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

Percentage Accurate: 85.3% → 89.5%

Time: 30.7s

Alternatives: 23

Speedup: 0.9×

• 49.4% 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: 89.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+272}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

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
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 5e+272)
     (- t_1 (* (* j 27.0) k))
     (fma c b (- (* t (fma (* x 18.0) (* y z) (* a -4.0))) (* 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 t_1 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 5e+272) {
		tmp = t_1 - ((j * 27.0) * k);
	} else {
		tmp = fma(c, b, ((t * fma((x * 18.0), (y * z), (a * -4.0))) - (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)
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= 5e+272)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(c, b, Float64(Float64(t * fma(Float64(x * 18.0), Float64(y * z), Float64(a * -4.0))) - Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(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]}, If[LessEqual[t$95$1, 5e+272], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(N[(t * N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.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)) < 4.99999999999999973e272

   1. Initial program 94.8%

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

   if 4.99999999999999973e272 < (-.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))

   1. Initial program 59.3%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in j around 0 80.9%

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

      1. associate--l+ 80.9%

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

      2. *-commutative 80.9%

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

      3. fma-def 84.5%

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

      4. cancel-sign-sub-inv 84.5%

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

      5. associate-*r* 84.6%

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

      6. metadata-eval 84.6%

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

      7. fma-def 84.6%

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

      8. *-commutative 84.6%

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

      9. *-commutative 84.6%

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

   7. Applied egg-rr 84.6%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+272}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, t \cdot \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, \left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right), b \cdot c\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 5e+299)
     t_1
     (+
      (fma x (fma -4.0 i (* (* y t) (* 18.0 z))) (* b c))
      (* j (* k -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((((((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 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = fma(x, fma(-4.0, i, ((y * t) * (18.0 * z))), (b * c)) + (j * (k * -27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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 <= 5e+299)
		tmp = t_1;
	else
		tmp = Float64(fma(x, fma(-4.0, i, Float64(Float64(y * t) * Float64(18.0 * z))), Float64(b * c)) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(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, 5e+299], t$95$1, N[(N[(x * N[(-4.0 * i + N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $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)) < 5.0000000000000003e299

   1. Initial program 98.7%

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

   if 5.0000000000000003e299 < (-.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 57.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in a around 0 68.8%

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

      1. associate-+r+ 68.8%

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

      2. associate-*r* 68.8%

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

      3. *-commutative 68.8%

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

      4. associate-*r* 71.7%

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

      5. associate-*l* 71.7%

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

      6. distribute-rgt-in 74.9%

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

      7. fma-def 74.9%

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

      8. fma-def 74.9%

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

      9. *-commutative 74.9%

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

      10. associate-*r* 77.9%

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

      11. associate-*l* 77.9%

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

      12. *-commutative 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, \left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right), b \cdot c\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(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 = fma(c, b, Float64(t * fma(Float64(x * 18.0), Float64(y * z), Float64(a * -4.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(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[(c * b + N[(t * N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $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 94.5%

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

   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 40.0%

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

   5. Taylor expanded in j around 0 46.7%

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

   6. Taylor expanded in i around 0 47.2%

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

      1. *-commutative 47.2%

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

      2. fma-def 53.8%

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

      3. cancel-sign-sub-inv 53.8%

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

      4. associate-*r* 53.8%

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

      5. metadata-eval 53.8%

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

      6. fma-def 53.8%

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

      7. *-commutative 53.8%

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

   8. Applied egg-rr 53.8%

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

4. Final simplification 89.7%

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

Alternative 4: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+272}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t_1 5e+272)
     (- t_1 (* (* j 27.0) k))
     (-
      (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
      (* 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 t_1 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 5e+272) {
		tmp = t_1 - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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) :: t_1
    real(8) :: tmp
    t_1 = ((((((x * 18.0d0) * y) * z) * t) - (t * (a * 4.0d0))) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= 5d+272) then
        tmp = t_1 - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (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 t_1 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 5e+272) {
		tmp = t_1 - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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):
	t_1 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= 5e+272:
		tmp = t_1 - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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)
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= 5e+272)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - 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)
	t_1 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= 5e+272)
		tmp = t_1 - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (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_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, 5e+272], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.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)) < 4.99999999999999973e272

   1. Initial program 94.8%

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

   if 4.99999999999999973e272 < (-.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))

   1. Initial program 59.3%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in j around 0 80.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+272}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 5.15 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* x i))))
        (t_2 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -4.5e+32)
     t_2
     (if (<= x 3.6e-274)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 5.15e-76)
         (+ (* j (* k -27.0)) (* t (* a -4.0)))
         (if (<= x 2.1e+40)
           t_1
           (if (<= x 7.1e+109)
             (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
             (if (<= x 1.55e+151) 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 * (x * i));
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -4.5e+32) {
		tmp = t_2;
	} else if (x <= 3.6e-274) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 5.15e-76) {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	} else if (x <= 2.1e+40) {
		tmp = t_1;
	} else if (x <= 7.1e+109) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 1.55e+151) {
		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 * (x * i))
    t_2 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-4.5d+32)) then
        tmp = t_2
    else if (x <= 3.6d-274) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 5.15d-76) then
        tmp = (j * (k * (-27.0d0))) + (t * (a * (-4.0d0)))
    else if (x <= 2.1d+40) then
        tmp = t_1
    else if (x <= 7.1d+109) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (x <= 1.55d+151) 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 * (x * i));
	double t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -4.5e+32) {
		tmp = t_2;
	} else if (x <= 3.6e-274) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 5.15e-76) {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	} else if (x <= 2.1e+40) {
		tmp = t_1;
	} else if (x <= 7.1e+109) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 1.55e+151) {
		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 * (x * i))
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if x <= -4.5e+32:
		tmp = t_2
	elif x <= 3.6e-274:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 5.15e-76:
		tmp = (j * (k * -27.0)) + (t * (a * -4.0))
	elif x <= 2.1e+40:
		tmp = t_1
	elif x <= 7.1e+109:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif x <= 1.55e+151:
		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(x * i)))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -4.5e+32)
		tmp = t_2;
	elseif (x <= 3.6e-274)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 5.15e-76)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(a * -4.0)));
	elseif (x <= 2.1e+40)
		tmp = t_1;
	elseif (x <= 7.1e+109)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (x <= 1.55e+151)
		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 * (x * i));
	t_2 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -4.5e+32)
		tmp = t_2;
	elseif (x <= 3.6e-274)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 5.15e-76)
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	elseif (x <= 2.1e+40)
		tmp = t_1;
	elseif (x <= 7.1e+109)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (x <= 1.55e+151)
		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[(x * i), $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]}, If[LessEqual[x, -4.5e+32], t$95$2, If[LessEqual[x, 3.6e-274], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.15e-76], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+40], t$95$1, If[LessEqual[x, 7.1e+109], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+151], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.5000000000000003e32 or 1.5500000000000001e151 < x

   1. Initial program 70.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around inf 70.4%

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

   if -4.5000000000000003e32 < x < 3.59999999999999983e-274

   1. Initial program 95.0%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in i around 0 84.5%

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

   6. Taylor expanded in t around 0 70.6%

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

   if 3.59999999999999983e-274 < x < 5.1500000000000002e-76

   1. Initial program 97.1%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in a around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

   7. Simplified 77.0%

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

   if 5.1500000000000002e-76 < x < 2.1000000000000001e40 or 7.1000000000000003e109 < x < 1.5500000000000001e151

   1. Initial program 77.1%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in j around 0 79.0%

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

   6. Taylor expanded in t around 0 72.8%

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

   if 2.1000000000000001e40 < x < 7.1000000000000003e109

   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 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 87.5%

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

   6. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 5.15 \cdot 10^{-76}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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) (* 4.0 (* x i)))))
   (if (<= x -3.6e+32)
     (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))
     (if (<= x 6.8e-274)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 2.15e-73)
         (+ (* j (* k -27.0)) (* t (* a -4.0)))
         (if (<= x 1.55e+40)
           t_1
           (if (<= x 7.2e+104)
             (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
             (if (<= x 1.7e+151)
               t_1
               (* x (- (* 18.0 (* t (* y z))) (* 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) - (4.0 * (x * i));
	double tmp;
	if (x <= -3.6e+32) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (x <= 6.8e-274) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.15e-73) {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	} else if (x <= 1.55e+40) {
		tmp = t_1;
	} else if (x <= 7.2e+104) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 1.7e+151) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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 = (b * c) - (4.0d0 * (x * i))
    if (x <= (-3.6d+32)) then
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    else if (x <= 6.8d-274) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 2.15d-73) then
        tmp = (j * (k * (-27.0d0))) + (t * (a * (-4.0d0)))
    else if (x <= 1.55d+40) then
        tmp = t_1
    else if (x <= 7.2d+104) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (x <= 1.7d+151) then
        tmp = t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (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) - (4.0 * (x * i));
	double tmp;
	if (x <= -3.6e+32) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (x <= 6.8e-274) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2.15e-73) {
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	} else if (x <= 1.55e+40) {
		tmp = t_1;
	} else if (x <= 7.2e+104) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 1.7e+151) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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) - (4.0 * (x * i))
	tmp = 0
	if x <= -3.6e+32:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	elif x <= 6.8e-274:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 2.15e-73:
		tmp = (j * (k * -27.0)) + (t * (a * -4.0))
	elif x <= 1.55e+40:
		tmp = t_1
	elif x <= 7.2e+104:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif x <= 1.7e+151:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (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(4.0 * Float64(x * i)))
	tmp = 0.0
	if (x <= -3.6e+32)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	elseif (x <= 6.8e-274)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 2.15e-73)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(a * -4.0)));
	elseif (x <= 1.55e+40)
		tmp = t_1;
	elseif (x <= 7.2e+104)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (x <= 1.7e+151)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - 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) - (4.0 * (x * i));
	tmp = 0.0;
	if (x <= -3.6e+32)
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	elseif (x <= 6.8e-274)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 2.15e-73)
		tmp = (j * (k * -27.0)) + (t * (a * -4.0));
	elseif (x <= 1.55e+40)
		tmp = t_1;
	elseif (x <= 7.2e+104)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (x <= 1.7e+151)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+32], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-274], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e-73], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+40], t$95$1, If[LessEqual[x, 7.2e+104], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+151], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.5999999999999997e32

   1. Initial program 71.4%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 70.1%

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

      1. expm1-log1p-u 47.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 47.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 47.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 47.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 70.1%

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

      3. associate-*r* 68.3%

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

      4. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if -3.5999999999999997e32 < x < 6.79999999999999962e-274

   1. Initial program 95.0%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in i around 0 84.5%

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

   6. Taylor expanded in t around 0 70.6%

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

   if 6.79999999999999962e-274 < x < 2.1499999999999999e-73

   1. Initial program 97.1%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in a around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

   7. Simplified 77.0%

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

   if 2.1499999999999999e-73 < x < 1.5499999999999999e40 or 7.20000000000000001e104 < x < 1.7e151

   1. Initial program 77.1%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in j around 0 79.0%

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

   6. Taylor expanded in t around 0 72.8%

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

   if 1.5499999999999999e40 < x < 7.20000000000000001e104

   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 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 87.5%

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

   6. Taylor expanded in t around inf 61.0%

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

   if 1.7e151 < x

   1. Initial program 67.8%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 70.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-73}:\\ \;\;\;\;t_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+110}:\\ \;\;\;\;t_2 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

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) (* 4.0 (* x i)))) (t_2 (* j (* k -27.0))))
   (if (<= x -2.8e+32)
     (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))
     (if (<= x 1.5e-274)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= x 2e-73)
         (+ t_2 (* t (* a -4.0)))
         (if (<= x 4.3e+61)
           t_1
           (if (<= x 4.8e+110)
             (+ t_2 (* 18.0 (* t (* y (* x z)))))
             (if (<= x 1.7e+151)
               t_1
               (* x (- (* 18.0 (* t (* y z))) (* 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) - (4.0 * (x * i));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -2.8e+32) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (x <= 1.5e-274) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2e-73) {
		tmp = t_2 + (t * (a * -4.0));
	} else if (x <= 4.3e+61) {
		tmp = t_1;
	} else if (x <= 4.8e+110) {
		tmp = t_2 + (18.0 * (t * (y * (x * z))));
	} else if (x <= 1.7e+151) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = j * (k * (-27.0d0))
    if (x <= (-2.8d+32)) then
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    else if (x <= 1.5d-274) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (x <= 2d-73) then
        tmp = t_2 + (t * (a * (-4.0d0)))
    else if (x <= 4.3d+61) then
        tmp = t_1
    else if (x <= 4.8d+110) then
        tmp = t_2 + (18.0d0 * (t * (y * (x * z))))
    else if (x <= 1.7d+151) then
        tmp = t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (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) - (4.0 * (x * i));
	double t_2 = j * (k * -27.0);
	double tmp;
	if (x <= -2.8e+32) {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	} else if (x <= 1.5e-274) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (x <= 2e-73) {
		tmp = t_2 + (t * (a * -4.0));
	} else if (x <= 4.3e+61) {
		tmp = t_1;
	} else if (x <= 4.8e+110) {
		tmp = t_2 + (18.0 * (t * (y * (x * z))));
	} else if (x <= 1.7e+151) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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) - (4.0 * (x * i))
	t_2 = j * (k * -27.0)
	tmp = 0
	if x <= -2.8e+32:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	elif x <= 1.5e-274:
		tmp = (b * c) - (27.0 * (j * k))
	elif x <= 2e-73:
		tmp = t_2 + (t * (a * -4.0))
	elif x <= 4.3e+61:
		tmp = t_1
	elif x <= 4.8e+110:
		tmp = t_2 + (18.0 * (t * (y * (x * z))))
	elif x <= 1.7e+151:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (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(4.0 * Float64(x * i)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (x <= -2.8e+32)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	elseif (x <= 1.5e-274)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 2e-73)
		tmp = Float64(t_2 + Float64(t * Float64(a * -4.0)));
	elseif (x <= 4.3e+61)
		tmp = t_1;
	elseif (x <= 4.8e+110)
		tmp = Float64(t_2 + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	elseif (x <= 1.7e+151)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - 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) - (4.0 * (x * i));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (x <= -2.8e+32)
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	elseif (x <= 1.5e-274)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (x <= 2e-73)
		tmp = t_2 + (t * (a * -4.0));
	elseif (x <= 4.3e+61)
		tmp = t_1;
	elseif (x <= 4.8e+110)
		tmp = t_2 + (18.0 * (t * (y * (x * z))));
	elseif (x <= 1.7e+151)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+32], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-274], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-73], N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+61], t$95$1, If[LessEqual[x, 4.8e+110], N[(t$95$2 + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+151], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.8e32

   1. Initial program 71.4%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 70.1%

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

      1. expm1-log1p-u 47.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-udef 47.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]

   7. Applied egg-rr 47.8%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot i\right) \]
   8. Step-by-step derivation

      1. expm1-def 47.8%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot i\right) \]

      2. expm1-log1p 70.1%

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

      3. associate-*r* 68.3%

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

      4. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if -2.8e32 < x < 1.49999999999999989e-274

   1. Initial program 95.0%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in i around 0 84.5%

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

   6. Taylor expanded in t around 0 70.6%

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

   if 1.49999999999999989e-274 < x < 1.99999999999999999e-73

   1. Initial program 97.1%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in a around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

   7. Simplified 77.0%

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

   if 1.99999999999999999e-73 < x < 4.3000000000000001e61 or 4.80000000000000025e110 < x < 1.7e151

   1. Initial program 78.0%

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

   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 j around 0 82.1%

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

   6. Taylor expanded in t around 0 69.5%

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

   if 4.3000000000000001e61 < x < 4.80000000000000025e110

   1. Initial program 89.0%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. *-commutative 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in x around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l* 68.0%

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

   10. Simplified 68.0%

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

   if 1.7e151 < x

   1. Initial program 67.8%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around inf 70.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-274}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+110}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-87} \lor \neg \left(t \leq 3.7 \cdot 10^{-144} \lor \neg \left(t \leq 9.5 \cdot 10^{-78}\right) \land t \leq 2100000000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))))
   (if (or (<= t -2.5e-87)
           (not
            (or (<= t 3.7e-144)
                (and (not (<= t 9.5e-78)) (<= t 2100000000.0)))))
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1)
     (- (* b c) (+ (* 4.0 (* x i)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if ((t <= -2.5e-87) || !((t <= 3.7e-144) || (!(t <= 9.5e-78) && (t <= 2100000000.0)))) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + 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 = 27.0d0 * (j * k)
    if ((t <= (-2.5d-87)) .or. (.not. (t <= 3.7d-144) .or. (.not. (t <= 9.5d-78)) .and. (t <= 2100000000.0d0))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + 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 = 27.0 * (j * k);
	double tmp;
	if ((t <= -2.5e-87) || !((t <= 3.7e-144) || (!(t <= 9.5e-78) && (t <= 2100000000.0)))) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + 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 = 27.0 * (j * k)
	tmp = 0
	if (t <= -2.5e-87) or not ((t <= 3.7e-144) or (not (t <= 9.5e-78) and (t <= 2100000000.0))):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + t_1)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if ((t <= -2.5e-87) || !((t <= 3.7e-144) || (!(t <= 9.5e-78) && (t <= 2100000000.0))))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + 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 = 27.0 * (j * k);
	tmp = 0.0;
	if ((t <= -2.5e-87) || ~(((t <= 3.7e-144) || (~((t <= 9.5e-78)) && (t <= 2100000000.0)))))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	else
		tmp = (b * c) - ((4.0 * (x * i)) + 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2.5e-87], N[Not[Or[LessEqual[t, 3.7e-144], And[N[Not[LessEqual[t, 9.5e-78]], $MachinePrecision], LessEqual[t, 2100000000.0]]]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000021e-87 or 3.7000000000000003e-144 < t < 9.4999999999999997e-78 or 2.1e9 < t

   1. Initial program 84.4%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in i around 0 85.3%

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

   if -2.50000000000000021e-87 < t < 3.7000000000000003e-144 or 9.4999999999999997e-78 < t < 2.1e9

   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 83.8%

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

   5. Taylor expanded in t around 0 91.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-87} \lor \neg \left(t \leq 3.7 \cdot 10^{-144} \lor \neg \left(t \leq 9.5 \cdot 10^{-78}\right) \land t \leq 2100000000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 920000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+166}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (* 27.0 (* j k)))
        (t_2 (- (* b c) (+ (* 4.0 (* x i)) t_1)))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -7e+142)
     t_3
     (if (<= t -1.35e+76)
       t_2
       (if (<= t -2.35e+27)
         (+ (* j (* k -27.0)) (* 18.0 (* t (* y (* x z)))))
         (if (<= t 920000000.0)
           t_2
           (if (<= t 3e+166) (- (+ (* b c) (* -4.0 (* t a))) t_1) 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 = 27.0 * (j * k);
	double t_2 = (b * c) - ((4.0 * (x * i)) + t_1);
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7e+142) {
		tmp = t_3;
	} else if (t <= -1.35e+76) {
		tmp = t_2;
	} else if (t <= -2.35e+27) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	} else if (t <= 920000000.0) {
		tmp = t_2;
	} else if (t <= 3e+166) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} 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 = 27.0d0 * (j * k)
    t_2 = (b * c) - ((4.0d0 * (x * i)) + t_1)
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-7d+142)) then
        tmp = t_3
    else if (t <= (-1.35d+76)) then
        tmp = t_2
    else if (t <= (-2.35d+27)) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (t * (y * (x * z))))
    else if (t <= 920000000.0d0) then
        tmp = t_2
    else if (t <= 3d+166) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    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 = 27.0 * (j * k);
	double t_2 = (b * c) - ((4.0 * (x * i)) + t_1);
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7e+142) {
		tmp = t_3;
	} else if (t <= -1.35e+76) {
		tmp = t_2;
	} else if (t <= -2.35e+27) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	} else if (t <= 920000000.0) {
		tmp = t_2;
	} else if (t <= 3e+166) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} 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 = 27.0 * (j * k)
	t_2 = (b * c) - ((4.0 * (x * i)) + t_1)
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -7e+142:
		tmp = t_3
	elif t <= -1.35e+76:
		tmp = t_2
	elif t <= -2.35e+27:
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))))
	elif t <= 920000000.0:
		tmp = t_2
	elif t <= 3e+166:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	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(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_1))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7e+142)
		tmp = t_3;
	elseif (t <= -1.35e+76)
		tmp = t_2;
	elseif (t <= -2.35e+27)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	elseif (t <= 920000000.0)
		tmp = t_2;
	elseif (t <= 3e+166)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	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 = 27.0 * (j * k);
	t_2 = (b * c) - ((4.0 * (x * i)) + t_1);
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7e+142)
		tmp = t_3;
	elseif (t <= -1.35e+76)
		tmp = t_2;
	elseif (t <= -2.35e+27)
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	elseif (t <= 920000000.0)
		tmp = t_2;
	elseif (t <= 3e+166)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+142], t$95$3, If[LessEqual[t, -1.35e+76], t$95$2, If[LessEqual[t, -2.35e+27], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 920000000.0], t$95$2, If[LessEqual[t, 3e+166], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.99999999999999995e142 or 2.99999999999999998e166 < t

   1. Initial program 81.0%

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

   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 j around 0 80.5%

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

   6. Taylor expanded in t around inf 82.1%

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

   if -6.99999999999999995e142 < t < -1.34999999999999995e76 or -2.34999999999999988e27 < t < 9.2e8

   1. Initial program 84.1%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in t around 0 83.3%

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

   if -1.34999999999999995e76 < t < -2.34999999999999988e27

   1. Initial program 77.6%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in x around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*l* 88.9%

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

   10. Simplified 88.9%

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

   if 9.2e8 < t < 2.99999999999999998e166

   1. Initial program 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 78.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 920000000:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+166}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{-26}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5.9 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* j (* k -27.0)) (* -4.0 (* x i)))))
   (if (<= (* b c) -1e-26)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= (* b c) -1.25e-194)
       t_1
       (if (<= (* b c) -1e-319)
         (+ (* -4.0 (* t a)) (* -27.0 (* j k)))
         (if (<= (* b c) 5.9e+178) t_1 (+ (* b c) (* k (* j -27.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (-4.0 * (x * i));
	double tmp;
	if ((b * c) <= -1e-26) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if ((b * c) <= -1.25e-194) {
		tmp = t_1;
	} else if ((b * c) <= -1e-319) {
		tmp = (-4.0 * (t * a)) + (-27.0 * (j * k));
	} else if ((b * c) <= 5.9e+178) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + ((-4.0d0) * (x * i))
    if ((b * c) <= (-1d-26)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if ((b * c) <= (-1.25d-194)) then
        tmp = t_1
    else if ((b * c) <= (-1d-319)) then
        tmp = ((-4.0d0) * (t * a)) + ((-27.0d0) * (j * k))
    else if ((b * c) <= 5.9d+178) then
        tmp = t_1
    else
        tmp = (b * c) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * (k * -27.0)) + (-4.0 * (x * i));
	double tmp;
	if ((b * c) <= -1e-26) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if ((b * c) <= -1.25e-194) {
		tmp = t_1;
	} else if ((b * c) <= -1e-319) {
		tmp = (-4.0 * (t * a)) + (-27.0 * (j * k));
	} else if ((b * c) <= 5.9e+178) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * (k * -27.0)) + (-4.0 * (x * i))
	tmp = 0
	if (b * c) <= -1e-26:
		tmp = (b * c) - (27.0 * (j * k))
	elif (b * c) <= -1.25e-194:
		tmp = t_1
	elif (b * c) <= -1e-319:
		tmp = (-4.0 * (t * a)) + (-27.0 * (j * k))
	elif (b * c) <= 5.9e+178:
		tmp = t_1
	else:
		tmp = (b * c) + (k * (j * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(-4.0 * Float64(x * i)))
	tmp = 0.0
	if (Float64(b * c) <= -1e-26)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= -1.25e-194)
		tmp = t_1;
	elseif (Float64(b * c) <= -1e-319)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(-27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 5.9e+178)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * (k * -27.0)) + (-4.0 * (x * i));
	tmp = 0.0;
	if ((b * c) <= -1e-26)
		tmp = (b * c) - (27.0 * (j * k));
	elseif ((b * c) <= -1.25e-194)
		tmp = t_1;
	elseif ((b * c) <= -1e-319)
		tmp = (-4.0 * (t * a)) + (-27.0 * (j * k));
	elseif ((b * c) <= 5.9e+178)
		tmp = t_1;
	else
		tmp = (b * c) + (k * (j * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e-26], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.25e-194], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1e-319], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.9e+178], t$95$1, N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1e-26

   1. Initial program 84.0%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in i around 0 84.3%

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

   6. Taylor expanded in t around 0 73.4%

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

   if -1e-26 < (*.f64 b c) < -1.2500000000000001e-194 or -9.99989e-320 < (*.f64 b c) < 5.89999999999999984e178

   1. Initial program 85.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in i around inf 59.1%

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

      1. *-commutative 59.1%

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

   7. Simplified 59.1%

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

   if -1.2500000000000001e-194 < (*.f64 b c) < -9.99989e-320

   1. Initial program 88.8%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in a around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*r* 67.2%

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

      4. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in t around 0 67.3%

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

   if 5.89999999999999984e178 < (*.f64 b c)

   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 85.1%

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

   5. Taylor expanded in i around 0 82.7%

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

   6. Taylor expanded in t around 0 70.0%

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

      1. sub-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

      4. metadata-eval 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-*l* 70.0%

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

   8. Applied egg-rr 70.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{-26}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{-194}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-319}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 5.9 \cdot 10^{+178}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := t_2 + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+27}:\\ \;\;\;\;t_2 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k)))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ t_2 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))))
   (if (<= t -5.5e+142)
     t_3
     (if (<= t -1.7e+76)
       t_1
       (if (<= t -2e+27)
         (+ t_2 (* 18.0 (* t (* y (* x z)))))
         (if (<= t 8.5e+111) t_1 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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -5.5e+142) {
		tmp = t_3;
	} else if (t <= -1.7e+76) {
		tmp = t_1;
	} else if (t <= -2e+27) {
		tmp = t_2 + (18.0 * (t * (y * (x * z))));
	} else if (t <= 8.5e+111) {
		tmp = t_1;
	} 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 = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    t_2 = j * (k * (-27.0d0))
    t_3 = t_2 + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    if (t <= (-5.5d+142)) then
        tmp = t_3
    else if (t <= (-1.7d+76)) then
        tmp = t_1
    else if (t <= (-2d+27)) then
        tmp = t_2 + (18.0d0 * (t * (y * (x * z))))
    else if (t <= 8.5d+111) then
        tmp = t_1
    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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	double t_2 = j * (k * -27.0);
	double t_3 = t_2 + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	double tmp;
	if (t <= -5.5e+142) {
		tmp = t_3;
	} else if (t <= -1.7e+76) {
		tmp = t_1;
	} else if (t <= -2e+27) {
		tmp = t_2 + (18.0 * (t * (y * (x * z))));
	} else if (t <= 8.5e+111) {
		tmp = t_1;
	} 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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	t_2 = j * (k * -27.0)
	t_3 = t_2 + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	tmp = 0
	if t <= -5.5e+142:
		tmp = t_3
	elif t <= -1.7e+76:
		tmp = t_1
	elif t <= -2e+27:
		tmp = t_2 + (18.0 * (t * (y * (x * z))))
	elif t <= 8.5e+111:
		tmp = t_1
	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(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(t_2 + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -5.5e+142)
		tmp = t_3;
	elseif (t <= -1.7e+76)
		tmp = t_1;
	elseif (t <= -2e+27)
		tmp = Float64(t_2 + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	elseif (t <= 8.5e+111)
		tmp = t_1;
	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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	t_2 = j * (k * -27.0);
	t_3 = t_2 + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -5.5e+142)
		tmp = t_3;
	elseif (t <= -1.7e+76)
		tmp = t_1;
	elseif (t <= -2e+27)
		tmp = t_2 + (18.0 * (t * (y * (x * z))));
	elseif (t <= 8.5e+111)
		tmp = t_1;
	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[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+142], t$95$3, If[LessEqual[t, -1.7e+76], t$95$1, If[LessEqual[t, -2e+27], N[(t$95$2 + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+111], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.50000000000000035e142 or 8.49999999999999983e111 < t

   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 91.1%

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

   5. Taylor expanded in t around inf 88.8%

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

   if -5.50000000000000035e142 < t < -1.6999999999999999e76 or -2e27 < t < 8.49999999999999983e111

   1. Initial program 85.4%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in t around 0 81.1%

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

   if -1.6999999999999999e76 < t < -2e27

   1. Initial program 77.6%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in x around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*l* 88.9%

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

   10. Simplified 88.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* x i)) (* 27.0 (* j k)))))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -7e+142)
     t_2
     (if (<= t -2.05e+76)
       t_1
       (if (<= t -2.35e+27)
         (+ (* j (* k -27.0)) (* 18.0 (* t (* y (* x z)))))
         (if (<= t 1.42e+166) 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 * (x * i)) + (27.0 * (j * k)));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7e+142) {
		tmp = t_2;
	} else if (t <= -2.05e+76) {
		tmp = t_1;
	} else if (t <= -2.35e+27) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	} else if (t <= 1.42e+166) {
		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 * (x * i)) + (27.0d0 * (j * k)))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-7d+142)) then
        tmp = t_2
    else if (t <= (-2.05d+76)) then
        tmp = t_1
    else if (t <= (-2.35d+27)) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (t * (y * (x * z))))
    else if (t <= 1.42d+166) 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 * (x * i)) + (27.0 * (j * k)));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7e+142) {
		tmp = t_2;
	} else if (t <= -2.05e+76) {
		tmp = t_1;
	} else if (t <= -2.35e+27) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	} else if (t <= 1.42e+166) {
		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 * (x * i)) + (27.0 * (j * k)))
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -7e+142:
		tmp = t_2
	elif t <= -2.05e+76:
		tmp = t_1
	elif t <= -2.35e+27:
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))))
	elif t <= 1.42e+166:
		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(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7e+142)
		tmp = t_2;
	elseif (t <= -2.05e+76)
		tmp = t_1;
	elseif (t <= -2.35e+27)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	elseif (t <= 1.42e+166)
		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 * (x * i)) + (27.0 * (j * k)));
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7e+142)
		tmp = t_2;
	elseif (t <= -2.05e+76)
		tmp = t_1;
	elseif (t <= -2.35e+27)
		tmp = (j * (k * -27.0)) + (18.0 * (t * (y * (x * z))));
	elseif (t <= 1.42e+166)
		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[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+142], t$95$2, If[LessEqual[t, -2.05e+76], t$95$1, If[LessEqual[t, -2.35e+27], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.42e+166], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999995e142 or 1.41999999999999995e166 < t

   1. Initial program 81.0%

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

   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 j around 0 80.5%

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

   6. Taylor expanded in t around inf 82.1%

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

   if -6.99999999999999995e142 < t < -2.0499999999999999e76 or -2.34999999999999988e27 < t < 1.41999999999999995e166

   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 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 t around 0 79.5%

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

   if -2.0499999999999999e76 < t < -2.34999999999999988e27

   1. Initial program 77.6%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in x around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*l* 88.9%

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

   10. Simplified 88.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+76}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+166}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+229}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (<= z 4e+229)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (- (+ (* b c) (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))) (* 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 (z <= 4e+229) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (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 (z <= 4d+229) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0)))) - (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 (z <= 4e+229) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (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 z <= 4e+229:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (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 (z <= 4e+229)
		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))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)))) - 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 (z <= 4e+229)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = ((b * c) + (t * ((18.0 * (z * (x * y))) - (a * 4.0)))) - (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[LessEqual[z, 4e+229], 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], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4e229

   1. Initial program 84.2%

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

   3. Simplified 89.6%

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

   if 4e229 < z

   1. Initial program 72.7%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in j around 0 67.6%

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

      1. expm1-log1p-u 39.1%

         \[\leadsto \left(b \cdot c + t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right) \]

      2. expm1-udef 39.1%

         \[\leadsto \left(b \cdot c + t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right) \]

   7. Applied egg-rr 39.1%

      \[\leadsto \left(b \cdot c + t \cdot \left(18 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right) \]
   8. Step-by-step derivation

      1. expm1-def 39.1%

         \[\leadsto \left(b \cdot c + t \cdot \left(18 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right) \]

      2. expm1-log1p 67.6%

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

      3. associate-*r* 78.2%

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

   9. Simplified 78.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+229}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-267}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5000000000:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+165}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -7.2e+142)
     t_1
     (if (<= t 1.12e-267)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= t 5000000000.0)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= t 8.2e+165) (+ (* -4.0 (* t a)) (* -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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7.2e+142) {
		tmp = t_1;
	} else if (t <= 1.12e-267) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 5000000000.0) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 8.2e+165) {
		tmp = (-4.0 * (t * a)) + (-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 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-7.2d+142)) then
        tmp = t_1
    else if (t <= 1.12d-267) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 5000000000.0d0) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 8.2d+165) then
        tmp = ((-4.0d0) * (t * a)) + ((-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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -7.2e+142) {
		tmp = t_1;
	} else if (t <= 1.12e-267) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 5000000000.0) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 8.2e+165) {
		tmp = (-4.0 * (t * a)) + (-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 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -7.2e+142:
		tmp = t_1
	elif t <= 1.12e-267:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 5000000000.0:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 8.2e+165:
		tmp = (-4.0 * (t * a)) + (-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(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -7.2e+142)
		tmp = t_1;
	elseif (t <= 1.12e-267)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 5000000000.0)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 8.2e+165)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -7.2e+142)
		tmp = t_1;
	elseif (t <= 1.12e-267)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 5000000000.0)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 8.2e+165)
		tmp = (-4.0 * (t * a)) + (-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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+142], t$95$1, If[LessEqual[t, 1.12e-267], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5000000000.0], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+165], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2000000000000003e142 or 8.2000000000000005e165 < t

   1. Initial program 81.0%

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

   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 j around 0 80.5%

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

   6. Taylor expanded in t around inf 82.1%

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

   if -7.2000000000000003e142 < t < 1.12000000000000006e-267

   1. Initial program 87.4%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in b around inf 64.5%

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

   if 1.12000000000000006e-267 < t < 5e9

   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 87.5%

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

   5. Taylor expanded in j around 0 73.6%

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

   6. Taylor expanded in t around 0 63.0%

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

   if 5e9 < t < 8.2000000000000005e165

   1. Initial program 87.0%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in a around inf 53.2%

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

      1. *-commutative 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-*r* 53.2%

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

      4. *-commutative 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in t around 0 53.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-267}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5000000000:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+165}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c - \left(t_1 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-119}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t_2 - a \cdot 4\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t_2 + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))) (t_2 (* 18.0 (* x (* y z)))))
   (if (<= j -1.4e+58)
     (- (* b c) (+ t_1 (* 27.0 (* j k))))
     (if (<= j 3.7e-119)
       (- (+ (* b c) (* t (- t_2 (* a 4.0)))) t_1)
       (+ (* j (* k -27.0)) (* t (+ t_2 (* a -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = 18.0 * (x * (y * z));
	double tmp;
	if (j <= -1.4e+58) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if (j <= 3.7e-119) {
		tmp = ((b * c) + (t * (t_2 - (a * 4.0)))) - t_1;
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_2 + (a * -4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = 18.0d0 * (x * (y * z))
    if (j <= (-1.4d+58)) then
        tmp = (b * c) - (t_1 + (27.0d0 * (j * k)))
    else if (j <= 3.7d-119) then
        tmp = ((b * c) + (t * (t_2 - (a * 4.0d0)))) - t_1
    else
        tmp = (j * (k * (-27.0d0))) + (t * (t_2 + (a * (-4.0d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = 18.0 * (x * (y * z));
	double tmp;
	if (j <= -1.4e+58) {
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	} else if (j <= 3.7e-119) {
		tmp = ((b * c) + (t * (t_2 - (a * 4.0)))) - t_1;
	} else {
		tmp = (j * (k * -27.0)) + (t * (t_2 + (a * -4.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = 18.0 * (x * (y * z))
	tmp = 0
	if j <= -1.4e+58:
		tmp = (b * c) - (t_1 + (27.0 * (j * k)))
	elif j <= 3.7e-119:
		tmp = ((b * c) + (t * (t_2 - (a * 4.0)))) - t_1
	else:
		tmp = (j * (k * -27.0)) + (t * (t_2 + (a * -4.0)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (j <= -1.4e+58)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))));
	elseif (j <= 3.7e-119)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_2 - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_2 + Float64(a * -4.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (j <= -1.4e+58)
		tmp = (b * c) - (t_1 + (27.0 * (j * k)));
	elseif (j <= 3.7e-119)
		tmp = ((b * c) + (t * (t_2 - (a * 4.0)))) - t_1;
	else
		tmp = (j * (k * -27.0)) + (t * (t_2 + (a * -4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.4e+58], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-119], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$2 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$2 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.3999999999999999e58

   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 72.3%

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

   5. Taylor expanded in t around 0 72.5%

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

   if -1.3999999999999999e58 < j < 3.7000000000000001e-119

   1. Initial program 86.3%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in j around 0 89.1%

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

   if 3.7000000000000001e-119 < j

   1. Initial program 83.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in t around inf 66.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+58}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-119}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;t \leq 4200000000:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_2\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+167}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_2 (* 27.0 (* j k))))
   (if (<= t -7e-18)
     (+ (* b c) t_1)
     (if (<= t 4200000000.0)
       (- (* b c) (+ (* 4.0 (* x i)) t_2))
       (if (<= t 5.8e+167) (- (+ (* b c) (* -4.0 (* t a))) t_2) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = 27.0 * (j * k);
	double tmp;
	if (t <= -7e-18) {
		tmp = (b * c) + t_1;
	} else if (t <= 4200000000.0) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_2);
	} else if (t <= 5.8e+167) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_2 = 27.0d0 * (j * k)
    if (t <= (-7d-18)) then
        tmp = (b * c) + t_1
    else if (t <= 4200000000.0d0) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + t_2)
    else if (t <= 5.8d+167) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_2
    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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = 27.0 * (j * k);
	double tmp;
	if (t <= -7e-18) {
		tmp = (b * c) + t_1;
	} else if (t <= 4200000000.0) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_2);
	} else if (t <= 5.8e+167) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_2;
	} 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_2 = 27.0 * (j * k)
	tmp = 0
	if t <= -7e-18:
		tmp = (b * c) + t_1
	elif t <= 4200000000.0:
		tmp = (b * c) - ((4.0 * (x * i)) + t_2)
	elif t <= 5.8e+167:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_2 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (t <= -7e-18)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= 4200000000.0)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_2));
	elseif (t <= 5.8e+167)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_2);
	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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_2 = 27.0 * (j * k);
	tmp = 0.0;
	if (t <= -7e-18)
		tmp = (b * c) + t_1;
	elseif (t <= 4200000000.0)
		tmp = (b * c) - ((4.0 * (x * i)) + t_2);
	elseif (t <= 5.8e+167)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_2;
	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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-18], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 4200000000.0], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+167], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.9999999999999997e-18

   1. Initial program 83.5%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in j around 0 76.5%

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

   6. Taylor expanded in i around 0 72.5%

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

   if -6.9999999999999997e-18 < t < 4.2e9

   1. Initial program 82.8%

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

   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 t around 0 85.5%

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

   if 4.2e9 < t < 5.79999999999999949e167

   1. Initial program 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 78.3%

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

   if 5.79999999999999949e167 < t

   1. Initial program 81.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in j around 0 88.9%

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

   6. Taylor expanded in t around inf 92.9%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 4200000000:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+167}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+71}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -9.2e-29)
   (* b c)
   (if (<= (* b c) 6.2e+71)
     (* -27.0 (* j k))
     (if (<= (* b c) 2.3e+182) (* a (* t -4.0)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -9.2e-29) {
		tmp = b * c;
	} else if ((b * c) <= 6.2e+71) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 2.3e+182) {
		tmp = a * (t * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-9.2d-29)) then
        tmp = b * c
    else if ((b * c) <= 6.2d+71) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 2.3d+182) then
        tmp = a * (t * (-4.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -9.2e-29) {
		tmp = b * c;
	} else if ((b * c) <= 6.2e+71) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 2.3e+182) {
		tmp = a * (t * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -9.2e-29:
		tmp = b * c
	elif (b * c) <= 6.2e+71:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 2.3e+182:
		tmp = a * (t * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -9.2e-29)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 6.2e+71)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 2.3e+182)
		tmp = Float64(a * Float64(t * -4.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -9.2e-29)
		tmp = b * c;
	elseif ((b * c) <= 6.2e+71)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 2.3e+182)
		tmp = a * (t * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -9.2e-29], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.2e+71], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.3e+182], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.19999999999999965e-29 or 2.3e182 < (*.f64 b c)

   1. Initial program 80.7%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in a around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. associate-*r* 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*r* 78.2%

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

      5. associate-*l* 78.2%

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

      6. distribute-rgt-in 78.2%

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

      7. fma-def 78.2%

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

      8. fma-def 78.2%

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

      9. *-commutative 78.2%

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

      10. associate-*r* 79.9%

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

      11. associate-*l* 79.9%

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

      12. *-commutative 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in i around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. associate-*r* 71.9%

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

      3. fma-def 74.7%

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

      4. *-commutative 74.7%

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

      5. *-commutative 74.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 74.8%

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

      8. *-commutative 74.8%

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

      9. associate-*r* 74.8%

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

      10. associate-*l* 74.8%

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

   10. Simplified 74.8%

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

   11. Taylor expanded in b around inf 60.5%

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

   if -9.19999999999999965e-29 < (*.f64 b c) < 6.20000000000000036e71

   1. Initial program 85.0%

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

   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 34.0%

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

   if 6.20000000000000036e71 < (*.f64 b c) < 2.3e182

   1. Initial program 88.9%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in a around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-*r* 51.4%

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

      4. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in t around 0 51.3%

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

   9. Taylor expanded in j around 0 45.8%

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

       1. associate-*r* 45.8%

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

       2. *-commutative 45.8%

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

       3. associate-*l* 45.8%

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

   11. Simplified 45.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.2 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+71}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{-26}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+72}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1e-26)
   (* b c)
   (if (<= (* b c) 4e+72)
     (* j (* k -27.0))
     (if (<= (* b c) 2.3e+182) (* a (* t -4.0)) (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e-26) {
		tmp = b * c;
	} else if ((b * c) <= 4e+72) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.3e+182) {
		tmp = a * (t * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1d-26)) then
        tmp = b * c
    else if ((b * c) <= 4d+72) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= 2.3d+182) then
        tmp = a * (t * (-4.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1e-26) {
		tmp = b * c;
	} else if ((b * c) <= 4e+72) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= 2.3e+182) {
		tmp = a * (t * -4.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1e-26:
		tmp = b * c
	elif (b * c) <= 4e+72:
		tmp = j * (k * -27.0)
	elif (b * c) <= 2.3e+182:
		tmp = a * (t * -4.0)
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1e-26)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 4e+72)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= 2.3e+182)
		tmp = Float64(a * Float64(t * -4.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1e-26)
		tmp = b * c;
	elseif ((b * c) <= 4e+72)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= 2.3e+182)
		tmp = a * (t * -4.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1e-26], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4e+72], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.3e+182], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1e-26 or 2.3e182 < (*.f64 b c)

   1. Initial program 80.7%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in a around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. associate-*r* 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*r* 78.2%

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

      5. associate-*l* 78.2%

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

      6. distribute-rgt-in 78.2%

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

      7. fma-def 78.2%

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

      8. fma-def 78.2%

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

      9. *-commutative 78.2%

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

      10. associate-*r* 79.9%

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

      11. associate-*l* 79.9%

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

      12. *-commutative 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in i around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. associate-*r* 71.9%

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

      3. fma-def 74.7%

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

      4. *-commutative 74.7%

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

      5. *-commutative 74.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 74.8%

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

      8. *-commutative 74.8%

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

      9. associate-*r* 74.8%

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

      10. associate-*l* 74.8%

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

   10. Simplified 74.8%

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

   11. Taylor expanded in b around inf 60.5%

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

   if -1e-26 < (*.f64 b c) < 3.99999999999999978e72

   1. Initial program 85.0%

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

   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 34.0%

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

      1. *-commutative 34.0%

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

      2. associate-*r* 34.1%

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

      3. *-commutative 34.1%

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

   7. Simplified 34.1%

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

   if 3.99999999999999978e72 < (*.f64 b c) < 2.3e182

   1. Initial program 88.9%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in a around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-*r* 51.4%

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

      4. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in t around 0 51.3%

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

   9. Taylor expanded in j around 0 45.8%

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

       1. associate-*r* 45.8%

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

       2. *-commutative 45.8%

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

       3. associate-*l* 45.8%

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

   11. Simplified 45.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{-26}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 4 \cdot 10^{+72}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2.3 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+65}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (<= j -1.4e+65)
   (- (* b c) (* 27.0 (* j k)))
   (if (<= j 6.8e-99)
     (- (* b c) (* 4.0 (* x i)))
     (+ (* -4.0 (* t a)) (* -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 (j <= -1.4e+65) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (j <= 6.8e-99) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * (t * a)) + (-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 (j <= (-1.4d+65)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (j <= 6.8d-99) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = ((-4.0d0) * (t * a)) + ((-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 (j <= -1.4e+65) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (j <= 6.8e-99) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * (t * a)) + (-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 j <= -1.4e+65:
		tmp = (b * c) - (27.0 * (j * k))
	elif j <= 6.8e-99:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (-4.0 * (t * a)) + (-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 (j <= -1.4e+65)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (j <= 6.8e-99)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + 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 (j <= -1.4e+65)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (j <= 6.8e-99)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (-4.0 * (t * a)) + (-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[LessEqual[j, -1.4e+65], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.8e-99], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.3999999999999999e65

   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 72.3%

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

   5. Taylor expanded in i around 0 74.5%

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

   6. Taylor expanded in t around 0 68.9%

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

   if -1.3999999999999999e65 < j < 6.80000000000000014e-99

   1. Initial program 86.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in j around 0 87.9%

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

   6. Taylor expanded in t around 0 60.4%

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

   if 6.80000000000000014e-99 < j

   1. Initial program 82.1%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in a around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. *-commutative 48.7%

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

      3. associate-*r* 48.7%

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

      4. *-commutative 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in t around 0 48.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+65}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-99}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + -27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{-31} \lor \neg \left(b \cdot c \leq 8.8 \cdot 10^{+95}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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) -6.5e-31) (not (<= (* b c) 8.8e+95)))
   (* 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) <= -6.5e-31) || !((b * c) <= 8.8e+95)) {
		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) <= (-6.5d-31)) .or. (.not. ((b * c) <= 8.8d+95))) 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) <= -6.5e-31) || !((b * c) <= 8.8e+95)) {
		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) <= -6.5e-31) or not ((b * c) <= 8.8e+95):
		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) <= -6.5e-31) || !(Float64(b * c) <= 8.8e+95))
		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) <= -6.5e-31) || ~(((b * c) <= 8.8e+95)))
		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], -6.5e-31], N[Not[LessEqual[N[(b * c), $MachinePrecision], 8.8e+95]], $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) < -6.49999999999999967e-31 or 8.7999999999999996e95 < (*.f64 b c)

   1. Initial program 80.7%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in a around 0 77.7%

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

      1. associate-+r+ 77.7%

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

      2. associate-*r* 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*r* 77.6%

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

      5. associate-*l* 77.6%

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

      6. distribute-rgt-in 77.6%

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

      7. fma-def 77.6%

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

      8. fma-def 77.6%

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

      9. *-commutative 77.6%

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

      10. associate-*r* 78.5%

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

      11. associate-*l* 78.5%

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

      12. *-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in i around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-*r* 68.7%

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

      3. fma-def 71.2%

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

      4. *-commutative 71.2%

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

      5. *-commutative 71.2%

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

      6. associate-*r* 72.1%

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

      7. associate-*l* 72.1%

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

      8. *-commutative 72.1%

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

      9. associate-*r* 72.1%

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

      10. associate-*l* 72.1%

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

   10. Simplified 72.1%

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

   11. Taylor expanded in b around inf 56.6%

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

   if -6.49999999999999967e-31 < (*.f64 b c) < 8.7999999999999996e95

   1. Initial program 85.8%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in j around inf 33.8%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.5 \cdot 10^{-31} \lor \neg \left(b \cdot c \leq 8.8 \cdot 10^{+95}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -3.2e+47)
   (+ (* b c) (* k (* j -27.0)))
   (if (<= k 1.5e+28)
     (- (* b c) (* 4.0 (* x i)))
     (+ (* b c) (* j (* k -27.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -3.2e+47) {
		tmp = (b * c) + (k * (j * -27.0));
	} else if (k <= 1.5e+28) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-3.2d+47)) then
        tmp = (b * c) + (k * (j * (-27.0d0)))
    else if (k <= 1.5d+28) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -3.2e+47) {
		tmp = (b * c) + (k * (j * -27.0));
	} else if (k <= 1.5e+28) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -3.2e+47:
		tmp = (b * c) + (k * (j * -27.0))
	elif k <= 1.5e+28:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -3.2e+47)
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)));
	elseif (k <= 1.5e+28)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -3.2e+47)
		tmp = (b * c) + (k * (j * -27.0));
	elseif (k <= 1.5e+28)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -3.2e+47], N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.5e+28], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -3.2e47

   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 85.9%

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

   5. Taylor expanded in i around 0 76.4%

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

   6. Taylor expanded in t around 0 69.2%

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

      1. sub-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. metadata-eval 69.2%

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

      5. *-commutative 69.2%

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

      6. associate-*l* 69.2%

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

   8. Applied egg-rr 69.2%

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

   if -3.2e47 < k < 1.5e28

   1. Initial program 87.8%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in j around 0 80.4%

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

   6. Taylor expanded in t around 0 49.4%

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

   if 1.5e28 < k

   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 80.6%

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

   5. Taylor expanded in b around inf 64.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{+47}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 45.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{+167}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t 6.5e+167) (+ (* b c) (* j (* k -27.0))) (* a (* t -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= 6.5e+167) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = a * (t * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (t <= 6.5d+167) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = a * (t * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= 6.5e+167) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = a * (t * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= 6.5e+167:
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = a * (t * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= 6.5e+167)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(a * Float64(t * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= 6.5e+167)
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = a * (t * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, 6.5e+167], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.5e167

   1. Initial program 83.6%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in b around inf 54.9%

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

   if 6.5e167 < t

   1. Initial program 81.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in a around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. *-commutative 51.3%

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

      3. associate-*r* 51.3%

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

      4. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in t around 0 51.3%

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

   9. Taylor expanded in j around 0 51.3%

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

       1. associate-*r* 51.3%

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

       2. *-commutative 51.3%

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

       3. associate-*l* 51.3%

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

   11. Simplified 51.3%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{+167}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 24.0% 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 83.4%

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

3. Simplified 89.2%

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

5. Taylor expanded in a around 0 76.4%

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

   1. associate-+r+ 76.4%

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

   2. associate-*r* 76.4%

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

   3. *-commutative 76.4%

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

   4. associate-*r* 76.9%

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

   5. associate-*l* 76.9%

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

   6. distribute-rgt-in 78.1%

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

   7. fma-def 78.1%

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

   8. fma-def 78.1%

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

   9. *-commutative 78.1%

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

   10. associate-*r* 79.7%

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

   11. associate-*l* 79.7%

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

   12. *-commutative 79.7%

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

7. Simplified 79.7%

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

8. Taylor expanded in i around 0 64.5%

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

   1. +-commutative 64.5%

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

   2. associate-*r* 64.8%

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

   3. fma-def 66.0%

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

   4. *-commutative 66.0%

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

   5. *-commutative 66.0%

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

   6. associate-*r* 65.3%

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

   7. associate-*l* 65.0%

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

   8. *-commutative 65.0%

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

   9. associate-*r* 65.0%

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

   10. associate-*l* 65.0%

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

10. Simplified 65.0%

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

11. Taylor expanded in b around inf 28.3%

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

12. Final simplification 28.3%

    \[\leadsto b \cdot c \]
13. Add Preprocessing

Developer target: 89.6% 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 2024018 
(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)))