- (+ (* b c) (* -4.0 (* t a))) t_1)))
   (if (<= t -1.6e+171)
     t_2
     (if (<= t -4.8e+60)
       t_3
       (if (<= t 2.25e+72)
         (- (* b c) (+ t_1 (* 27.0 (* j k))))
         (if (<= t 1.22e+217)
           t_3
           (if (<= t 3.6e+246)
             (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
             (if (<= t 5e+275) t_3 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))));
	double t_3 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double tmp;
	if (t <= -1.6e+171) {
		tmp = t_2;
	} else if (t <= -4.8e+60) {
		tmp = t_3;
	} else if (t <= 2.25e+72) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if (t <= 1.22e+217) {
		tmp = t_3;
	} else if (t <= 3.6e+246) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 5e+275) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = (j * (k * (-27.0d0))) + (18.0d0 * (t * (z * (x * y))))
    t_3 = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    if (t <= (-1.6d+171)) then
        tmp = t_2
    else if (t <= (-4.8d+60)) then
        tmp = t_3
    else if (t <= 2.25d+72) then
        tmp = (b * c) - (t_1 + (27.0d0 * (j * k)))
    else if (t <= 1.22d+217) then
        tmp = t_3
    else if (t <= 3.6d+246) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t <= 5d+275) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))));
	double t_3 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double tmp;
	if (t <= -1.6e+171) {
		tmp = t_2;
	} else if (t <= -4.8e+60) {
		tmp = t_3;
	} else if (t <= 2.25e+72) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if (t <= 1.22e+217) {
		tmp = t_3;
	} else if (t <= 3.6e+246) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t <= 5e+275) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))))
	t_3 = ((b * c) + (-4.0 * (t * a))) - t_1
	tmp = 0
	if t <= -1.6e+171:
		tmp = t_2
	elif t <= -4.8e+60:
		tmp = t_3
	elif t <= 2.25e+72:
		tmp = (b * c) - (t_1 + (27.0 * (j * k)))
	elif t <= 1.22e+217:
		tmp = t_3
	elif t <= 3.6e+246:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t <= 5e+275:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))))
	t_3 = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1)
	tmp = 0.0
	if (t <= -1.6e+171)
		tmp = t_2;
	elseif (t <= -4.8e+60)
		tmp = t_3;
	elseif (t <= 2.25e+72)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	elseif (t <= 1.22e+217)
		tmp = t_3;
	elseif (t <= 3.6e+246)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t <= 5e+275)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))));
	t_3 = ((b * c) + (-4.0 * (t * a))) - t_1;
	tmp = 0.0;
	if (t <= -1.6e+171)
		tmp = t_2;
	elseif (t <= -4.8e+60)
		tmp = t_3;
	elseif (t <= 2.25e+72)
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	elseif (t <= 1.22e+217)
		tmp = t_3;
	elseif (t <= 3.6e+246)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t <= 5e+275)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t, -1.6e+171], t$95$2, If[LessEqual[t, -4.8e+60], t$95$3, If[LessEqual[t, 2.25e+72], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+217], t$95$3, If[LessEqual[t, 3.6e+246], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+275], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.60000000000000006e171 or 5.0000000000000003e275 < t

   1. Initial program 71.3%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in y around inf 69.3%

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

      1. *-commutative 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in x around 0 69.3%

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

      1. associate-*r* 69.4%

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

   10. Simplified 69.4%

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

   if -1.60000000000000006e171 < t < -4.8e60 or 2.2499999999999999e72 < t < 1.2200000000000001e217 or 3.6e246 < t < 5.0000000000000003e275

   1. Initial program 81.4%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in j around 0 91.1%

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

   6. Taylor expanded in y around 0 74.1%

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

   if -4.8e60 < t < 2.2499999999999999e72

   1. Initial program 91.6%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around 0 85.3%

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

   if 1.2200000000000001e217 < t < 3.6e246

   1. Initial program 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 92.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+171}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+72}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+217}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+275}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ t_3 := j \cdot \left(k \cdot -27\right)\\ t_4 := t\_3 + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+125}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-48}:\\ \;\;\;\;t\_3 + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (- (+ (* b c) (* -4.0 (* t a))) t_1))
        (t_3 (* j (* k -27.0)))
        (t_4 (+ t_3 (* t (+ (* a -4.0) (* 18.0 (* x (* y z))))))))
   (if (<= t -6.8e+125)
     t_4
     (if (<= t -2e-41)
       t_2
       (if (<= t -1.7e-48)
         (+ t_3 (* 18.0 (* t (* z (* x y)))))
         (if (<= t -1.15e-104)
           t_2
           (if (<= t 1.85e+53) (- (* b c) (+ t_1 (* 27.0 (* j k)))) t_4)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double t_3 = j * (k * -27.0);
	double t_4 = t_3 + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -6.8e+125) {
		tmp = t_4;
	} else if (t <= -2e-41) {
		tmp = t_2;
	} else if (t <= -1.7e-48) {
		tmp = t_3 + (18.0 * (t * (z * (x * y))));
	} else if (t <= -1.15e-104) {
		tmp = t_2;
	} else if (t <= 1.85e+53) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    t_3 = j * (k * (-27.0d0))
    t_4 = t_3 + (t * ((a * (-4.0d0)) + (18.0d0 * (x * (y * z)))))
    if (t <= (-6.8d+125)) then
        tmp = t_4
    else if (t <= (-2d-41)) then
        tmp = t_2
    else if (t <= (-1.7d-48)) then
        tmp = t_3 + (18.0d0 * (t * (z * (x * y))))
    else if (t <= (-1.15d-104)) then
        tmp = t_2
    else if (t <= 1.85d+53) then
        tmp = (b * c) - (t_1 + (27.0d0 * (j * k)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double t_3 = j * (k * -27.0);
	double t_4 = t_3 + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	double tmp;
	if (t <= -6.8e+125) {
		tmp = t_4;
	} else if (t <= -2e-41) {
		tmp = t_2;
	} else if (t <= -1.7e-48) {
		tmp = t_3 + (18.0 * (t * (z * (x * y))));
	} else if (t <= -1.15e-104) {
		tmp = t_2;
	} else if (t <= 1.85e+53) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = ((b * c) + (-4.0 * (t * a))) - t_1
	t_3 = j * (k * -27.0)
	t_4 = t_3 + (t * ((a * -4.0) + (18.0 * (x * (y * z)))))
	tmp = 0
	if t <= -6.8e+125:
		tmp = t_4
	elif t <= -2e-41:
		tmp = t_2
	elif t <= -1.7e-48:
		tmp = t_3 + (18.0 * (t * (z * (x * y))))
	elif t <= -1.15e-104:
		tmp = t_2
	elif t <= 1.85e+53:
		tmp = (b * c) - (t_1 + (27.0 * (j * k)))
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1)
	t_3 = Float64(j * Float64(k * -27.0))
	t_4 = Float64(t_3 + Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(x * Float64(y * z))))))
	tmp = 0.0
	if (t <= -6.8e+125)
		tmp = t_4;
	elseif (t <= -2e-41)
		tmp = t_2;
	elseif (t <= -1.7e-48)
		tmp = Float64(t_3 + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))));
	elseif (t <= -1.15e-104)
		tmp = t_2;
	elseif (t <= 1.85e+53)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = ((b * c) + (-4.0 * (t * a))) - t_1;
	t_3 = j * (k * -27.0);
	t_4 = t_3 + (t * ((a * -4.0) + (18.0 * (x * (y * z)))));
	tmp = 0.0;
	if (t <= -6.8e+125)
		tmp = t_4;
	elseif (t <= -2e-41)
		tmp = t_2;
	elseif (t <= -1.7e-48)
		tmp = t_3 + (18.0 * (t * (z * (x * y))));
	elseif (t <= -1.15e-104)
		tmp = t_2;
	elseif (t <= 1.85e+53)
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+125], t$95$4, If[LessEqual[t, -2e-41], t$95$2, If[LessEqual[t, -1.7e-48], N[(t$95$3 + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-104], t$95$2, If[LessEqual[t, 1.85e+53], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.7999999999999998e125 or 1.85e53 < t

   1. Initial program 78.5%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 84.5%

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

   if -6.7999999999999998e125 < t < -2.00000000000000001e-41 or -1.70000000000000014e-48 < t < -1.15e-104

   1. Initial program 97.2%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in j around 0 84.4%

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

   6. Taylor expanded in y around 0 74.0%

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

   if -2.00000000000000001e-41 < t < -1.70000000000000014e-48

   1. Initial program 100.0%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in x around 0 61.9%

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

      1. associate-*r* 100.0%

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

   10. Simplified 100.0%

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

   if -1.15e-104 < t < 1.85e53

   1. Initial program 89.8%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around 0 92.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+125}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-104}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_4 := t\_2 + t \cdot \left(a \cdot -4 + t\_3\right)\\ t_5 := b \cdot c - \left(t\_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(t\_3 - a \cdot 4\right) - t\_1\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-7}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-48}:\\ \;\;\;\;t\_2 + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+53}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* j (* k -27.0)))
        (t_3 (* 18.0 (* x (* y z))))
        (t_4 (+ t_2 (* t (+ (* a -4.0) t_3))))
        (t_5 (- (* b c) (+ t_1 (* 27.0 (* j k))))))
   (if (<= t -8.2e+68)
     (- (* t (- t_3 (* a 4.0))) t_1)
     (if (<= t -3.45e-7)
       t_5
       (if (<= t -5.5e-19)
         t_4
         (if (<= t -2.35e-48)
           (+ t_2 (* 18.0 (* t (* z (* x y)))))
           (if (<= t 1.35e+53) t_5 t_4)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = j * (k * -27.0);
	double t_3 = 18.0 * (x * (y * z));
	double t_4 = t_2 + (t * ((a * -4.0) + t_3));
	double t_5 = (b * c) - (t_1 + (27.0 * (j * k)));
	double tmp;
	if (t <= -8.2e+68) {
		tmp = (t * (t_3 - (a * 4.0))) - t_1;
	} else if (t <= -3.45e-7) {
		tmp = t_5;
	} else if (t <= -5.5e-19) {
		tmp = t_4;
	} else if (t <= -2.35e-48) {
		tmp = t_2 + (18.0 * (t * (z * (x * y))));
	} else if (t <= 1.35e+53) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = j * (k * (-27.0d0))
    t_3 = 18.0d0 * (x * (y * z))
    t_4 = t_2 + (t * ((a * (-4.0d0)) + t_3))
    t_5 = (b * c) - (t_1 + (27.0d0 * (j * k)))
    if (t <= (-8.2d+68)) then
        tmp = (t * (t_3 - (a * 4.0d0))) - t_1
    else if (t <= (-3.45d-7)) then
        tmp = t_5
    else if (t <= (-5.5d-19)) then
        tmp = t_4
    else if (t <= (-2.35d-48)) then
        tmp = t_2 + (18.0d0 * (t * (z * (x * y))))
    else if (t <= 1.35d+53) then
        tmp = t_5
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = j * (k * -27.0);
	double t_3 = 18.0 * (x * (y * z));
	double t_4 = t_2 + (t * ((a * -4.0) + t_3));
	double t_5 = (b * c) - (t_1 + (27.0 * (j * k)));
	double tmp;
	if (t <= -8.2e+68) {
		tmp = (t * (t_3 - (a * 4.0))) - t_1;
	} else if (t <= -3.45e-7) {
		tmp = t_5;
	} else if (t <= -5.5e-19) {
		tmp = t_4;
	} else if (t <= -2.35e-48) {
		tmp = t_2 + (18.0 * (t * (z * (x * y))));
	} else if (t <= 1.35e+53) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = j * (k * -27.0)
	t_3 = 18.0 * (x * (y * z))
	t_4 = t_2 + (t * ((a * -4.0) + t_3))
	t_5 = (b * c) - (t_1 + (27.0 * (j * k)))
	tmp = 0
	if t <= -8.2e+68:
		tmp = (t * (t_3 - (a * 4.0))) - t_1
	elif t <= -3.45e-7:
		tmp = t_5
	elif t <= -5.5e-19:
		tmp = t_4
	elif t <= -2.35e-48:
		tmp = t_2 + (18.0 * (t * (z * (x * y))))
	elif t <= 1.35e+53:
		tmp = t_5
	else:
		tmp = t_4
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_4 = Float64(t_2 + Float64(t * Float64(Float64(a * -4.0) + t_3)))
	t_5 = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))))
	tmp = 0.0
	if (t <= -8.2e+68)
		tmp = Float64(Float64(t * Float64(t_3 - Float64(a * 4.0))) - t_1);
	elseif (t <= -3.45e-7)
		tmp = t_5;
	elseif (t <= -5.5e-19)
		tmp = t_4;
	elseif (t <= -2.35e-48)
		tmp = Float64(t_2 + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))));
	elseif (t <= 1.35e+53)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = j * (k * -27.0);
	t_3 = 18.0 * (x * (y * z));
	t_4 = t_2 + (t * ((a * -4.0) + t_3));
	t_5 = (b * c) - (t_1 + (27.0 * (j * k)));
	tmp = 0.0;
	if (t <= -8.2e+68)
		tmp = (t * (t_3 - (a * 4.0))) - t_1;
	elseif (t <= -3.45e-7)
		tmp = t_5;
	elseif (t <= -5.5e-19)
		tmp = t_4;
	elseif (t <= -2.35e-48)
		tmp = t_2 + (18.0 * (t * (z * (x * y))));
	elseif (t <= 1.35e+53)
		tmp = t_5;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(t * N[(N[(a * -4.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+68], N[(N[(t * N[(t$95$3 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -3.45e-7], t$95$5, If[LessEqual[t, -5.5e-19], t$95$4, If[LessEqual[t, -2.35e-48], N[(t$95$2 + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+53], t$95$5, t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.1999999999999998e68

   1. Initial program 79.9%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in j around 0 78.3%

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

   6. Taylor expanded in b around 0 81.7%

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

   if -8.1999999999999998e68 < t < -3.4499999999999998e-7 or -2.3499999999999999e-48 < t < 1.3500000000000001e53

   1. Initial program 90.7%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in t around 0 90.0%

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

   if -3.4499999999999998e-7 < t < -5.4999999999999996e-19 or 1.3500000000000001e53 < t

   1. Initial program 81.8%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 83.8%

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

   if -5.4999999999999996e-19 < t < -2.3499999999999999e-48

   1. Initial program 99.8%

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

   3. Simplified 59.3%

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

   5. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

   7. Simplified 45.4%

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

   8. Taylor expanded in x around 0 45.4%

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

      1. associate-*r* 85.9%

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

   10. Simplified 85.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-7}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+161}:\\ \;\;\;\;t\_1 + t\_3\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+218}:\\ \;\;\;\;b \cdot c + t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* 18.0 (* t (* z (* x y))))))
        (t_3 (* -4.0 (* t a))))
   (if (<= t -9.5e+127)
     t_2
     (if (<= t 1.4e+54)
       (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
       (if (<= t 2.9e+161)
         (+ t_1 t_3)
         (if (<= t 4.7e+179)
           t_2
           (if (<= t 1.05e+218)
             (+ (* b c) t_3)
             (+ (* b c) (* 18.0 (* t (* x (* y z))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (18.0 * (t * (z * (x * y))));
	double t_3 = -4.0 * (t * a);
	double tmp;
	if (t <= -9.5e+127) {
		tmp = t_2;
	} else if (t <= 1.4e+54) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if (t <= 2.9e+161) {
		tmp = t_1 + t_3;
	} else if (t <= 4.7e+179) {
		tmp = t_2;
	} else if (t <= 1.05e+218) {
		tmp = (b * c) + t_3;
	} else {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = j * (k * (-27.0d0))
    t_2 = t_1 + (18.0d0 * (t * (z * (x * y))))
    t_3 = (-4.0d0) * (t * a)
    if (t <= (-9.5d+127)) then
        tmp = t_2
    else if (t <= 1.4d+54) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else if (t <= 2.9d+161) then
        tmp = t_1 + t_3
    else if (t <= 4.7d+179) then
        tmp = t_2
    else if (t <= 1.05d+218) then
        tmp = (b * c) + t_3
    else
        tmp = (b * c) + (18.0d0 * (t * (x * (y * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (18.0 * (t * (z * (x * y))));
	double t_3 = -4.0 * (t * a);
	double tmp;
	if (t <= -9.5e+127) {
		tmp = t_2;
	} else if (t <= 1.4e+54) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else if (t <= 2.9e+161) {
		tmp = t_1 + t_3;
	} else if (t <= 4.7e+179) {
		tmp = t_2;
	} else if (t <= 1.05e+218) {
		tmp = (b * c) + t_3;
	} else {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (18.0 * (t * (z * (x * y))))
	t_3 = -4.0 * (t * a)
	tmp = 0
	if t <= -9.5e+127:
		tmp = t_2
	elif t <= 1.4e+54:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	elif t <= 2.9e+161:
		tmp = t_1 + t_3
	elif t <= 4.7e+179:
		tmp = t_2
	elif t <= 1.05e+218:
		tmp = (b * c) + t_3
	else:
		tmp = (b * c) + (18.0 * (t * (x * (y * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))))
	t_3 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (t <= -9.5e+127)
		tmp = t_2;
	elseif (t <= 1.4e+54)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	elseif (t <= 2.9e+161)
		tmp = Float64(t_1 + t_3);
	elseif (t <= 4.7e+179)
		tmp = t_2;
	elseif (t <= 1.05e+218)
		tmp = Float64(Float64(b * c) + t_3);
	else
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (18.0 * (t * (z * (x * y))));
	t_3 = -4.0 * (t * a);
	tmp = 0.0;
	if (t <= -9.5e+127)
		tmp = t_2;
	elseif (t <= 1.4e+54)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	elseif (t <= 2.9e+161)
		tmp = t_1 + t_3;
	elseif (t <= 4.7e+179)
		tmp = t_2;
	elseif (t <= 1.05e+218)
		tmp = (b * c) + t_3;
	else
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+127], t$95$2, If[LessEqual[t, 1.4e+54], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+161], N[(t$95$1 + t$95$3), $MachinePrecision], If[LessEqual[t, 4.7e+179], t$95$2, If[LessEqual[t, 1.05e+218], N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.49999999999999975e127 or 2.90000000000000016e161 < t < 4.70000000000000007e179

   1. Initial program 71.7%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in y around inf 64.8%

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

      1. *-commutative 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in x around 0 64.8%

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

      1. associate-*r* 64.9%

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

   10. Simplified 64.9%

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

   if -9.49999999999999975e127 < t < 1.40000000000000008e54

   1. Initial program 91.9%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in t around 0 84.0%

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

   if 1.40000000000000008e54 < t < 2.90000000000000016e161

   1. Initial program 88.2%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around inf 71.5%

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

   if 4.70000000000000007e179 < t < 1.0499999999999999e218

   1. Initial program 84.6%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around 0 100.0%

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

   6. Taylor expanded in x around 0 77.0%

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

   if 1.0499999999999999e218 < t

   1. Initial program 78.5%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around 0 96.4%

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

   6. Taylor expanded in a around 0 67.5%

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

   7. Taylor expanded in i around 0 68.3%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+161}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+179}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+218}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.5e-19)
   (+ (* x (* (* y t) (* 18.0 z))) (* j (* k -27.0)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.5e-19) {
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-1.5d-19)) then
        tmp = (x * ((y * t) * (18.0d0 * z))) + (j * (k * (-27.0d0)))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.5e-19) {
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.5e-19:
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.5e-19)
		tmp = Float64(Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.5e-19)
		tmp = (x * ((y * t) * (18.0 * z))) + (j * (k * -27.0));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.5e-19], N[(N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -1.49999999999999996e-19

   1. Initial program 81.2%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-*r* 53.6%

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

      3. associate-*l* 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

      6. associate-*r* 54.9%

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

      7. associate-*l* 54.9%

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

      8. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -1.49999999999999996e-19 < k

   1. Initial program 89.2%

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

   3. Simplified 91.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{+125}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + t\_1\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(t\_2 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (* 4.0 (* x i))))
   (if (<= t -9.8e+125)
     (+ (* j (* k -27.0)) (* t (+ (* a -4.0) t_1)))
     (if (<= t 1.9e+111)
       (- (+ (* b c) (* -4.0 (* t a))) (+ t_2 (* 27.0 (* j k))))
       (- (+ (* b c) (* t (- t_1 (* a 4.0)))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -9.8e+125) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1));
	} else if (t <= 1.9e+111) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    if (t <= (-9.8d+125)) then
        tmp = (j * (k * (-27.0d0))) + (t * ((a * (-4.0d0)) + t_1))
    else if (t <= 1.9d+111) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (t_2 + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -9.8e+125) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1));
	} else if (t <= 1.9e+111) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	tmp = 0
	if t <= -9.8e+125:
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1))
	elif t <= 1.9e+111:
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -9.8e+125)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(a * -4.0) + t_1)));
	elseif (t <= 1.9e+111)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(t_2 + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -9.8e+125)
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1));
	elseif (t <= 1.9e+111)
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.8e+125], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+111], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.80000000000000032e125

   1. Initial program 74.9%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around inf 84.9%

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

   if -9.80000000000000032e125 < t < 1.89999999999999988e111

   1. Initial program 92.5%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 91.1%

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

   if 1.89999999999999988e111 < t

   1. Initial program 75.4%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in j around 0 92.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+125}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+52} \lor \neg \left(t \leq -2.45 \cdot 10^{-7} \lor \neg \left(t \leq -1.2 \cdot 10^{-76}\right) \land t \leq 6.8 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.4e+52)
         (not (or (<= t -2.45e-7) (and (not (<= t -1.2e-76)) (<= t 6.8e+73)))))
   (+ (* b c) (* -4.0 (* t a)))
   (+ (* j (* k -27.0)) (* -4.0 (* x i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.4e+52) || !((t <= -2.45e-7) || (!(t <= -1.2e-76) && (t <= 6.8e+73)))) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 ((t <= (-2.4d+52)) .or. (.not. (t <= (-2.45d-7)) .or. (.not. (t <= (-1.2d-76))) .and. (t <= 6.8d+73))) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else
        tmp = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((t <= -2.4e+52) || !((t <= -2.45e-7) || (!(t <= -1.2e-76) && (t <= 6.8e+73)))) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else {
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -2.4e+52) or not ((t <= -2.45e-7) or (not (t <= -1.2e-76) and (t <= 6.8e+73))):
		tmp = (b * c) + (-4.0 * (t * a))
	else:
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.4e+52) || !((t <= -2.45e-7) || (!(t <= -1.2e-76) && (t <= 6.8e+73))))
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -2.4e+52) || ~(((t <= -2.45e-7) || (~((t <= -1.2e-76)) && (t <= 6.8e+73)))))
		tmp = (b * c) + (-4.0 * (t * a));
	else
		tmp = (j * (k * -27.0)) + (-4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.4e+52], N[Not[Or[LessEqual[t, -2.45e-7], And[N[Not[LessEqual[t, -1.2e-76]], $MachinePrecision], LessEqual[t, 6.8e+73]]]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e52 or -2.4499999999999998e-7 < t < -1.20000000000000007e-76 or 6.8000000000000003e73 < t

   1. Initial program 82.4%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in j around 0 83.8%

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

   6. Taylor expanded in x around 0 50.9%

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

   if -2.4e52 < t < -2.4499999999999998e-7 or -1.20000000000000007e-76 < t < 6.8000000000000003e73

   1. Initial program 90.5%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in i around inf 73.6%

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

      1. *-commutative 73.6%

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

   7. Simplified 73.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+52} \lor \neg \left(t \leq -2.45 \cdot 10^{-7} \lor \neg \left(t \leq -1.2 \cdot 10^{-76}\right) \land t \leq 6.8 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t\_1 + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-299}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* -4.0 (* t a))))
        (t_3 (- (* b c) (* x (* 4.0 i)))))
   (if (<= x -3.8e+61)
     t_3
     (if (<= x -3.65e-258)
       t_2
       (if (<= x 1.6e-299) (+ (* b c) t_1) (if (<= x 3.3e-24) t_2 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double t_3 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (x <= -3.8e+61) {
		tmp = t_3;
	} else if (x <= -3.65e-258) {
		tmp = t_2;
	} else if (x <= 1.6e-299) {
		tmp = (b * c) + t_1;
	} else if (x <= 3.3e-24) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (t * a))
    t_3 = (b * c) - (x * (4.0d0 * i))
    if (x <= (-3.8d+61)) then
        tmp = t_3
    else if (x <= (-3.65d-258)) then
        tmp = t_2
    else if (x <= 1.6d-299) then
        tmp = (b * c) + t_1
    else if (x <= 3.3d-24) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double t_3 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (x <= -3.8e+61) {
		tmp = t_3;
	} else if (x <= -3.65e-258) {
		tmp = t_2;
	} else if (x <= 1.6e-299) {
		tmp = (b * c) + t_1;
	} else if (x <= 3.3e-24) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (t * a))
	t_3 = (b * c) - (x * (4.0 * i))
	tmp = 0
	if x <= -3.8e+61:
		tmp = t_3
	elif x <= -3.65e-258:
		tmp = t_2
	elif x <= 1.6e-299:
		tmp = (b * c) + t_1
	elif x <= 3.3e-24:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	t_3 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -3.8e+61)
		tmp = t_3;
	elseif (x <= -3.65e-258)
		tmp = t_2;
	elseif (x <= 1.6e-299)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 3.3e-24)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (t * a));
	t_3 = (b * c) - (x * (4.0 * i));
	tmp = 0.0;
	if (x <= -3.8e+61)
		tmp = t_3;
	elseif (x <= -3.65e-258)
		tmp = t_2;
	elseif (x <= 1.6e-299)
		tmp = (b * c) + t_1;
	elseif (x <= 3.3e-24)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+61], t$95$3, If[LessEqual[x, -3.65e-258], t$95$2, If[LessEqual[x, 1.6e-299], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 3.3e-24], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.79999999999999995e61 or 3.29999999999999984e-24 < x

   1. Initial program 78.7%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in t around 0 64.5%

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

   6. Taylor expanded in i around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-*r* 55.9%

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

      3. *-commutative 55.9%

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

      4. associate-*l* 55.9%

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

   8. Simplified 55.9%

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

   if -3.79999999999999995e61 < x < -3.6500000000000001e-258 or 1.60000000000000004e-299 < x < 3.29999999999999984e-24

   1. Initial program 94.1%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 66.4%

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

   if -3.6500000000000001e-258 < x < 1.60000000000000004e-299

   1. Initial program 92.1%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in b around inf 77.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;x \leq -3.65 \cdot 10^{-258}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-299}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + t\_1\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+185}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(t\_2 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t\_1 - a \cdot 4\right) - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (* 4.0 (* x i))))
   (if (<= t -1.15e+126)
     (+ (* j (* k -27.0)) (* t (+ (* a -4.0) t_1)))
     (if (<= t 5.6e+185)
       (- (+ (* b c) (* -4.0 (* t a))) (+ t_2 (* 27.0 (* j k))))
       (- (* t (- t_1 (* a 4.0))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -1.15e+126) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1));
	} else if (t <= 5.6e+185) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = (t * (t_1 - (a * 4.0))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    t_2 = 4.0d0 * (x * i)
    if (t <= (-1.15d+126)) then
        tmp = (j * (k * (-27.0d0))) + (t * ((a * (-4.0d0)) + t_1))
    else if (t <= 5.6d+185) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (t_2 + (27.0d0 * (j * k)))
    else
        tmp = (t * (t_1 - (a * 4.0d0))) - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -1.15e+126) {
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1));
	} else if (t <= 5.6e+185) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = (t * (t_1 - (a * 4.0))) - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	tmp = 0
	if t <= -1.15e+126:
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1))
	elif t <= 5.6e+185:
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)))
	else:
		tmp = (t * (t_1 - (a * 4.0))) - t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -1.15e+126)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(a * -4.0) + t_1)));
	elseif (t <= 5.6e+185)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(t_2 + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(t * Float64(t_1 - Float64(a * 4.0))) - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -1.15e+126)
		tmp = (j * (k * -27.0)) + (t * ((a * -4.0) + t_1));
	elseif (t <= 5.6e+185)
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	else
		tmp = (t * (t_1 - (a * 4.0))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+126], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+185], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e126

   1. Initial program 74.9%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around inf 84.9%

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

   if -1.15e126 < t < 5.59999999999999964e185

   1. Initial program 90.7%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around 0 89.3%

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

   if 5.59999999999999964e185 < t

   1. Initial program 78.9%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in j around 0 97.4%

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

   6. Taylor expanded in b around 0 97.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4 + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+185}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t\_1\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(t \cdot \left(z \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))))
   (if (<= x -3.6e+161)
     (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
     (if (<= x -3.1e+27)
       (- (* b c) (+ (* 4.0 (* x i)) t_1))
       (if (<= x 3.8e+57)
         (- (+ (* b c) (* -4.0 (* t a))) t_1)
         (* x (- (* y (* t (* z (- -18.0)))) (* 4.0 i))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if (x <= -3.6e+161) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -3.1e+27) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else if (x <= 3.8e+57) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    if (x <= (-3.6d+161)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (x <= (-3.1d+27)) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + t_1)
    else if (x <= 3.8d+57) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else
        tmp = x * ((y * (t * (z * -(-18.0d0)))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 tmp;
	if (x <= -3.6e+161) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (x <= -3.1e+27) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else if (x <= 3.8e+57) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else {
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	tmp = 0
	if x <= -3.6e+161:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif x <= -3.1e+27:
		tmp = (b * c) - ((4.0 * (x * i)) + t_1)
	elif x <= 3.8e+57:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	else:
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (x <= -3.6e+161)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (x <= -3.1e+27)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	elseif (x <= 3.8e+57)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(x * Float64(Float64(y * Float64(t * Float64(z * Float64(-(-18.0))))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	tmp = 0.0;
	if (x <= -3.6e+161)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (x <= -3.1e+27)
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	elseif (x <= 3.8e+57)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	else
		tmp = x * ((y * (t * (z * -(-18.0)))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+161], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e+27], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+57], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x * N[(N[(y * N[(t * N[(z * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.59999999999999984e161

   1. Initial program 73.2%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 85.5%

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

   if -3.59999999999999984e161 < x < -3.09999999999999996e27

   1. Initial program 80.5%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in t around 0 73.7%

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

   if -3.09999999999999996e27 < x < 3.7999999999999999e57

   1. Initial program 94.4%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around 0 80.6%

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

   if 3.7999999999999999e57 < x

   1. Initial program 80.3%

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

   3. Simplified 86.3%

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

      1. associate-*r* 83.3%

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

      2. distribute-rgt-out-- 80.3%

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

      3. associate-+l- 80.3%

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

      4. associate-*r* 83.2%

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

      5. *-commutative 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. fma-neg 83.2%

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

   6. Applied egg-rr 83.2%

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

   7. Taylor expanded in t around 0 86.2%

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

      1. fma-def 87.8%

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

      2. cancel-sign-sub-inv 87.8%

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

      3. metadata-eval 87.8%

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

      4. *-commutative 87.8%

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

   9. Simplified 87.8%

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

   10. Taylor expanded in x around -inf 80.6%

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

       1. associate-*r* 80.6%

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

       2. neg-mul-1 80.6%

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

       3. cancel-sign-sub-inv 80.6%

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

       4. *-commutative 80.6%

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

       5. associate-*r* 80.6%

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

       6. metadata-eval 80.6%

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

   12. Simplified 80.6%

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

   13. Taylor expanded in t around 0 80.6%

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

       1. *-commutative 80.6%

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

       2. associate-*r* 80.6%

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

       3. *-commutative 80.6%

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

       4. associate-*r* 80.6%

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

       5. associate-*l* 78.1%

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

   15. Simplified 78.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+27}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(t \cdot \left(z \cdot \left(--18\right)\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -1.24 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-147}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a)))) (t_2 (* x (* i -4.0))))
   (if (<= x -1.24e+95)
     t_2
     (if (<= x -1.3e-103)
       t_1
       (if (<= x -1.35e-147) (* -27.0 (* j k)) (if (<= x 2.8e+60) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (x <= -1.24e+95) {
		tmp = t_2;
	} else if (x <= -1.3e-103) {
		tmp = t_1;
	} else if (x <= -1.35e-147) {
		tmp = -27.0 * (j * k);
	} else if (x <= 2.8e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = x * (i * (-4.0d0))
    if (x <= (-1.24d+95)) then
        tmp = t_2
    else if (x <= (-1.3d-103)) then
        tmp = t_1
    else if (x <= (-1.35d-147)) then
        tmp = (-27.0d0) * (j * k)
    else if (x <= 2.8d+60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (-4.0 * (t * a));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (x <= -1.24e+95) {
		tmp = t_2;
	} else if (x <= -1.3e-103) {
		tmp = t_1;
	} else if (x <= -1.35e-147) {
		tmp = -27.0 * (j * k);
	} else if (x <= 2.8e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = x * (i * -4.0)
	tmp = 0
	if x <= -1.24e+95:
		tmp = t_2
	elif x <= -1.3e-103:
		tmp = t_1
	elif x <= -1.35e-147:
		tmp = -27.0 * (j * k)
	elif x <= 2.8e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (x <= -1.24e+95)
		tmp = t_2;
	elseif (x <= -1.3e-103)
		tmp = t_1;
	elseif (x <= -1.35e-147)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (x <= 2.8e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if (x <= -1.24e+95)
		tmp = t_2;
	elseif (x <= -1.3e-103)
		tmp = t_1;
	elseif (x <= -1.35e-147)
		tmp = -27.0 * (j * k);
	elseif (x <= 2.8e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.24e+95], t$95$2, If[LessEqual[x, -1.3e-103], t$95$1, If[LessEqual[x, -1.35e-147], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.23999999999999997e95 or 2.8e60 < x

   1. Initial program 77.3%

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

   3. Simplified 83.9%

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

      1. associate-*r* 79.2%

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

      2. distribute-rgt-out-- 77.3%

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

      3. associate-+l- 77.3%

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

      4. associate-*r* 81.0%

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

      5. *-commutative 81.0%

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

      6. *-commutative 81.0%

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

      7. associate-*l* 81.0%

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

      8. fma-neg 81.0%

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

   6. Applied egg-rr 81.0%

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

   7. Taylor expanded in i around inf 50.7%

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

      1. *-commutative 50.7%

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

      2. associate-*l* 50.7%

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

      3. metadata-eval 50.7%

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

      4. distribute-lft-neg-in 50.7%

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

      5. *-commutative 50.7%

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

      6. distribute-lft-neg-in 50.7%

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

      7. associate-*l* 50.7%

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

      8. distribute-rgt-neg-in 50.7%

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

      9. distribute-lft-neg-in 50.7%

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

      10. metadata-eval 50.7%

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

   9. Simplified 50.7%

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

   if -1.23999999999999997e95 < x < -1.29999999999999998e-103 or -1.35e-147 < x < 2.8e60

   1. Initial program 92.9%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in j around 0 68.3%

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

   6. Taylor expanded in x around 0 50.7%

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

   if -1.29999999999999998e-103 < x < -1.35e-147

   1. Initial program 99.8%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around inf 65.1%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.24 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-103}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-147}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))) (t_2 (* x (* i -4.0))))
   (if (<= x -3.8e+146)
     t_2
     (if (<= x 2.75e-235)
       t_1
       (if (<= x 2.8e-41)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 3.1e+60) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (x <= -3.8e+146) {
		tmp = t_2;
	} else if (x <= 2.75e-235) {
		tmp = t_1;
	} else if (x <= 2.8e-41) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.1e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    t_2 = x * (i * (-4.0d0))
    if (x <= (-3.8d+146)) then
        tmp = t_2
    else if (x <= 2.75d-235) then
        tmp = t_1
    else if (x <= 2.8d-41) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 3.1d+60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (x <= -3.8e+146) {
		tmp = t_2;
	} else if (x <= 2.75e-235) {
		tmp = t_1;
	} else if (x <= 2.8e-41) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 3.1e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	t_2 = x * (i * -4.0)
	tmp = 0
	if x <= -3.8e+146:
		tmp = t_2
	elif x <= 2.75e-235:
		tmp = t_1
	elif x <= 2.8e-41:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 3.1e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (x <= -3.8e+146)
		tmp = t_2;
	elseif (x <= 2.75e-235)
		tmp = t_1;
	elseif (x <= 2.8e-41)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 3.1e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if (x <= -3.8e+146)
		tmp = t_2;
	elseif (x <= 2.75e-235)
		tmp = t_1;
	elseif (x <= 2.8e-41)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 3.1e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+146], t$95$2, If[LessEqual[x, 2.75e-235], t$95$1, If[LessEqual[x, 2.8e-41], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.79999999999999979e146 or 3.1000000000000001e60 < x

   1. Initial program 78.1%

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

   3. Simplified 85.3%

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

      1. associate-*r* 80.2%

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

      2. distribute-rgt-out-- 78.1%

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

      3. associate-+l- 78.1%

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

      4. associate-*r* 82.2%

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

      5. *-commutative 82.2%

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

      6. *-commutative 82.2%

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

      7. associate-*l* 82.2%

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

      8. fma-neg 82.2%

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

   6. Applied egg-rr 82.2%

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

   7. Taylor expanded in i around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-*l* 51.8%

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

      3. metadata-eval 51.8%

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

      4. distribute-lft-neg-in 51.8%

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

      5. *-commutative 51.8%

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

      6. distribute-lft-neg-in 51.8%

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

      7. associate-*l* 51.8%

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

      8. distribute-rgt-neg-in 51.8%

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

      9. distribute-lft-neg-in 51.8%

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

      10. metadata-eval 51.8%

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

   9. Simplified 51.8%

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

   if -3.79999999999999979e146 < x < 2.7499999999999999e-235 or 2.8000000000000002e-41 < x < 3.1000000000000001e60

   1. Initial program 90.6%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around inf 58.9%

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

   if 2.7499999999999999e-235 < x < 2.8000000000000002e-41

   1. Initial program 96.8%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in j around 0 67.0%

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

   6. Taylor expanded in x around 0 50.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))) (t_2 (- (* b c) (* x (* 4.0 i)))))
   (if (<= x -5.8e+55)
     t_2
     (if (<= x 3.7e-237)
       t_1
       (if (<= x 5.5e-39)
         (+ (* b c) (* -4.0 (* t a)))
         (if (<= x 2.2e+59) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double t_2 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (x <= -5.8e+55) {
		tmp = t_2;
	} else if (x <= 3.7e-237) {
		tmp = t_1;
	} else if (x <= 5.5e-39) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.2e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    t_2 = (b * c) - (x * (4.0d0 * i))
    if (x <= (-5.8d+55)) then
        tmp = t_2
    else if (x <= 3.7d-237) then
        tmp = t_1
    else if (x <= 5.5d-39) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 2.2d+59) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (j * (k * -27.0));
	double t_2 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (x <= -5.8e+55) {
		tmp = t_2;
	} else if (x <= 3.7e-237) {
		tmp = t_1;
	} else if (x <= 5.5e-39) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 2.2e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	t_2 = (b * c) - (x * (4.0 * i))
	tmp = 0
	if x <= -5.8e+55:
		tmp = t_2
	elif x <= 3.7e-237:
		tmp = t_1
	elif x <= 5.5e-39:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 2.2e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -5.8e+55)
		tmp = t_2;
	elseif (x <= 3.7e-237)
		tmp = t_1;
	elseif (x <= 5.5e-39)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 2.2e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	t_2 = (b * c) - (x * (4.0 * i));
	tmp = 0.0;
	if (x <= -5.8e+55)
		tmp = t_2;
	elseif (x <= 3.7e-237)
		tmp = t_1;
	elseif (x <= 5.5e-39)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 2.2e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+55], t$95$2, If[LessEqual[x, 3.7e-237], t$95$1, If[LessEqual[x, 5.5e-39], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7999999999999997e55 or 2.2e59 < x

   1. Initial program 77.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in t around 0 65.0%

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

   6. Taylor expanded in i around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-*r* 56.7%

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

      3. *-commutative 56.7%

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

      4. associate-*l* 56.7%

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

   8. Simplified 56.7%

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

   if -5.7999999999999997e55 < x < 3.7000000000000001e-237 or 5.50000000000000018e-39 < x < 2.2e59

   1. Initial program 93.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in b around inf 59.6%

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

   if 3.7000000000000001e-237 < x < 5.50000000000000018e-39

   1. Initial program 96.8%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in j around 0 67.0%

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

   6. Taylor expanded in x around 0 50.4%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+55}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-237}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+62}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= x -1.35e+147)
     t_1
     (if (<= x 4e-166)
       (* j (* k -27.0))
       (if (<= x 1.12e+21)
         (* b c)
         (if (<= x 8.5e+62) (* -27.0 (* j k)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (x <= -1.35e+147) {
		tmp = t_1;
	} else if (x <= 4e-166) {
		tmp = j * (k * -27.0);
	} else if (x <= 1.12e+21) {
		tmp = b * c;
	} else if (x <= 8.5e+62) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if (x <= (-1.35d+147)) then
        tmp = t_1
    else if (x <= 4d-166) then
        tmp = j * (k * (-27.0d0))
    else if (x <= 1.12d+21) then
        tmp = b * c
    else if (x <= 8.5d+62) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (x <= -1.35e+147) {
		tmp = t_1;
	} else if (x <= 4e-166) {
		tmp = j * (k * -27.0);
	} else if (x <= 1.12e+21) {
		tmp = b * c;
	} else if (x <= 8.5e+62) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if x <= -1.35e+147:
		tmp = t_1
	elif x <= 4e-166:
		tmp = j * (k * -27.0)
	elif x <= 1.12e+21:
		tmp = b * c
	elif x <= 8.5e+62:
		tmp = -27.0 * (j * k)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (x <= -1.35e+147)
		tmp = t_1;
	elseif (x <= 4e-166)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= 1.12e+21)
		tmp = Float64(b * c);
	elseif (x <= 8.5e+62)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if (x <= -1.35e+147)
		tmp = t_1;
	elseif (x <= 4e-166)
		tmp = j * (k * -27.0);
	elseif (x <= 1.12e+21)
		tmp = b * c;
	elseif (x <= 8.5e+62)
		tmp = -27.0 * (j * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+147], t$95$1, If[LessEqual[x, 4e-166], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+21], N[(b * c), $MachinePrecision], If[LessEqual[x, 8.5e+62], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.34999999999999999e147 or 8.4999999999999997e62 < x

   1. Initial program 78.1%

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

   3. Simplified 85.3%

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

      1. associate-*r* 80.2%

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

      2. distribute-rgt-out-- 78.1%

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

      3. associate-+l- 78.1%

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

      4. associate-*r* 82.2%

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

      5. *-commutative 82.2%

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

      6. *-commutative 82.2%

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

      7. associate-*l* 82.2%

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

      8. fma-neg 82.2%

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

   6. Applied egg-rr 82.2%

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

   7. Taylor expanded in i around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-*l* 51.8%

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

      3. metadata-eval 51.8%

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

      4. distribute-lft-neg-in 51.8%

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

      5. *-commutative 51.8%

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

      6. distribute-lft-neg-in 51.8%

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

      7. associate-*l* 51.8%

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

      8. distribute-rgt-neg-in 51.8%

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

      9. distribute-lft-neg-in 51.8%

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

      10. metadata-eval 51.8%

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

   9. Simplified 51.8%

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

   if -1.34999999999999999e147 < x < 4.00000000000000016e-166

   1. Initial program 91.5%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in j around inf 39.8%

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

      1. *-commutative 39.8%

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

      2. associate-*r* 39.8%

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

      3. *-commutative 39.8%

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

   7. Simplified 39.8%

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

   if 4.00000000000000016e-166 < x < 1.12e21

   1. Initial program 91.7%

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

   3. Simplified 91.9%

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

      1. associate-*r* 100.0%

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

      2. distribute-rgt-out-- 91.7%

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

      3. associate-+l- 91.7%

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

      4. associate-*r* 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. associate-*l* 83.6%

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

      8. fma-neg 87.7%

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

   6. Applied egg-rr 87.7%

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

   7. Taylor expanded in t around 0 91.9%

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

      1. fma-def 91.9%

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

      2. cancel-sign-sub-inv 91.9%

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

      3. metadata-eval 91.9%

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

      4. *-commutative 91.9%

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

   9. Simplified 91.9%

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

   10. Taylor expanded in b around inf 30.6%

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

   if 1.12e21 < x < 8.4999999999999997e62

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around inf 48.7%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+21}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+62}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= x -3.7e+146)
     t_1
     (if (<= x 4.6e-164)
       (* k (* j -27.0))
       (if (<= x 3.3e+18)
         (* b c)
         (if (<= x 2.6e+63) (* -27.0 (* j k)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (x <= -3.7e+146) {
		tmp = t_1;
	} else if (x <= 4.6e-164) {
		tmp = k * (j * -27.0);
	} else if (x <= 3.3e+18) {
		tmp = b * c;
	} else if (x <= 2.6e+63) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if (x <= (-3.7d+146)) then
        tmp = t_1
    else if (x <= 4.6d-164) then
        tmp = k * (j * (-27.0d0))
    else if (x <= 3.3d+18) then
        tmp = b * c
    else if (x <= 2.6d+63) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (x <= -3.7e+146) {
		tmp = t_1;
	} else if (x <= 4.6e-164) {
		tmp = k * (j * -27.0);
	} else if (x <= 3.3e+18) {
		tmp = b * c;
	} else if (x <= 2.6e+63) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if x <= -3.7e+146:
		tmp = t_1
	elif x <= 4.6e-164:
		tmp = k * (j * -27.0)
	elif x <= 3.3e+18:
		tmp = b * c
	elif x <= 2.6e+63:
		tmp = -27.0 * (j * k)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (x <= -3.7e+146)
		tmp = t_1;
	elseif (x <= 4.6e-164)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (x <= 3.3e+18)
		tmp = Float64(b * c);
	elseif (x <= 2.6e+63)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if (x <= -3.7e+146)
		tmp = t_1;
	elseif (x <= 4.6e-164)
		tmp = k * (j * -27.0);
	elseif (x <= 3.3e+18)
		tmp = b * c;
	elseif (x <= 2.6e+63)
		tmp = -27.0 * (j * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+146], t$95$1, If[LessEqual[x, 4.6e-164], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+18], N[(b * c), $MachinePrecision], If[LessEqual[x, 2.6e+63], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.70000000000000004e146 or 2.6000000000000001e63 < x

   1. Initial program 78.1%

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

   3. Simplified 85.3%

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

      1. associate-*r* 80.2%

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

      2. distribute-rgt-out-- 78.1%

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

      3. associate-+l- 78.1%

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

      4. associate-*r* 82.2%

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

      5. *-commutative 82.2%

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

      6. *-commutative 82.2%

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

      7. associate-*l* 82.2%

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

      8. fma-neg 82.2%

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

   6. Applied egg-rr 82.2%

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

   7. Taylor expanded in i around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-*l* 51.8%

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

      3. metadata-eval 51.8%

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

      4. distribute-lft-neg-in 51.8%

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

      5. *-commutative 51.8%

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

      6. distribute-lft-neg-in 51.8%

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

      7. associate-*l* 51.8%

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

      8. distribute-rgt-neg-in 51.8%

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

      9. distribute-lft-neg-in 51.8%

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

      10. metadata-eval 51.8%

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

   9. Simplified 51.8%

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

   if -3.70000000000000004e146 < x < 4.59999999999999971e-164

   1. Initial program 91.5%

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

   3. Simplified 90.1%

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

      1. associate-*r* 94.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. associate-+l- 91.5%

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

      4. associate-*r* 87.8%

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

      5. *-commutative 87.8%

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

      6. *-commutative 87.8%

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

      7. associate-*l* 87.8%

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

      8. fma-neg 87.8%

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

   6. Applied egg-rr 87.8%

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

   7. Taylor expanded in j around inf 39.8%

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

      1. associate-*r* 39.8%

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

      2. *-commutative 39.8%

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

   9. Simplified 39.8%

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

   if 4.59999999999999971e-164 < x < 3.3e18

   1. Initial program 91.7%

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

   3. Simplified 91.9%

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

      1. associate-*r* 100.0%

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

      2. distribute-rgt-out-- 91.7%

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

      3. associate-+l- 91.7%

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

      4. associate-*r* 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. associate-*l* 83.6%

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

      8. fma-neg 87.7%

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

   6. Applied egg-rr 87.7%

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

   7. Taylor expanded in t around 0 91.9%

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

      1. fma-def 91.9%

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

      2. cancel-sign-sub-inv 91.9%

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

      3. metadata-eval 91.9%

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

      4. *-commutative 91.9%

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

   9. Simplified 91.9%

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

   10. Taylor expanded in b around inf 30.6%

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

   if 3.3e18 < x < 2.6000000000000001e63

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around inf 48.7%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-164}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.2 \cdot 10^{+232} \lor \neg \left(b \cdot c \leq 1.4 \cdot 10^{+64}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -7.2e+232) (not (<= (* b c) 1.4e+64)))
   (* 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);
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) <= -7.2e+232) || !((b * c) <= 1.4e+64)) {
		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.
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) <= (-7.2d+232)) .or. (.not. ((b * c) <= 1.4d+64))) 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;
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) <= -7.2e+232) || !((b * c) <= 1.4e+64)) {
		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])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -7.2e+232) or not ((b * c) <= 1.4e+64):
		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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -7.2e+232) || !(Float64(b * c) <= 1.4e+64))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -7.2e+232) || ~(((b * c) <= 1.4e+64)))
		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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -7.2e+232], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.4e+64]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -7.19999999999999986e232 or 1.40000000000000012e64 < (*.f64 b c)

   1. Initial program 84.9%

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

   3. Simplified 90.9%

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

      1. associate-*r* 89.5%

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

      2. distribute-rgt-out-- 85.0%

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

      3. associate-+l- 85.0%

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

      4. associate-*r* 86.4%

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

      5. *-commutative 86.4%

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

      6. *-commutative 86.4%

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

      7. associate-*l* 86.4%

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

      8. fma-neg 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in t around 0 90.9%

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

      1. fma-def 95.5%

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

      2. cancel-sign-sub-inv 95.5%

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

      3. metadata-eval 95.5%

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

      4. *-commutative 95.5%

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

   9. Simplified 95.5%

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

   10. Taylor expanded in b around inf 52.6%

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

   if -7.19999999999999986e232 < (*.f64 b c) < 1.40000000000000012e64

   1. Initial program 87.3%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in j around inf 29.2%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.2 \cdot 10^{+232} \lor \neg \left(b \cdot c \leq 1.4 \cdot 10^{+64}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.1% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

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

Derivation

1. Initial program 86.7%

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

3. Simplified 88.7%

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

   1. associate-*r* 89.9%

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

   2. distribute-rgt-out-- 86.7%

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

   3. associate-+l- 86.7%

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

   4. associate-*r* 85.6%

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

   5. *-commutative 85.6%

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

   6. *-commutative 85.6%

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

   7. associate-*l* 85.6%

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

   8. fma-neg 86.0%

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

6. Applied egg-rr 86.0%

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

7. Taylor expanded in t around 0 88.7%

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

   1. fma-def 89.9%

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

   2. cancel-sign-sub-inv 89.9%

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

   3. metadata-eval 89.9%

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

   4. *-commutative 89.9%

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

9. Simplified 89.9%

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

10. Taylor expanded in b around inf 17.5%

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

11. Final simplification 17.5%

    \[\leadsto b \cdot c \]
12. Add Preprocessing

Developer target: 89.3% accurate, 0.8× 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 2024041 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

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