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

Percentage Accurate: 85.1% → 90.3%

Time: 39.7s

Alternatives: 22

Speedup: 1.0×

• 50.4% 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: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot t\\ t_2 := \sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t_1, i \cdot -4\right), b \cdot c\right) - t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;t_2 \cdot \left(t_2 \cdot t_2\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot t_1 - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* (* y z) t))
        (t_2 (cbrt (fma t (- (* z (* x (* 18.0 y))) (* a 4.0)) (* b c))))
        (t_3 (* (* j 27.0) k)))
   (if (<= x -3.6e+62)
     (- (fma x (fma 18.0 t_1 (* i -4.0)) (* b c)) t_3)
     (if (<= x 3.8e-97)
       (- (* t_2 (* t_2 t_2)) (+ (* x (* i 4.0)) (* j (* 27.0 k))))
       (-
        (- (+ (* b c) (* x (- (* 18.0 t_1) (* i 4.0)))) (* 4.0 (* t a)))
        t_3)))))

C

assert(y < z);
assert(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 = (y * z) * t;
	double t_2 = cbrt(fma(t, ((z * (x * (18.0 * y))) - (a * 4.0)), (b * c)));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (x <= -3.6e+62) {
		tmp = fma(x, fma(18.0, t_1, (i * -4.0)), (b * c)) - t_3;
	} else if (x <= 3.8e-97) {
		tmp = (t_2 * (t_2 * t_2)) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * t_1) - (i * 4.0)))) - (4.0 * (t * a))) - t_3;
	}
	return tmp;
}

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(y * z) * t)
	t_2 = cbrt(fma(t, Float64(Float64(z * Float64(x * Float64(18.0 * y))) - Float64(a * 4.0)), Float64(b * c)))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -3.6e+62)
		tmp = Float64(fma(x, fma(18.0, t_1, Float64(i * -4.0)), Float64(b * c)) - t_3);
	elseif (x <= 3.8e-97)
		tmp = Float64(Float64(t_2 * Float64(t_2 * t_2)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * t_1) - Float64(i * 4.0)))) - Float64(4.0 * Float64(t * a))) - t_3);
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(y * z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -3.6e+62], N[(N[(x * N[(18.0 * t$95$1 + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[x, 3.8e-97], N[(N[(t$95$2 * N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6e62

   1. Initial program 72.5%

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

   2. Taylor expanded in a around 0 74.1%

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

      1. sub-neg 74.1%

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

      2. +-commutative 74.1%

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

      3. associate-+l+ 74.1%

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

      4. associate-*r* 74.1%

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

      5. *-commutative 74.1%

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

      6. associate-*r* 81.1%

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

      7. associate-*r* 81.1%

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

      8. distribute-lft-neg-in 81.1%

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

      9. metadata-eval 81.1%

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

      10. associate-*r* 81.1%

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

      11. distribute-rgt-in 86.7%

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

      12. metadata-eval 86.7%

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

      13. cancel-sign-sub-inv 86.7%

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

      14. +-commutative 86.7%

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

      15. fma-def 88.5%

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

   4. Simplified 88.5%

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

   if -3.6e62 < x < 3.8000000000000001e-97

   1. Initial program 90.6%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around 0 88.4%

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

      1. associate-*r* 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 92.2%

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

      4. *-commutative 92.2%

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

      5. associate-*l* 92.1%

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

   6. Simplified 92.1%

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

      1. add-cube-cbrt 91.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right) + b \cdot c} \cdot \sqrt[3]{t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right) + b \cdot c}\right) \cdot \sqrt[3]{t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right) + b \cdot c}} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. fma-def 91.6%

         \[\leadsto \left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}} \cdot \sqrt[3]{t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right) + b \cdot c}\right) \cdot \sqrt[3]{t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right) + b \cdot c} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. fma-def 91.6%

         \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)} \cdot \sqrt[3]{\color{blue}{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}}\right) \cdot \sqrt[3]{t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right) + b \cdot c} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. fma-def 92.4%

         \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)} \cdot \sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}\right) \cdot \sqrt[3]{\color{blue}{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Applied egg-rr 92.4%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)} \cdot \sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if 3.8000000000000001e-97 < x

   1. Initial program 84.3%

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

   2. Taylor expanded in x around 0 94.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, \left(y \cdot z\right) \cdot t, i \cdot -4\right), b \cdot c\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;\sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)} \cdot \left(\sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)} \cdot \sqrt[3]{\mathsf{fma}\left(t, z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4, b \cdot c\right)}\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 2: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot t\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -9 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t_1, i \cdot -4\right), b \cdot c\right) - t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-97}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot t_1 - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* (* y z) t)) (t_2 (* (* j 27.0) k)))
   (if (<= x -9e+61)
     (- (fma x (fma 18.0 t_1 (* i -4.0)) (* b c)) t_2)
     (if (<= x 3.5e-97)
       (-
        (+ (* b c) (* t (- (* z (* x (* 18.0 y))) (* a 4.0))))
        (+ (* x (* i 4.0)) (* j (* 27.0 k))))
       (-
        (- (+ (* b c) (* x (- (* 18.0 t_1) (* i 4.0)))) (* 4.0 (* t a)))
        t_2)))))

C

assert(y < z);
assert(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 = (y * z) * t;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -9e+61) {
		tmp = fma(x, fma(18.0, t_1, (i * -4.0)), (b * c)) - t_2;
	} else if (x <= 3.5e-97) {
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	} else {
		tmp = (((b * c) + (x * ((18.0 * t_1) - (i * 4.0)))) - (4.0 * (t * a))) - t_2;
	}
	return tmp;
}

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(y * z) * t)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -9e+61)
		tmp = Float64(fma(x, fma(18.0, t_1, Float64(i * -4.0)), Float64(b * c)) - t_2);
	elseif (x <= 3.5e-97)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(x * Float64(18.0 * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * t_1) - Float64(i * 4.0)))) - Float64(4.0 * Float64(t * a))) - t_2);
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(y * z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -9e+61], N[(N[(x * N[(18.0 * t$95$1 + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, 3.5e-97], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e61

   1. Initial program 72.5%

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

   2. Taylor expanded in a around 0 74.1%

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

      1. sub-neg 74.1%

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

      2. +-commutative 74.1%

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

      3. associate-+l+ 74.1%

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

      4. associate-*r* 74.1%

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

      5. *-commutative 74.1%

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

      6. associate-*r* 81.1%

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

      7. associate-*r* 81.1%

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

      8. distribute-lft-neg-in 81.1%

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

      9. metadata-eval 81.1%

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

      10. associate-*r* 81.1%

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

      11. distribute-rgt-in 86.7%

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

      12. metadata-eval 86.7%

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

      13. cancel-sign-sub-inv 86.7%

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

      14. +-commutative 86.7%

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

      15. fma-def 88.5%

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

   4. Simplified 88.5%

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

   if -9e61 < x < 3.50000000000000019e-97

   1. Initial program 90.6%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around 0 88.4%

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

      1. associate-*r* 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 92.2%

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

      4. *-commutative 92.2%

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

      5. associate-*l* 92.1%

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

   6. Simplified 92.1%

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

   if 3.50000000000000019e-97 < x

   1. Initial program 84.3%

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

   2. Taylor expanded in x around 0 94.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, \left(y \cdot z\right) \cdot t, i \cdot -4\right), b \cdot c\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-97}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 3: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;4 \cdot \left(x \cdot \left(-i\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - t_1\\ \mathbf{elif}\;t_1 \leq 10^{+124}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+298)
     (- (* 4.0 (* x (- i))) (* 27.0 (* j k)))
     (if (<= t_1 -4e+16)
       (- (* b c) t_1)
       (if (<= t_1 2e-227)
         (* x (- (* i (- 4.0)) (* -18.0 (* z (* y t)))))
         (if (<= t_1 2e-120)
           (* b c)
           (if (<= t_1 5e+15)
             (* x (- (* 18.0 (* (* y z) t)) (* i 4.0)))
             (if (<= t_1 2e+80)
               (- (* t (* -4.0 a)) t_1)
               (if (<= t_1 1e+124)
                 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
                 (- (* -4.0 (* x i)) t_1))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+298) {
		tmp = (4.0 * (x * -i)) - (27.0 * (j * k));
	} else if (t_1 <= -4e+16) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 2e-227) {
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	} else if (t_1 <= 2e-120) {
		tmp = b * c;
	} else if (t_1 <= 5e+15) {
		tmp = x * ((18.0 * ((y * z) * t)) - (i * 4.0));
	} else if (t_1 <= 2e+80) {
		tmp = (t * (-4.0 * a)) - t_1;
	} else if (t_1 <= 1e+124) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (-4.0 * (x * i)) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+298)) then
        tmp = (4.0d0 * (x * -i)) - (27.0d0 * (j * k))
    else if (t_1 <= (-4d+16)) then
        tmp = (b * c) - t_1
    else if (t_1 <= 2d-227) then
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * (z * (y * t))))
    else if (t_1 <= 2d-120) then
        tmp = b * c
    else if (t_1 <= 5d+15) then
        tmp = x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0))
    else if (t_1 <= 2d+80) then
        tmp = (t * ((-4.0d0) * a)) - t_1
    else if (t_1 <= 1d+124) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = ((-4.0d0) * (x * i)) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+298) {
		tmp = (4.0 * (x * -i)) - (27.0 * (j * k));
	} else if (t_1 <= -4e+16) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= 2e-227) {
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	} else if (t_1 <= 2e-120) {
		tmp = b * c;
	} else if (t_1 <= 5e+15) {
		tmp = x * ((18.0 * ((y * z) * t)) - (i * 4.0));
	} else if (t_1 <= 2e+80) {
		tmp = (t * (-4.0 * a)) - t_1;
	} else if (t_1 <= 1e+124) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = (-4.0 * (x * i)) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+298:
		tmp = (4.0 * (x * -i)) - (27.0 * (j * k))
	elif t_1 <= -4e+16:
		tmp = (b * c) - t_1
	elif t_1 <= 2e-227:
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))))
	elif t_1 <= 2e-120:
		tmp = b * c
	elif t_1 <= 5e+15:
		tmp = x * ((18.0 * ((y * z) * t)) - (i * 4.0))
	elif t_1 <= 2e+80:
		tmp = (t * (-4.0 * a)) - t_1
	elif t_1 <= 1e+124:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = (-4.0 * (x * i)) - t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+298)
		tmp = Float64(Float64(4.0 * Float64(x * Float64(-i))) - Float64(27.0 * Float64(j * k)));
	elseif (t_1 <= -4e+16)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= 2e-227)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(z * Float64(y * t)))));
	elseif (t_1 <= 2e-120)
		tmp = Float64(b * c);
	elseif (t_1 <= 5e+15)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0)));
	elseif (t_1 <= 2e+80)
		tmp = Float64(Float64(t * Float64(-4.0 * a)) - t_1);
	elseif (t_1 <= 1e+124)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+298)
		tmp = (4.0 * (x * -i)) - (27.0 * (j * k));
	elseif (t_1 <= -4e+16)
		tmp = (b * c) - t_1;
	elseif (t_1 <= 2e-227)
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	elseif (t_1 <= 2e-120)
		tmp = b * c;
	elseif (t_1 <= 5e+15)
		tmp = x * ((18.0 * ((y * z) * t)) - (i * 4.0));
	elseif (t_1 <= 2e+80)
		tmp = (t * (-4.0 * a)) - t_1;
	elseif (t_1 <= 1e+124)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = (-4.0 * (x * i)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+298], N[(N[(4.0 * N[(x * (-i)), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e+16], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 2e-227], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-120], N[(b * c), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+80], N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1e+124], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if (*.f64 (*.f64 j 27) k) < -1.9999999999999999e298

   1. Initial program 70.0%

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

   2. Taylor expanded in b around 0 70.0%

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

      1. *-commutative 70.0%

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

      2. distribute-lft-out 70.0%

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

      3. *-commutative 70.0%

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

      4. *-commutative 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 85.0%

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

   if -1.9999999999999999e298 < (*.f64 (*.f64 j 27) k) < -4e16

   1. Initial program 95.3%

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

   2. Taylor expanded in x around 0 95.3%

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

   3. Taylor expanded in b around inf 71.4%

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

   if -4e16 < (*.f64 (*.f64 j 27) k) < 1.99999999999999989e-227

   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 87.2%

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

   4. Taylor expanded in x around 0 87.2%

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

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-*l* 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in x around -inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. cancel-sign-sub-inv 55.3%

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

      3. associate-*r* 58.0%

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

      4. metadata-eval 58.0%

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

   9. Simplified 58.0%

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

   if 1.99999999999999989e-227 < (*.f64 (*.f64 j 27) k) < 1.99999999999999996e-120

   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 71.5%

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

   4. Taylor expanded in b around inf 56.6%

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

   if 1.99999999999999996e-120 < (*.f64 (*.f64 j 27) k) < 5e15

   1. Initial program 91.0%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in x around inf 57.1%

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

   if 5e15 < (*.f64 (*.f64 j 27) k) < 2e80

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0 86.5%

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

   3. Taylor expanded in a around inf 65.6%

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

      1. associate-*r* 65.6%

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

   5. Simplified 65.6%

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

   if 2e80 < (*.f64 (*.f64 j 27) k) < 9.99999999999999948e123

   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 100.0%

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

   4. Taylor expanded in t around inf 86.3%

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

   if 9.99999999999999948e123 < (*.f64 (*.f64 j 27) k)

   1. Initial program 88.2%

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

   2. Taylor expanded in x around 0 88.4%

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

   3. Taylor expanded in x around inf 85.6%

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

   4. Taylor expanded in t around 0 86.0%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 8 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+298}:\\ \;\;\;\;4 \cdot \left(x \cdot \left(-i\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+124}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 4: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - t_1\\ t_3 := -4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (- (* x (- (* 18.0 (* (* y z) t)) (* i 4.0))) t_1))
        (t_3 (+ (* -4.0 (* t a)) (- (* b c) (* j (* 27.0 k))))))
   (if (<= x -6.5e+148)
     t_2
     (if (<= x -8.4e+130)
       (- (* b c) t_1)
       (if (<= x -2.05e+105)
         (- (* 18.0 (* t (* x (* y z)))) (* 4.0 (+ (* t a) (* x i))))
         (if (<= x -5.6e+52)
           (- (- (* b c) (* 4.0 (* x i))) t_1)
           (if (<= x -4.9e-92)
             t_2
             (if (<= x 1.38e+82)
               t_3
               (if (<= x 3.8e+111)
                 (* x (- (* i (- 4.0)) (* -18.0 (* z (* y t)))))
                 (if (<= x 3.8e+151) t_3 t_2))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1;
	double t_3 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	double tmp;
	if (x <= -6.5e+148) {
		tmp = t_2;
	} else if (x <= -8.4e+130) {
		tmp = (b * c) - t_1;
	} else if (x <= -2.05e+105) {
		tmp = (18.0 * (t * (x * (y * z)))) - (4.0 * ((t * a) + (x * i)));
	} else if (x <= -5.6e+52) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= -4.9e-92) {
		tmp = t_2;
	} else if (x <= 1.38e+82) {
		tmp = t_3;
	} else if (x <= 3.8e+111) {
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	} else if (x <= 3.8e+151) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0))) - t_1
    t_3 = ((-4.0d0) * (t * a)) + ((b * c) - (j * (27.0d0 * k)))
    if (x <= (-6.5d+148)) then
        tmp = t_2
    else if (x <= (-8.4d+130)) then
        tmp = (b * c) - t_1
    else if (x <= (-2.05d+105)) then
        tmp = (18.0d0 * (t * (x * (y * z)))) - (4.0d0 * ((t * a) + (x * i)))
    else if (x <= (-5.6d+52)) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (x <= (-4.9d-92)) then
        tmp = t_2
    else if (x <= 1.38d+82) then
        tmp = t_3
    else if (x <= 3.8d+111) then
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * (z * (y * t))))
    else if (x <= 3.8d+151) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1;
	double t_3 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	double tmp;
	if (x <= -6.5e+148) {
		tmp = t_2;
	} else if (x <= -8.4e+130) {
		tmp = (b * c) - t_1;
	} else if (x <= -2.05e+105) {
		tmp = (18.0 * (t * (x * (y * z)))) - (4.0 * ((t * a) + (x * i)));
	} else if (x <= -5.6e+52) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= -4.9e-92) {
		tmp = t_2;
	} else if (x <= 1.38e+82) {
		tmp = t_3;
	} else if (x <= 3.8e+111) {
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	} else if (x <= 3.8e+151) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1
	t_3 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)))
	tmp = 0
	if x <= -6.5e+148:
		tmp = t_2
	elif x <= -8.4e+130:
		tmp = (b * c) - t_1
	elif x <= -2.05e+105:
		tmp = (18.0 * (t * (x * (y * z)))) - (4.0 * ((t * a) + (x * i)))
	elif x <= -5.6e+52:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif x <= -4.9e-92:
		tmp = t_2
	elif x <= 1.38e+82:
		tmp = t_3
	elif x <= 3.8e+111:
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))))
	elif x <= 3.8e+151:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0))) - t_1)
	t_3 = Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b * c) - Float64(j * Float64(27.0 * k))))
	tmp = 0.0
	if (x <= -6.5e+148)
		tmp = t_2;
	elseif (x <= -8.4e+130)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (x <= -2.05e+105)
		tmp = Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))));
	elseif (x <= -5.6e+52)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (x <= -4.9e-92)
		tmp = t_2;
	elseif (x <= 1.38e+82)
		tmp = t_3;
	elseif (x <= 3.8e+111)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(z * Float64(y * t)))));
	elseif (x <= 3.8e+151)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1;
	t_3 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	tmp = 0.0;
	if (x <= -6.5e+148)
		tmp = t_2;
	elseif (x <= -8.4e+130)
		tmp = (b * c) - t_1;
	elseif (x <= -2.05e+105)
		tmp = (18.0 * (t * (x * (y * z)))) - (4.0 * ((t * a) + (x * i)));
	elseif (x <= -5.6e+52)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (x <= -4.9e-92)
		tmp = t_2;
	elseif (x <= 1.38e+82)
		tmp = t_3;
	elseif (x <= 3.8e+111)
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	elseif (x <= 3.8e+151)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+148], t$95$2, If[LessEqual[x, -8.4e+130], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -2.05e+105], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e+52], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -4.9e-92], t$95$2, If[LessEqual[x, 1.38e+82], t$95$3, If[LessEqual[x, 3.8e+111], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+151], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.49999999999999947e148 or -5.6e52 < x < -4.9e-92 or 3.8e151 < x

   1. Initial program 80.1%

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

   2. Taylor expanded in x around 0 90.6%

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

   3. Taylor expanded in x around inf 83.2%

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

   if -6.49999999999999947e148 < x < -8.39999999999999962e130

   1. Initial program 34.4%

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

   2. Taylor expanded in x around 0 66.4%

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

   3. Taylor expanded in b around inf 99.0%

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

   if -8.39999999999999962e130 < x < -2.0500000000000001e105

   1. Initial program 83.3%

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

   2. Taylor expanded in b around 0 83.3%

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

      1. *-commutative 83.3%

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

      2. distribute-lft-out 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in j around 0 100.0%

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

   if -2.0500000000000001e105 < x < -5.6e52

   1. Initial program 87.4%

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

   2. Taylor expanded in t around 0 93.7%

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

   if -4.9e-92 < x < 1.3799999999999999e82 or 3.79999999999999976e111 < x < 3.8e151

   1. Initial program 92.2%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in x around 0 81.5%

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

      1. associate--l+ 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*r* 81.5%

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

      4. *-commutative 81.5%

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

      5. associate-*l* 80.7%

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

   6. Applied egg-rr 80.7%

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

   if 1.3799999999999999e82 < x < 3.79999999999999976e111

   1. Initial program 43.5%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in x around 0 62.6%

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

      1. associate-*r* 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*r* 43.5%

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

      4. *-commutative 43.5%

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

      5. associate-*l* 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in x around -inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. cancel-sign-sub-inv 81.0%

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

      3. associate-*r* 99.7%

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

      4. metadata-eval 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 5: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+132}:\\ \;\;\;\;t_1 - t_2\\ \mathbf{elif}\;x \leq 10^{-97}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) (* x (- (* 18.0 (* (* y z) t)) (* i 4.0)))))
        (t_2 (* (* j 27.0) k)))
   (if (<= x -5.2e+132)
     (- t_1 t_2)
     (if (<= x 1e-97)
       (-
        (+ (* b c) (* t (- (* z (* x (* 18.0 y))) (* a 4.0))))
        (+ (* x (* i 4.0)) (* j (* 27.0 k))))
       (- (- t_1 (* 4.0 (* t a))) t_2)))))

C

assert(y < z);
assert(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) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -5.2e+132) {
		tmp = t_1 - t_2;
	} else if (x <= 1e-97) {
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	} else {
		tmp = (t_1 - (4.0 * (t * a))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) + (x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0)))
    t_2 = (j * 27.0d0) * k
    if (x <= (-5.2d+132)) then
        tmp = t_1 - t_2
    else if (x <= 1d-97) then
        tmp = ((b * c) + (t * ((z * (x * (18.0d0 * y))) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (27.0d0 * k)))
    else
        tmp = (t_1 - (4.0d0 * (t * a))) - t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -5.2e+132) {
		tmp = t_1 - t_2;
	} else if (x <= 1e-97) {
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	} else {
		tmp = (t_1 - (4.0 * (t * a))) - t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)))
	t_2 = (j * 27.0) * k
	tmp = 0
	if x <= -5.2e+132:
		tmp = t_1 - t_2
	elif x <= 1e-97:
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)))
	else:
		tmp = (t_1 - (4.0 * (t * a))) - t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0))))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -5.2e+132)
		tmp = Float64(t_1 - t_2);
	elseif (x <= 1e-97)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(x * Float64(18.0 * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(t_1 - Float64(4.0 * Float64(t * a))) - t_2);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -5.2e+132)
		tmp = t_1 - t_2;
	elseif (x <= 1e-97)
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	else
		tmp = (t_1 - (4.0 * (t * a))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -5.2e+132], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[x, 1e-97], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2e132

   1. Initial program 62.3%

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

   2. Taylor expanded in x around 0 82.3%

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

   3. Taylor expanded in a around 0 87.7%

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

   if -5.2e132 < x < 1.00000000000000004e-97

   1. Initial program 90.5%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in x around 0 88.6%

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

      1. associate-*r* 88.6%

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

      2. *-commutative 88.6%

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

      3. associate-*r* 91.9%

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

      4. *-commutative 91.9%

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

      5. associate-*l* 91.8%

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

   6. Simplified 91.8%

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

   if 1.00000000000000004e-97 < x

   1. Initial program 84.3%

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

   2. Taylor expanded in x around 0 94.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+132}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 10^{-97}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 6: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+131}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.7e+131)
   (- (+ (* b c) (* x (- (* 18.0 (* (* y z) t)) (* i 4.0)))) (* (* j 27.0) k))
   (-
    (+ (* b c) (* t (- (* z (* x (* 18.0 y))) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* 27.0 k))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.7e+131) {
		tmp = ((b * c) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-3.7d+131)) then
        tmp = ((b * c) + (x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0)))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * ((z * (x * (18.0d0 * y))) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 (x <= -3.7e+131) {
		tmp = ((b * c) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -3.7e+131:
		tmp = ((b * c) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -3.7e+131)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(x * Float64(18.0 * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.7e+131)
		tmp = ((b * c) + (x * ((18.0 * ((y * z) * t)) - (i * 4.0)))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * ((z * (x * (18.0 * y))) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -3.7e+131], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.69999999999999995e131

   1. Initial program 62.3%

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

   2. Taylor expanded in x around 0 82.3%

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

   3. Taylor expanded in a around 0 87.7%

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

   if -3.69999999999999995e131 < x

   1. Initial program 88.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*r* 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-*l* 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+131}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 7: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ t_2 := x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ t_3 := x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* -4.0 (* t a)) (- (* b c) (* j (* 27.0 k)))))
        (t_2 (* x (- (* i (- 4.0)) (* -18.0 (* z (* y t))))))
        (t_3 (* x (- (* 18.0 (* (* y z) t)) (* i 4.0)))))
   (if (<= x -9.5e+187)
     t_3
     (if (<= x -1.9e+133)
       (- (* b c) (* (* j 27.0) k))
       (if (<= x -3.1e+91)
         t_2
         (if (<= x -5.9e+26)
           t_1
           (if (<= x -2.1e-80) t_3 (if (<= x 2.2e+82) t_1 t_2))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	double t_2 = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	double t_3 = x * ((18.0 * ((y * z) * t)) - (i * 4.0));
	double tmp;
	if (x <= -9.5e+187) {
		tmp = t_3;
	} else if (x <= -1.9e+133) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= -3.1e+91) {
		tmp = t_2;
	} else if (x <= -5.9e+26) {
		tmp = t_1;
	} else if (x <= -2.1e-80) {
		tmp = t_3;
	} else if (x <= 2.2e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * a)) + ((b * c) - (j * (27.0d0 * k)))
    t_2 = x * ((i * -4.0d0) - ((-18.0d0) * (z * (y * t))))
    t_3 = x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0))
    if (x <= (-9.5d+187)) then
        tmp = t_3
    else if (x <= (-1.9d+133)) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (x <= (-3.1d+91)) then
        tmp = t_2
    else if (x <= (-5.9d+26)) then
        tmp = t_1
    else if (x <= (-2.1d-80)) then
        tmp = t_3
    else if (x <= 2.2d+82) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	double t_2 = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	double t_3 = x * ((18.0 * ((y * z) * t)) - (i * 4.0));
	double tmp;
	if (x <= -9.5e+187) {
		tmp = t_3;
	} else if (x <= -1.9e+133) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= -3.1e+91) {
		tmp = t_2;
	} else if (x <= -5.9e+26) {
		tmp = t_1;
	} else if (x <= -2.1e-80) {
		tmp = t_3;
	} else if (x <= 2.2e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)))
	t_2 = x * ((i * -4.0) - (-18.0 * (z * (y * t))))
	t_3 = x * ((18.0 * ((y * z) * t)) - (i * 4.0))
	tmp = 0
	if x <= -9.5e+187:
		tmp = t_3
	elif x <= -1.9e+133:
		tmp = (b * c) - ((j * 27.0) * k)
	elif x <= -3.1e+91:
		tmp = t_2
	elif x <= -5.9e+26:
		tmp = t_1
	elif x <= -2.1e-80:
		tmp = t_3
	elif x <= 2.2e+82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b * c) - Float64(j * Float64(27.0 * k))))
	t_2 = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(z * Float64(y * t)))))
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -9.5e+187)
		tmp = t_3;
	elseif (x <= -1.9e+133)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (x <= -3.1e+91)
		tmp = t_2;
	elseif (x <= -5.9e+26)
		tmp = t_1;
	elseif (x <= -2.1e-80)
		tmp = t_3;
	elseif (x <= 2.2e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	t_2 = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	t_3 = x * ((18.0 * ((y * z) * t)) - (i * 4.0));
	tmp = 0.0;
	if (x <= -9.5e+187)
		tmp = t_3;
	elseif (x <= -1.9e+133)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (x <= -3.1e+91)
		tmp = t_2;
	elseif (x <= -5.9e+26)
		tmp = t_1;
	elseif (x <= -2.1e-80)
		tmp = t_3;
	elseif (x <= 2.2e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+187], t$95$3, If[LessEqual[x, -1.9e+133], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e+91], t$95$2, If[LessEqual[x, -5.9e+26], t$95$1, If[LessEqual[x, -2.1e-80], t$95$3, If[LessEqual[x, 2.2e+82], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.4999999999999996e187 or -5.9000000000000003e26 < x < -2.10000000000000001e-80

   1. Initial program 74.9%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around inf 69.3%

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

   if -9.4999999999999996e187 < x < -1.9000000000000001e133

   1. Initial program 64.2%

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

   2. Taylor expanded in x around 0 81.7%

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

   3. Taylor expanded in b around inf 73.1%

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

   if -1.9000000000000001e133 < x < -3.09999999999999998e91 or 2.2000000000000001e82 < x

   1. Initial program 80.5%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around 0 86.7%

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

      1. associate-*r* 86.7%

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

      2. *-commutative 86.7%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-*l* 80.5%

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

   6. Simplified 80.5%

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

   7. Taylor expanded in x around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. cancel-sign-sub-inv 71.4%

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

      3. associate-*r* 76.8%

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

      4. metadata-eval 76.8%

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

   9. Simplified 76.8%

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

   if -3.09999999999999998e91 < x < -5.9000000000000003e26 or -2.10000000000000001e-80 < x < 2.2000000000000001e82

   1. Initial program 91.2%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 79.0%

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

      1. associate--l+ 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*r* 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-*l* 78.4%

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

   6. Applied egg-rr 78.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 8: 82.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{-73} \lor \neg \left(i \leq 2.45 \cdot 10^{+70}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -6.8e-73) (not (<= i 2.45e+70)))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* (* j 27.0) k))
   (-
    (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
    (* 27.0 (* j k)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -6.8e-73) || !(i <= 2.45e+70)) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((i <= (-6.8d-73)) .or. (.not. (i <= 2.45d+70))) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -6.8e-73) || !(i <= 2.45e+70)) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -6.8e-73) or not (i <= 2.45e+70):
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -6.8e-73) || !(i <= 2.45e+70))
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - 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(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -6.8e-73) || ~((i <= 2.45e+70)))
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -6.8e-73], N[Not[LessEqual[i, 2.45e+70]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.80000000000000042e-73 or 2.45000000000000014e70 < i

   1. Initial program 85.6%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. distribute-lft-out 85.3%

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

      2. *-commutative 85.3%

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

      3. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   if -6.80000000000000042e-73 < i < 2.45000000000000014e70

   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 86.0%

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

   4. Taylor expanded in i around 0 84.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{-73} \lor \neg \left(i \leq 2.45 \cdot 10^{+70}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 9: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{-137}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) -5.2e+61)
   (* b c)
   (if (<= (* b c) -3.5e-223)
     (* t (* -4.0 a))
     (if (<= (* b c) 4.3e-137)
       (* (* j k) -27.0)
       (if (<= (* b c) 1.1e-7)
         (* x (* i -4.0))
         (if (<= (* b c) 2.4e+53) (* k (* j -27.0)) (* b c)))))))

C

assert(y < z);
assert(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) <= -5.2e+61) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e-223) {
		tmp = t * (-4.0 * a);
	} else if ((b * c) <= 4.3e-137) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.1e-7) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 2.4e+53) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-5.2d+61)) then
        tmp = b * c
    else if ((b * c) <= (-3.5d-223)) then
        tmp = t * ((-4.0d0) * a)
    else if ((b * c) <= 4.3d-137) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 1.1d-7) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 2.4d+53) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -5.2e+61) {
		tmp = b * c;
	} else if ((b * c) <= -3.5e-223) {
		tmp = t * (-4.0 * a);
	} else if ((b * c) <= 4.3e-137) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.1e-7) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 2.4e+53) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5.2e+61:
		tmp = b * c
	elif (b * c) <= -3.5e-223:
		tmp = t * (-4.0 * a)
	elif (b * c) <= 4.3e-137:
		tmp = (j * k) * -27.0
	elif (b * c) <= 1.1e-7:
		tmp = x * (i * -4.0)
	elif (b * c) <= 2.4e+53:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5.2e+61)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.5e-223)
		tmp = Float64(t * Float64(-4.0 * a));
	elseif (Float64(b * c) <= 4.3e-137)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 1.1e-7)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 2.4e+53)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5.2e+61)
		tmp = b * c;
	elseif ((b * c) <= -3.5e-223)
		tmp = t * (-4.0 * a);
	elseif ((b * c) <= 4.3e-137)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 1.1e-7)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 2.4e+53)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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], -5.2e+61], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.5e-223], N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.3e-137], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.1e-7], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.4e+53], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -5.19999999999999945e61 or 2.4e53 < (*.f64 b c)

   1. Initial program 80.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around inf 51.0%

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

   if -5.19999999999999945e61 < (*.f64 b c) < -3.50000000000000009e-223

   1. Initial program 90.6%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in a around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. *-commutative 41.5%

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

      3. associate-*r* 41.5%

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

   6. Simplified 41.5%

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

   if -3.50000000000000009e-223 < (*.f64 b c) < 4.2999999999999998e-137

   1. Initial program 89.4%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in j around inf 43.9%

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

   if 4.2999999999999998e-137 < (*.f64 b c) < 1.1000000000000001e-7

   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 87.4%

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

   4. Taylor expanded in i around inf 40.7%

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

      1. associate-*r* 40.7%

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

      2. *-commutative 40.7%

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

   6. Simplified 40.7%

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

   if 1.1000000000000001e-7 < (*.f64 b c) < 2.4e53

   1. Initial program 82.6%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in j around inf 54.0%

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

      1. associate-*r* 54.1%

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

   6. Simplified 54.1%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+61}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.5 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{-137}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 10: 37.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.3 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.65 \cdot 10^{-189}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{-139}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) -1.3e+144)
   (* b c)
   (if (<= (* b c) -1.65e-189)
     (* 18.0 (* x (* y (* z t))))
     (if (<= (* b c) 6.8e-139)
       (* (* j k) -27.0)
       (if (<= (* b c) 1.8e-7)
         (* x (* i -4.0))
         (if (<= (* b c) 9.5e+52) (* k (* j -27.0)) (* b c)))))))

C

assert(y < z);
assert(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) <= -1.3e+144) {
		tmp = b * c;
	} else if ((b * c) <= -1.65e-189) {
		tmp = 18.0 * (x * (y * (z * t)));
	} else if ((b * c) <= 6.8e-139) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.8e-7) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 9.5e+52) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-1.3d+144)) then
        tmp = b * c
    else if ((b * c) <= (-1.65d-189)) then
        tmp = 18.0d0 * (x * (y * (z * t)))
    else if ((b * c) <= 6.8d-139) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 1.8d-7) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 9.5d+52) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -1.3e+144) {
		tmp = b * c;
	} else if ((b * c) <= -1.65e-189) {
		tmp = 18.0 * (x * (y * (z * t)));
	} else if ((b * c) <= 6.8e-139) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 1.8e-7) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 9.5e+52) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.3e+144:
		tmp = b * c
	elif (b * c) <= -1.65e-189:
		tmp = 18.0 * (x * (y * (z * t)))
	elif (b * c) <= 6.8e-139:
		tmp = (j * k) * -27.0
	elif (b * c) <= 1.8e-7:
		tmp = x * (i * -4.0)
	elif (b * c) <= 9.5e+52:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.3e+144)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.65e-189)
		tmp = Float64(18.0 * Float64(x * Float64(y * Float64(z * t))));
	elseif (Float64(b * c) <= 6.8e-139)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 1.8e-7)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 9.5e+52)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.3e+144)
		tmp = b * c;
	elseif ((b * c) <= -1.65e-189)
		tmp = 18.0 * (x * (y * (z * t)));
	elseif ((b * c) <= 6.8e-139)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 1.8e-7)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 9.5e+52)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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], -1.3e+144], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.65e-189], N[(18.0 * N[(x * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.8e-139], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.8e-7], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+52], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.2999999999999999e144 or 9.49999999999999994e52 < (*.f64 b c)

   1. Initial program 81.7%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around inf 54.5%

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

   if -1.2999999999999999e144 < (*.f64 b c) < -1.65e-189

   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 91.9%

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

   4. Taylor expanded in y around inf 33.1%

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

      1. *-commutative 33.1%

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

      2. associate-*l* 35.1%

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

      3. associate-*l* 37.1%

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

   6. Simplified 37.1%

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

   if -1.65e-189 < (*.f64 b c) < 6.79999999999999998e-139

   1. Initial program 90.2%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in j around inf 43.6%

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

   if 6.79999999999999998e-139 < (*.f64 b c) < 1.79999999999999997e-7

   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 87.4%

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

   4. Taylor expanded in i around inf 40.7%

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

      1. associate-*r* 40.7%

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

      2. *-commutative 40.7%

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

   6. Simplified 40.7%

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

   if 1.79999999999999997e-7 < (*.f64 b c) < 9.49999999999999994e52

   1. Initial program 82.6%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in j around inf 54.0%

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

      1. associate-*r* 54.1%

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

   6. Simplified 54.1%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.3 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.65 \cdot 10^{-189}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{-139}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 11: 78.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+100}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+222}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 -1.15e+100)
   (* 18.0 (* t (* y (* x z))))
   (if (<= z 1.5e+222)
     (- (+ (* b c) (* -4.0 (* t a))) (+ (* x (* i 4.0)) (* j (* 27.0 k))))
     (- (* x (- (* 18.0 (* (* y z) t)) (* i 4.0))) (* (* j 27.0) k)))))

C

assert(y < z);
assert(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 <= -1.15e+100) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (z <= 1.5e+222) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 <= (-1.15d+100)) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    else if (z <= 1.5d+222) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((x * (i * 4.0d0)) + (j * (27.0d0 * k)))
    else
        tmp = (x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 <= -1.15e+100) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (z <= 1.5e+222) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -1.15e+100:
		tmp = 18.0 * (t * (y * (x * z)))
	elif z <= 1.5e+222:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (i * 4.0)) + (j * (27.0 * k)))
	else:
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - ((j * 27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -1.15e+100)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	elseif (z <= 1.5e+222)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -1.15e+100)
		tmp = 18.0 * (t * (y * (x * z)));
	elseif (z <= 1.5e+222)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((x * (i * 4.0)) + (j * (27.0 * k)));
	else
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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, -1.15e+100], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+222], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999995e100

   1. Initial program 86.4%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. associate-*r* 84.6%

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

      2. *-commutative 84.6%

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

      3. associate-*r* 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-*l* 91.0%

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

   6. Simplified 91.0%

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

   7. Taylor expanded in z around inf 42.8%

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

      1. *-commutative 42.8%

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

      2. *-commutative 42.8%

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

      3. associate-*r* 47.1%

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

   9. Simplified 47.1%

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

   if -1.14999999999999995e100 < z < 1.50000000000000007e222

   1. Initial program 84.8%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around 0 82.2%

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

   if 1.50000000000000007e222 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in x around 0 78.0%

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

   3. Taylor expanded in x around inf 72.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+100}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+222}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 12: 78.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+53}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= z -1.45e+53)
     (* 18.0 (* t (* y (* x z))))
     (if (<= z 2.3e+220)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
       (- (* x (- (* 18.0 (* (* y z) t)) (* i 4.0))) t_1)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (z <= -1.45e+53) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (z <= 2.3e+220) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (z <= (-1.45d+53)) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    else if (z <= 2.3d+220) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = (x * ((18.0d0 * ((y * z) * t)) - (i * 4.0d0))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (z <= -1.45e+53) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (z <= 2.3e+220) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if z <= -1.45e+53:
		tmp = 18.0 * (t * (y * (x * z)))
	elif z <= 2.3e+220:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (z <= -1.45e+53)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	elseif (z <= 2.3e+220)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(Float64(y * z) * t)) - Float64(i * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (z <= -1.45e+53)
		tmp = 18.0 * (t * (y * (x * z)));
	elseif (z <= 2.3e+220)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = (x * ((18.0 * ((y * z) * t)) - (i * 4.0))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[z, -1.45e+53], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+220], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4500000000000001e53

   1. Initial program 87.6%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in x around 0 84.4%

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

      1. associate-*r* 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r* 89.5%

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

      4. *-commutative 89.5%

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

      5. associate-*l* 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in z around inf 41.2%

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

      1. *-commutative 41.2%

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

      2. *-commutative 41.2%

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

      3. associate-*r* 44.5%

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

   9. Simplified 44.5%

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

   if -1.4500000000000001e53 < z < 2.29999999999999997e220

   1. Initial program 84.3%

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

   2. Taylor expanded in y around 0 83.7%

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

      1. distribute-lft-out 83.7%

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

      2. *-commutative 83.7%

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

      3. *-commutative 83.7%

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

   4. Simplified 83.7%

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

   if 2.29999999999999997e220 < z

   1. Initial program 83.2%

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

   2. Taylor expanded in x around 0 78.0%

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

   3. Taylor expanded in x around inf 72.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+53}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+220}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right) - i \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 13: 67.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -4400 \lor \neg \left(c \leq 9.6 \cdot 10^{+65}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= c -4400.0) (not (<= c 9.6e+65)))
   (+ (* -4.0 (* t a)) (- (* b c) (* j (* 27.0 k))))
   (- (* -4.0 (+ (* t a) (* x i))) (* (* j 27.0) k))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c <= -4400.0) || !(c <= 9.6e+65)) {
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((c <= (-4400.0d0)) .or. (.not. (c <= 9.6d+65))) then
        tmp = ((-4.0d0) * (t * a)) + ((b * c) - (j * (27.0d0 * k)))
    else
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((c <= -4400.0) || !(c <= 9.6e+65)) {
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	} else {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c <= -4400.0) or not (c <= 9.6e+65):
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)))
	else:
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((c <= -4400.0) || !(c <= 9.6e+65))
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b * c) - Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c <= -4400.0) || ~((c <= 9.6e+65)))
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	else
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[c, -4400.0], N[Not[LessEqual[c, 9.6e+65]], $MachinePrecision]], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4400 or 9.6000000000000007e65 < c

   1. Initial program 79.6%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around 0 64.9%

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

      1. associate--l+ 64.9%

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

      2. *-commutative 64.9%

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

      3. associate-*r* 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-*l* 64.9%

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

   6. Applied egg-rr 64.9%

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

   if -4400 < c < 9.6000000000000007e65

   1. Initial program 89.4%

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

   2. Taylor expanded in b around 0 82.6%

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

      1. *-commutative 82.6%

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

      2. distribute-lft-out 82.6%

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

      3. *-commutative 82.6%

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

      4. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in y around 0 74.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4400 \lor \neg \left(c \leq 9.6 \cdot 10^{+65}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 14: 70.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-95}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.3e-95)
   (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))
   (if (<= x 4e+83)
     (+ (* -4.0 (* t a)) (- (* b c) (* j (* 27.0 k))))
     (* x (- (* i (- 4.0)) (* -18.0 (* z (* y t))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.3e-95) {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	} else if (x <= 4e+83) {
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	} else {
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-2.3d-95)) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    else if (x <= 4d+83) then
        tmp = ((-4.0d0) * (t * a)) + ((b * c) - (j * (27.0d0 * k)))
    else
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * (z * (y * t))))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 (x <= -2.3e-95) {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	} else if (x <= 4e+83) {
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	} else {
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -2.3e-95:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	elif x <= 4e+83:
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)))
	else:
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.3e-95)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 4e+83)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b * c) - Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(z * Float64(y * t)))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -2.3e-95)
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	elseif (x <= 4e+83)
		tmp = (-4.0 * (t * a)) + ((b * c) - (j * (27.0 * k)));
	else
		tmp = x * ((i * -4.0) - (-18.0 * (z * (y * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.3e-95], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+83], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.29999999999999999e-95

   1. Initial program 78.3%

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

   2. Taylor expanded in t around 0 69.6%

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

   if -2.29999999999999999e-95 < x < 4.00000000000000012e83

   1. Initial program 91.9%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 81.2%

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

      1. associate--l+ 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*r* 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-*l* 80.4%

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

   6. Applied egg-rr 80.4%

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

   if 4.00000000000000012e83 < x

   1. Initial program 78.6%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in x around 0 86.2%

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

      1. associate-*r* 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-*l* 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in x around -inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. cancel-sign-sub-inv 69.9%

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

      3. associate-*r* 76.4%

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

      4. metadata-eval 76.4%

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

   9. Simplified 76.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-95}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c - j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 15: 47.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* (* j 27.0) k))) (t_2 (* x (* z (* y (* 18.0 t))))))
   (if (<= y -3.9e+212)
     t_2
     (if (<= y -4.2e+137)
       t_1
       (if (<= y -8.5e+108)
         t_2
         (if (<= y 9.8e+95) t_1 (* 18.0 (* t (* x (* y z))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - ((j * 27.0) * k);
	double t_2 = x * (z * (y * (18.0 * t)));
	double tmp;
	if (y <= -3.9e+212) {
		tmp = t_2;
	} else if (y <= -4.2e+137) {
		tmp = t_1;
	} else if (y <= -8.5e+108) {
		tmp = t_2;
	} else if (y <= 9.8e+95) {
		tmp = t_1;
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - ((j * 27.0d0) * k)
    t_2 = x * (z * (y * (18.0d0 * t)))
    if (y <= (-3.9d+212)) then
        tmp = t_2
    else if (y <= (-4.2d+137)) then
        tmp = t_1
    else if (y <= (-8.5d+108)) then
        tmp = t_2
    else if (y <= 9.8d+95) then
        tmp = t_1
    else
        tmp = 18.0d0 * (t * (x * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - ((j * 27.0) * k);
	double t_2 = x * (z * (y * (18.0 * t)));
	double tmp;
	if (y <= -3.9e+212) {
		tmp = t_2;
	} else if (y <= -4.2e+137) {
		tmp = t_1;
	} else if (y <= -8.5e+108) {
		tmp = t_2;
	} else if (y <= 9.8e+95) {
		tmp = t_1;
	} else {
		tmp = 18.0 * (t * (x * (y * z)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - ((j * 27.0) * k)
	t_2 = x * (z * (y * (18.0 * t)))
	tmp = 0
	if y <= -3.9e+212:
		tmp = t_2
	elif y <= -4.2e+137:
		tmp = t_1
	elif y <= -8.5e+108:
		tmp = t_2
	elif y <= 9.8e+95:
		tmp = t_1
	else:
		tmp = 18.0 * (t * (x * (y * z)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(x * Float64(z * Float64(y * Float64(18.0 * t))))
	tmp = 0.0
	if (y <= -3.9e+212)
		tmp = t_2;
	elseif (y <= -4.2e+137)
		tmp = t_1;
	elseif (y <= -8.5e+108)
		tmp = t_2;
	elseif (y <= 9.8e+95)
		tmp = t_1;
	else
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - ((j * 27.0) * k);
	t_2 = x * (z * (y * (18.0 * t)));
	tmp = 0.0;
	if (y <= -3.9e+212)
		tmp = t_2;
	elseif (y <= -4.2e+137)
		tmp = t_1;
	elseif (y <= -8.5e+108)
		tmp = t_2;
	elseif (y <= 9.8e+95)
		tmp = t_1;
	else
		tmp = 18.0 * (t * (x * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+212], t$95$2, If[LessEqual[y, -4.2e+137], t$95$1, If[LessEqual[y, -8.5e+108], t$95$2, If[LessEqual[y, 9.8e+95], t$95$1, N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000001e212 or -4.1999999999999998e137 < y < -8.50000000000000016e108

   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 70.4%

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

   4. Taylor expanded in y around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*l* 59.5%

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

      3. *-commutative 59.5%

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

      4. associate-*l* 59.5%

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

      5. *-commutative 59.5%

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

      6. associate-*l* 59.5%

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

      7. associate-*r* 59.6%

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

      8. associate-*r* 63.0%

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

   6. Simplified 63.0%

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

   if -3.9000000000000001e212 < y < -4.1999999999999998e137 or -8.50000000000000016e108 < y < 9.7999999999999998e95

   1. Initial program 88.9%

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

   2. Taylor expanded in x around 0 91.2%

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

   3. Taylor expanded in b around inf 53.3%

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

   if 9.7999999999999998e95 < y

   1. Initial program 78.3%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in y around inf 48.2%

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

      1. *-commutative 48.2%

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

   6. Simplified 48.2%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+137}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+95}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 16: 36.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5.7 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) -8.5e+62)
   (* b c)
   (if (<= (* b c) -3.6e-223)
     (* t (* -4.0 a))
     (if (<= (* b c) 5.7e+53) (* j (* k -27.0)) (* b c)))))

C

assert(y < z);
assert(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) <= -8.5e+62) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-223) {
		tmp = t * (-4.0 * a);
	} else if ((b * c) <= 5.7e+53) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-8.5d+62)) then
        tmp = b * c
    else if ((b * c) <= (-3.6d-223)) then
        tmp = t * ((-4.0d0) * a)
    else if ((b * c) <= 5.7d+53) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -8.5e+62) {
		tmp = b * c;
	} else if ((b * c) <= -3.6e-223) {
		tmp = t * (-4.0 * a);
	} else if ((b * c) <= 5.7e+53) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -8.5e+62:
		tmp = b * c
	elif (b * c) <= -3.6e-223:
		tmp = t * (-4.0 * a)
	elif (b * c) <= 5.7e+53:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -8.5e+62)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -3.6e-223)
		tmp = Float64(t * Float64(-4.0 * a));
	elseif (Float64(b * c) <= 5.7e+53)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -8.5e+62)
		tmp = b * c;
	elseif ((b * c) <= -3.6e-223)
		tmp = t * (-4.0 * a);
	elseif ((b * c) <= 5.7e+53)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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], -8.5e+62], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-223], N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.7e+53], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -8.4999999999999997e62 or 5.70000000000000017e53 < (*.f64 b c)

   1. Initial program 80.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around inf 51.0%

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

   if -8.4999999999999997e62 < (*.f64 b c) < -3.6000000000000004e-223

   1. Initial program 90.6%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in a around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. *-commutative 41.5%

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

      3. associate-*r* 41.5%

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

   6. Simplified 41.5%

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

   if -3.6000000000000004e-223 < (*.f64 b c) < 5.70000000000000017e53

   1. Initial program 86.9%

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

   2. Taylor expanded in x around 0 90.8%

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

   3. Taylor expanded in j around inf 39.2%

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

      1. *-commutative 39.2%

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

      2. associate-*l* 38.3%

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

   5. Simplified 38.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 5.7 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17: 51.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - t_1\\ \mathbf{if}\;c \leq -4800:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (* b c) t_1)))
   (if (<= c -4800.0)
     t_2
     (if (<= c -5.4e-216)
       (+ (* -4.0 (* x i)) (* j (* k -27.0)))
       (if (<= c 6e+71) (- (* t (* -4.0 a)) t_1) t_2)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - t_1;
	double tmp;
	if (c <= -4800.0) {
		tmp = t_2;
	} else if (c <= -5.4e-216) {
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0));
	} else if (c <= 6e+71) {
		tmp = (t * (-4.0 * a)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = (j * 27.0d0) * k
    t_2 = (b * c) - t_1
    if (c <= (-4800.0d0)) then
        tmp = t_2
    else if (c <= (-5.4d-216)) then
        tmp = ((-4.0d0) * (x * i)) + (j * (k * (-27.0d0)))
    else if (c <= 6d+71) then
        tmp = (t * ((-4.0d0) * a)) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - t_1;
	double tmp;
	if (c <= -4800.0) {
		tmp = t_2;
	} else if (c <= -5.4e-216) {
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0));
	} else if (c <= 6e+71) {
		tmp = (t * (-4.0 * a)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) - t_1
	tmp = 0
	if c <= -4800.0:
		tmp = t_2
	elif c <= -5.4e-216:
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0))
	elif c <= 6e+71:
		tmp = (t * (-4.0 * a)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) - t_1)
	tmp = 0.0
	if (c <= -4800.0)
		tmp = t_2;
	elseif (c <= -5.4e-216)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(j * Float64(k * -27.0)));
	elseif (c <= 6e+71)
		tmp = Float64(Float64(t * Float64(-4.0 * a)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (c <= -4800.0)
		tmp = t_2;
	elseif (c <= -5.4e-216)
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0));
	elseif (c <= 6e+71)
		tmp = (t * (-4.0 * a)) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[c, -4800.0], t$95$2, If[LessEqual[c, -5.4e-216], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e+71], N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4800 or 6.00000000000000025e71 < c

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0 82.1%

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

   3. Taylor expanded in b around inf 56.6%

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

   if -4800 < c < -5.3999999999999998e-216

   1. Initial program 93.9%

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

   2. Taylor expanded in b around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. distribute-lft-out 86.6%

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

      3. *-commutative 86.6%

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

      4. *-commutative 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in t around 0 61.6%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 61.6%

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

      2. associate-*r* 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-*r* 59.7%

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

      5. distribute-neg-in 59.7%

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

      6. distribute-lft-neg-in 59.7%

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

      7. metadata-eval 59.7%

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

      8. distribute-rgt-neg-in 59.7%

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

      9. *-commutative 59.7%

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

      10. distribute-rgt-neg-in 59.7%

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

      11. metadata-eval 59.7%

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

   7. Simplified 59.7%

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

   if -5.3999999999999998e-216 < c < 6.00000000000000025e71

   1. Initial program 86.9%

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

   2. Taylor expanded in x around 0 88.0%

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

   3. Taylor expanded in a around inf 54.1%

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

      1. associate-*r* 54.1%

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

   5. Simplified 54.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4800:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 18: 51.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+105} \lor \neg \left(i \leq 9.6 \cdot 10^{+108}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -1.05e+105) (not (<= i 9.6e+108)))
   (+ (* -4.0 (* x i)) (* j (* k -27.0)))
   (- (* b c) (* (* j 27.0) k))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -1.05e+105) || !(i <= 9.6e+108)) {
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((i <= (-1.05d+105)) .or. (.not. (i <= 9.6d+108))) then
        tmp = ((-4.0d0) * (x * i)) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -1.05e+105) || !(i <= 9.6e+108)) {
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -1.05e+105) or not (i <= 9.6e+108):
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0))
	else:
		tmp = (b * c) - ((j * 27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -1.05e+105) || !(i <= 9.6e+108))
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -1.05e+105) || ~((i <= 9.6e+108)))
		tmp = (-4.0 * (x * i)) + (j * (k * -27.0));
	else
		tmp = (b * c) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -1.05e+105], N[Not[LessEqual[i, 9.6e+108]], $MachinePrecision]], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.05000000000000005e105 or 9.60000000000000074e108 < i

   1. Initial program 84.3%

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

   2. Taylor expanded in b around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. distribute-lft-out 78.2%

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

      3. *-commutative 78.2%

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

      4. *-commutative 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in t around 0 64.5%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 64.5%

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

      2. associate-*r* 64.5%

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

      3. *-commutative 64.5%

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

      4. associate-*r* 64.5%

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

      5. distribute-neg-in 64.5%

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

      6. distribute-lft-neg-in 64.5%

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

      7. metadata-eval 64.5%

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

      8. distribute-rgt-neg-in 64.5%

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

      9. *-commutative 64.5%

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

      10. distribute-rgt-neg-in 64.5%

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

      11. metadata-eval 64.5%

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

   7. Simplified 64.5%

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

   if -1.05000000000000005e105 < i < 9.60000000000000074e108

   1. Initial program 85.3%

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

   2. Taylor expanded in x around 0 86.5%

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

   3. Taylor expanded in b around inf 54.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+105} \lor \neg \left(i \leq 9.6 \cdot 10^{+108}\right):\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 19: 51.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;i \leq -9.2 \cdot 10^{+101}:\\ \;\;\;\;t_1 + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 2.02 \cdot 10^{+108}:\\ \;\;\;\;b \cdot c - t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))) (t_2 (* (* j 27.0) k)))
   (if (<= i -9.2e+101)
     (+ t_1 (* j (* k -27.0)))
     (if (<= i 2.02e+108) (- (* b c) t_2) (- t_1 t_2)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (i <= -9.2e+101) {
		tmp = t_1 + (j * (k * -27.0));
	} else if (i <= 2.02e+108) {
		tmp = (b * c) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = (j * 27.0d0) * k
    if (i <= (-9.2d+101)) then
        tmp = t_1 + (j * (k * (-27.0d0)))
    else if (i <= 2.02d+108) then
        tmp = (b * c) - t_2
    else
        tmp = t_1 - t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (i <= -9.2e+101) {
		tmp = t_1 + (j * (k * -27.0));
	} else if (i <= 2.02e+108) {
		tmp = (b * c) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	t_2 = (j * 27.0) * k
	tmp = 0
	if i <= -9.2e+101:
		tmp = t_1 + (j * (k * -27.0))
	elif i <= 2.02e+108:
		tmp = (b * c) - t_2
	else:
		tmp = t_1 - t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (i <= -9.2e+101)
		tmp = Float64(t_1 + Float64(j * Float64(k * -27.0)));
	elseif (i <= 2.02e+108)
		tmp = Float64(Float64(b * c) - t_2);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (i <= -9.2e+101)
		tmp = t_1 + (j * (k * -27.0));
	elseif (i <= 2.02e+108)
		tmp = (b * c) - t_2;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[i, -9.2e+101], N[(t$95$1 + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.02e+108], N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.2000000000000005e101

   1. Initial program 90.5%

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

   2. Taylor expanded in b around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. distribute-lft-out 87.9%

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

      3. *-commutative 87.9%

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

      4. *-commutative 87.9%

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

   4. Simplified 87.9%

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

   5. Taylor expanded in t around 0 72.4%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 72.4%

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

      2. associate-*r* 72.4%

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

      3. *-commutative 72.4%

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

      4. associate-*r* 72.4%

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

      5. distribute-neg-in 72.4%

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

      6. distribute-lft-neg-in 72.4%

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

      7. metadata-eval 72.4%

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

      8. distribute-rgt-neg-in 72.4%

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

      9. *-commutative 72.4%

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

      10. distribute-rgt-neg-in 72.4%

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

      11. metadata-eval 72.4%

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

   7. Simplified 72.4%

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

   if -9.2000000000000005e101 < i < 2.02000000000000007e108

   1. Initial program 85.3%

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

   2. Taylor expanded in x around 0 86.5%

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

   3. Taylor expanded in b around inf 54.5%

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

   if 2.02000000000000007e108 < i

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0 84.3%

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

   3. Taylor expanded in x around inf 65.3%

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

   4. Taylor expanded in t around 0 59.6%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{+101}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 2.02 \cdot 10^{+108}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 20: 37.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+53}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) -8.2e+33)
   (* b c)
   (if (<= (* b c) 3e+53) (* (* j k) -27.0) (* b c))))

C

assert(y < z);
assert(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) <= -8.2e+33) {
		tmp = b * c;
	} else if ((b * c) <= 3e+53) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-8.2d+33)) then
        tmp = b * c
    else if ((b * c) <= 3d+53) then
        tmp = (j * k) * (-27.0d0)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -8.2e+33) {
		tmp = b * c;
	} else if ((b * c) <= 3e+53) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -8.2e+33:
		tmp = b * c
	elif (b * c) <= 3e+53:
		tmp = (j * k) * -27.0
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -8.2e+33)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 3e+53)
		tmp = Float64(Float64(j * k) * -27.0);
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -8.2e+33)
		tmp = b * c;
	elseif ((b * c) <= 3e+53)
		tmp = (j * k) * -27.0;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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], -8.2e+33], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3e+53], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -8.1999999999999999e33 or 2.99999999999999998e53 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in b around inf 49.7%

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

   if -8.1999999999999999e33 < (*.f64 b c) < 2.99999999999999998e53

   1. Initial program 87.6%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in j around inf 35.6%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3 \cdot 10^{+53}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21: 37.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) -8.2e+33)
   (* b c)
   (if (<= (* b c) 5.4e+51) (* j (* k -27.0)) (* b c))))

C

assert(y < z);
assert(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) <= -8.2e+33) {
		tmp = b * c;
	} else if ((b * c) <= 5.4e+51) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-8.2d+33)) then
        tmp = b * c
    else if ((b * c) <= 5.4d+51) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -8.2e+33) {
		tmp = b * c;
	} else if ((b * c) <= 5.4e+51) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -8.2e+33:
		tmp = b * c
	elif (b * c) <= 5.4e+51:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -8.2e+33)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 5.4e+51)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -8.2e+33)
		tmp = b * c;
	elseif ((b * c) <= 5.4e+51)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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], -8.2e+33], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5.4e+51], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -8.1999999999999999e33 or 5.39999999999999983e51 < (*.f64 b c)

   1. Initial program 81.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in b around inf 49.7%

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

   if -8.1999999999999999e33 < (*.f64 b c) < 5.39999999999999983e51

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 89.0%

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

   3. Taylor expanded in j around inf 35.6%

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

      1. *-commutative 35.6%

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

      2. associate-*l* 34.9%

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

   5. Simplified 34.9%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22: 24.1% accurate, 10.3× speedup

Math

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

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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(y < z);
assert(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: y and z should be sorted in increasing order before calling this function.
NOTE: 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 y < z;
assert 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

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 84.9%

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

3. Simplified 86.2%

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

4. Taylor expanded in b around inf 24.3%

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

5. Final simplification 24.3%

   \[\leadsto b \cdot c \]

Developer target: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023279 
(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)))