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

Percentage Accurate: 85.5% → 90.6%

Time: 25.1s

Alternatives: 15

Speedup: 1.0×

• 50.8% 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: 85.5% 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: 90.6% accurate, 0.5× speedup

Math

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

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
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY)
     t_1
     (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))))

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

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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	}
	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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	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(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	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 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	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[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(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]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in x around inf 44.7%

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

      1. associate-*r* 44.7%

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

      2. *-commutative 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around 0 58.3%

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

4. Final simplification 88.5%

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

Alternative 2: 37.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -1.18 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -820:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{-101}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* t (* z (* x y))))))
   (if (<= (* b c) -1.18e+162)
     (* b c)
     (if (<= (* b c) -820.0)
       t_1
       (if (<= (* b c) -5e-66)
         (* k (* j -27.0))
         (if (<= (* b c) 8.2e-195)
           t_1
           (if (<= (* b c) 9.8e-101)
             (* -27.0 (* j k))
             (if (<= (* b c) 2.9e+131) t_1 (* 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 t_1 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if ((b * c) <= -1.18e+162) {
		tmp = b * c;
	} else if ((b * c) <= -820.0) {
		tmp = t_1;
	} else if ((b * c) <= -5e-66) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 8.2e-195) {
		tmp = t_1;
	} else if ((b * c) <= 9.8e-101) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 2.9e+131) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (z * (x * y)))
    if ((b * c) <= (-1.18d+162)) then
        tmp = b * c
    else if ((b * c) <= (-820.0d0)) then
        tmp = t_1
    else if ((b * c) <= (-5d-66)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 8.2d-195) then
        tmp = t_1
    else if ((b * c) <= 9.8d-101) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 2.9d+131) then
        tmp = t_1
    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 t_1 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if ((b * c) <= -1.18e+162) {
		tmp = b * c;
	} else if ((b * c) <= -820.0) {
		tmp = t_1;
	} else if ((b * c) <= -5e-66) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 8.2e-195) {
		tmp = t_1;
	} else if ((b * c) <= 9.8e-101) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 2.9e+131) {
		tmp = t_1;
	} 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):
	t_1 = 18.0 * (t * (z * (x * y)))
	tmp = 0
	if (b * c) <= -1.18e+162:
		tmp = b * c
	elif (b * c) <= -820.0:
		tmp = t_1
	elif (b * c) <= -5e-66:
		tmp = k * (j * -27.0)
	elif (b * c) <= 8.2e-195:
		tmp = t_1
	elif (b * c) <= 9.8e-101:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 2.9e+131:
		tmp = t_1
	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)
	t_1 = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (Float64(b * c) <= -1.18e+162)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -820.0)
		tmp = t_1;
	elseif (Float64(b * c) <= -5e-66)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 8.2e-195)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.8e-101)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 2.9e+131)
		tmp = t_1;
	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)
	t_1 = 18.0 * (t * (z * (x * y)));
	tmp = 0.0;
	if ((b * c) <= -1.18e+162)
		tmp = b * c;
	elseif ((b * c) <= -820.0)
		tmp = t_1;
	elseif ((b * c) <= -5e-66)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 8.2e-195)
		tmp = t_1;
	elseif ((b * c) <= 9.8e-101)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 2.9e+131)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.18e+162], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -820.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5e-66], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.2e-195], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.8e-101], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.9e+131], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.1800000000000001e162 or 2.9000000000000001e131 < (*.f64 b c)

   1. Initial program 79.9%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in b around inf 68.6%

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

   if -1.1800000000000001e162 < (*.f64 b c) < -820 or -4.99999999999999962e-66 < (*.f64 b c) < 8.20000000000000024e-195 or 9.8000000000000001e-101 < (*.f64 b c) < 2.9000000000000001e131

   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 85.1%

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

   4. Taylor expanded in y around inf 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-*l* 43.2%

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

      3. *-commutative 43.2%

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

      4. *-commutative 43.2%

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

      5. *-commutative 43.2%

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

      6. associate-*l* 43.3%

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

   6. Simplified 43.3%

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

   7. Taylor expanded in x around 0 43.2%

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

      1. *-commutative 43.2%

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

      2. *-commutative 43.2%

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

      3. associate-*l* 42.5%

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

   9. Simplified 42.5%

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

   if -820 < (*.f64 b c) < -4.99999999999999962e-66

   1. Initial program 75.5%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in j around inf 57.5%

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

      1. associate-*r* 57.4%

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

   6. Simplified 57.4%

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

   if 8.20000000000000024e-195 < (*.f64 b c) < 9.8000000000000001e-101

   1. Initial program 87.5%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in j around inf 51.2%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.18 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -820:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-66}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 8.2 \cdot 10^{-195}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{-101}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 3: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -3.1 \cdot 10^{+169}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -26:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-70}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.22 \cdot 10^{-98}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.08 \cdot 10^{+129}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* t (* z (* x y))))))
   (if (<= (* b c) -3.1e+169)
     (* b c)
     (if (<= (* b c) -26.0)
       t_1
       (if (<= (* b c) -2.9e-70)
         (* k (* j -27.0))
         (if (<= (* b c) 1.15e-194)
           t_1
           (if (<= (* b c) 1.22e-98)
             (* -27.0 (* j k))
             (if (<= (* b c) 1.08e+129)
               (* 18.0 (* x (* y (* z t))))
               (* 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 t_1 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if ((b * c) <= -3.1e+169) {
		tmp = b * c;
	} else if ((b * c) <= -26.0) {
		tmp = t_1;
	} else if ((b * c) <= -2.9e-70) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.15e-194) {
		tmp = t_1;
	} else if ((b * c) <= 1.22e-98) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.08e+129) {
		tmp = 18.0 * (x * (y * (z * t)));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (z * (x * y)))
    if ((b * c) <= (-3.1d+169)) then
        tmp = b * c
    else if ((b * c) <= (-26.0d0)) then
        tmp = t_1
    else if ((b * c) <= (-2.9d-70)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.15d-194) then
        tmp = t_1
    else if ((b * c) <= 1.22d-98) then
        tmp = (-27.0d0) * (j * k)
    else if ((b * c) <= 1.08d+129) then
        tmp = 18.0d0 * (x * (y * (z * t)))
    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 t_1 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if ((b * c) <= -3.1e+169) {
		tmp = b * c;
	} else if ((b * c) <= -26.0) {
		tmp = t_1;
	} else if ((b * c) <= -2.9e-70) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.15e-194) {
		tmp = t_1;
	} else if ((b * c) <= 1.22e-98) {
		tmp = -27.0 * (j * k);
	} else if ((b * c) <= 1.08e+129) {
		tmp = 18.0 * (x * (y * (z * t)));
	} 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):
	t_1 = 18.0 * (t * (z * (x * y)))
	tmp = 0
	if (b * c) <= -3.1e+169:
		tmp = b * c
	elif (b * c) <= -26.0:
		tmp = t_1
	elif (b * c) <= -2.9e-70:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.15e-194:
		tmp = t_1
	elif (b * c) <= 1.22e-98:
		tmp = -27.0 * (j * k)
	elif (b * c) <= 1.08e+129:
		tmp = 18.0 * (x * (y * (z * t)))
	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)
	t_1 = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (Float64(b * c) <= -3.1e+169)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -26.0)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.9e-70)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.15e-194)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.22e-98)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (Float64(b * c) <= 1.08e+129)
		tmp = Float64(18.0 * Float64(x * Float64(y * Float64(z * t))));
	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)
	t_1 = 18.0 * (t * (z * (x * y)));
	tmp = 0.0;
	if ((b * c) <= -3.1e+169)
		tmp = b * c;
	elseif ((b * c) <= -26.0)
		tmp = t_1;
	elseif ((b * c) <= -2.9e-70)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.15e-194)
		tmp = t_1;
	elseif ((b * c) <= 1.22e-98)
		tmp = -27.0 * (j * k);
	elseif ((b * c) <= 1.08e+129)
		tmp = 18.0 * (x * (y * (z * t)));
	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_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.1e+169], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -26.0], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.9e-70], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.15e-194], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.22e-98], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.08e+129], N[(18.0 * N[(x * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -3.1e169 or 1.08e129 < (*.f64 b c)

   1. Initial program 79.9%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in b around inf 68.6%

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

   if -3.1e169 < (*.f64 b c) < -26 or -2.89999999999999971e-70 < (*.f64 b c) < 1.15000000000000001e-194

   1. Initial program 78.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in y around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. associate-*l* 47.0%

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

      3. *-commutative 47.0%

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

      4. *-commutative 47.0%

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

      5. *-commutative 47.0%

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

      6. associate-*l* 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in x around 0 47.0%

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

      1. *-commutative 47.0%

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

      2. *-commutative 47.0%

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

      3. associate-*l* 47.0%

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

   9. Simplified 47.0%

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

   if -26 < (*.f64 b c) < -2.89999999999999971e-70

   1. Initial program 75.5%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in j around inf 57.5%

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

      1. associate-*r* 57.4%

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

   6. Simplified 57.4%

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

   if 1.15000000000000001e-194 < (*.f64 b c) < 1.2200000000000001e-98

   1. Initial program 87.5%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in j around inf 51.2%

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

   if 1.2200000000000001e-98 < (*.f64 b c) < 1.08e129

   1. Initial program 82.0%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in y around inf 34.2%

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

      1. *-commutative 34.2%

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

      2. associate-*l* 34.0%

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

      3. *-commutative 34.0%

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

      4. *-commutative 34.0%

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

      5. associate-*l* 38.5%

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

   6. Simplified 38.5%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.1 \cdot 10^{+169}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -26:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-70}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{-194}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.22 \cdot 10^{-98}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.08 \cdot 10^{+129}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 4: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq -1.78 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8.2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -3.2 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{-199}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* x (* z (* y t))))) (t_2 (* -27.0 (* j k))))
   (if (<= (* b c) -1.78e+162)
     (* b c)
     (if (<= (* b c) -8.2e-12)
       t_1
       (if (<= (* b c) -3.2e-67)
         t_2
         (if (<= (* b c) 3.9e-199)
           (* 18.0 (* t (* z (* x y))))
           (if (<= (* b c) 3.8e-97)
             t_2
             (if (<= (* b c) 1.02e+131) t_1 (* 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 t_1 = 18.0 * (x * (z * (y * t)));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if ((b * c) <= -1.78e+162) {
		tmp = b * c;
	} else if ((b * c) <= -8.2e-12) {
		tmp = t_1;
	} else if ((b * c) <= -3.2e-67) {
		tmp = t_2;
	} else if ((b * c) <= 3.9e-199) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else if ((b * c) <= 3.8e-97) {
		tmp = t_2;
	} else if ((b * c) <= 1.02e+131) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (z * (y * t)))
    t_2 = (-27.0d0) * (j * k)
    if ((b * c) <= (-1.78d+162)) then
        tmp = b * c
    else if ((b * c) <= (-8.2d-12)) then
        tmp = t_1
    else if ((b * c) <= (-3.2d-67)) then
        tmp = t_2
    else if ((b * c) <= 3.9d-199) then
        tmp = 18.0d0 * (t * (z * (x * y)))
    else if ((b * c) <= 3.8d-97) then
        tmp = t_2
    else if ((b * c) <= 1.02d+131) then
        tmp = t_1
    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 t_1 = 18.0 * (x * (z * (y * t)));
	double t_2 = -27.0 * (j * k);
	double tmp;
	if ((b * c) <= -1.78e+162) {
		tmp = b * c;
	} else if ((b * c) <= -8.2e-12) {
		tmp = t_1;
	} else if ((b * c) <= -3.2e-67) {
		tmp = t_2;
	} else if ((b * c) <= 3.9e-199) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else if ((b * c) <= 3.8e-97) {
		tmp = t_2;
	} else if ((b * c) <= 1.02e+131) {
		tmp = t_1;
	} 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):
	t_1 = 18.0 * (x * (z * (y * t)))
	t_2 = -27.0 * (j * k)
	tmp = 0
	if (b * c) <= -1.78e+162:
		tmp = b * c
	elif (b * c) <= -8.2e-12:
		tmp = t_1
	elif (b * c) <= -3.2e-67:
		tmp = t_2
	elif (b * c) <= 3.9e-199:
		tmp = 18.0 * (t * (z * (x * y)))
	elif (b * c) <= 3.8e-97:
		tmp = t_2
	elif (b * c) <= 1.02e+131:
		tmp = t_1
	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)
	t_1 = Float64(18.0 * Float64(x * Float64(z * Float64(y * t))))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (Float64(b * c) <= -1.78e+162)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -8.2e-12)
		tmp = t_1;
	elseif (Float64(b * c) <= -3.2e-67)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.9e-199)
		tmp = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))));
	elseif (Float64(b * c) <= 3.8e-97)
		tmp = t_2;
	elseif (Float64(b * c) <= 1.02e+131)
		tmp = t_1;
	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)
	t_1 = 18.0 * (x * (z * (y * t)));
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if ((b * c) <= -1.78e+162)
		tmp = b * c;
	elseif ((b * c) <= -8.2e-12)
		tmp = t_1;
	elseif ((b * c) <= -3.2e-67)
		tmp = t_2;
	elseif ((b * c) <= 3.9e-199)
		tmp = 18.0 * (t * (z * (x * y)));
	elseif ((b * c) <= 3.8e-97)
		tmp = t_2;
	elseif ((b * c) <= 1.02e+131)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.78e+162], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -8.2e-12], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -3.2e-67], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.9e-199], N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.8e-97], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1.02e+131], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.77999999999999998e162 or 1.0199999999999999e131 < (*.f64 b c)

   1. Initial program 79.9%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in b around inf 68.6%

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

   if -1.77999999999999998e162 < (*.f64 b c) < -8.19999999999999979e-12 or 3.8000000000000001e-97 < (*.f64 b c) < 1.0199999999999999e131

   1. Initial program 76.5%

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

   3. Simplified 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 y around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. associate-*l* 39.0%

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

      3. *-commutative 39.0%

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

      4. *-commutative 39.0%

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

      5. *-commutative 39.0%

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

      6. associate-*l* 40.6%

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

   6. Simplified 40.6%

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

   if -8.19999999999999979e-12 < (*.f64 b c) < -3.20000000000000021e-67 or 3.9000000000000001e-199 < (*.f64 b c) < 3.8000000000000001e-97

   1. Initial program 83.3%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in j around inf 54.6%

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

   if -3.20000000000000021e-67 < (*.f64 b c) < 3.9000000000000001e-199

   1. Initial program 81.4%

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

   3. Simplified 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 y around inf 45.7%

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

      1. *-commutative 45.7%

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

      2. associate-*l* 45.6%

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

      3. *-commutative 45.6%

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

      4. *-commutative 45.6%

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

      5. *-commutative 45.6%

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

      6. associate-*l* 45.6%

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

   6. Simplified 45.6%

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

   7. Taylor expanded in x around 0 45.7%

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

      1. *-commutative 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-*l* 46.6%

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

   9. Simplified 46.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.78 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -8.2 \cdot 10^{-12}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -3.2 \cdot 10^{-67}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 3.9 \cdot 10^{-199}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.02 \cdot 10^{+131}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 5: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+219}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+188}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 -2.5e+219)
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (if (<= x 4.5e+188)
     (-
      (+ (* b c) (* t (- (* (* x y) (* 18.0 z)) (* a 4.0))))
      (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
     (+ (* b c) (* t (* (* x 18.0) (* 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 tmp;
	if (x <= -2.5e+219) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if (x <= 4.5e+188) {
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (b * c) + (t * ((x * 18.0) * (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) :: tmp
    if (x <= (-2.5d+219)) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else if (x <= 4.5d+188) then
        tmp = ((b * c) + (t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (b * c) + (t * ((x * 18.0d0) * (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 tmp;
	if (x <= -2.5e+219) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else if (x <= 4.5e+188) {
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (b * c) + (t * ((x * 18.0) * (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):
	tmp = 0
	if x <= -2.5e+219:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	elif x <= 4.5e+188:
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (b * c) + (t * ((x * 18.0) * (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)
	tmp = 0.0
	if (x <= -2.5e+219)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	elseif (x <= 4.5e+188)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(x * 18.0) * 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)
	tmp = 0.0;
	if (x <= -2.5e+219)
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	elseif (x <= 4.5e+188)
		tmp = ((b * c) + (t * (((x * y) * (18.0 * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (b * c) + (t * ((x * 18.0) * (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_] := If[LessEqual[x, -2.5e+219], 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], If[LessEqual[x, 4.5e+188], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5e219

   1. Initial program 40.3%

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

   3. Simplified 52.4%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. associate-*r* 61.1%

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

      2. *-commutative 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in i around 0 78.7%

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

   if -2.5e219 < x < 4.5000000000000001e188

   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 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 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*r* 90.5%

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

      3. associate-*l* 90.5%

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

   6. Simplified 90.5%

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

   if 4.5000000000000001e188 < x

   1. Initial program 52.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in x around inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in i around 0 68.6%

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

   8. Taylor expanded in x around inf 68.6%

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

      1. associate-*r* 68.6%

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

      2. *-commutative 68.6%

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

   10. Simplified 68.6%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+219}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+188}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 6: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+231}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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 -1.2e+231)
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 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 (x <= -1.2e+231) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.2d+231)) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert 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 <= -1.2e+231) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[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 <= -1.2e+231:
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

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 <= -1.2e+231)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

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 <= -1.2e+231)
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: 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, -1.2e+231], 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[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000003e231

   1. Initial program 39.0%

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

   3. Simplified 52.3%

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

   4. Taylor expanded in x around inf 61.8%

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

      1. associate-*r* 61.8%

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

      2. *-commutative 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in i around 0 81.1%

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

   if -1.20000000000000003e231 < x

   1. Initial program 83.6%

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

   3. Simplified 86.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+231}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 7: 36.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -1.75 \cdot 10^{+199}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.1 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* t (* a -4.0))))
   (if (<= (* b c) -1.75e+199)
     (* b c)
     (if (<= (* b c) -1.6e-231)
       t_1
       (if (<= (* b c) -1.1e-301)
         t_2
         (if (<= (* b c) 6.2e-101)
           t_1
           (if (<= (* b c) 1.6e+42)
             t_2
             (if (<= (* b c) 1e+92) t_1 (* 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 t_1 = -27.0 * (j * k);
	double t_2 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -1.75e+199) {
		tmp = b * c;
	} else if ((b * c) <= -1.6e-231) {
		tmp = t_1;
	} else if ((b * c) <= -1.1e-301) {
		tmp = t_2;
	} else if ((b * c) <= 6.2e-101) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e+42) {
		tmp = t_2;
	} else if ((b * c) <= 1e+92) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = t * (a * (-4.0d0))
    if ((b * c) <= (-1.75d+199)) then
        tmp = b * c
    else if ((b * c) <= (-1.6d-231)) then
        tmp = t_1
    else if ((b * c) <= (-1.1d-301)) then
        tmp = t_2
    else if ((b * c) <= 6.2d-101) then
        tmp = t_1
    else if ((b * c) <= 1.6d+42) then
        tmp = t_2
    else if ((b * c) <= 1d+92) then
        tmp = t_1
    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 t_1 = -27.0 * (j * k);
	double t_2 = t * (a * -4.0);
	double tmp;
	if ((b * c) <= -1.75e+199) {
		tmp = b * c;
	} else if ((b * c) <= -1.6e-231) {
		tmp = t_1;
	} else if ((b * c) <= -1.1e-301) {
		tmp = t_2;
	} else if ((b * c) <= 6.2e-101) {
		tmp = t_1;
	} else if ((b * c) <= 1.6e+42) {
		tmp = t_2;
	} else if ((b * c) <= 1e+92) {
		tmp = t_1;
	} 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):
	t_1 = -27.0 * (j * k)
	t_2 = t * (a * -4.0)
	tmp = 0
	if (b * c) <= -1.75e+199:
		tmp = b * c
	elif (b * c) <= -1.6e-231:
		tmp = t_1
	elif (b * c) <= -1.1e-301:
		tmp = t_2
	elif (b * c) <= 6.2e-101:
		tmp = t_1
	elif (b * c) <= 1.6e+42:
		tmp = t_2
	elif (b * c) <= 1e+92:
		tmp = t_1
	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)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.75e+199)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -1.6e-231)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.1e-301)
		tmp = t_2;
	elseif (Float64(b * c) <= 6.2e-101)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.6e+42)
		tmp = t_2;
	elseif (Float64(b * c) <= 1e+92)
		tmp = t_1;
	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)
	t_1 = -27.0 * (j * k);
	t_2 = t * (a * -4.0);
	tmp = 0.0;
	if ((b * c) <= -1.75e+199)
		tmp = b * c;
	elseif ((b * c) <= -1.6e-231)
		tmp = t_1;
	elseif ((b * c) <= -1.1e-301)
		tmp = t_2;
	elseif ((b * c) <= 6.2e-101)
		tmp = t_1;
	elseif ((b * c) <= 1.6e+42)
		tmp = t_2;
	elseif ((b * c) <= 1e+92)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.75e+199], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.6e-231], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.1e-301], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 6.2e-101], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.6e+42], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 1e+92], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.7499999999999999e199 or 1e92 < (*.f64 b c)

   1. Initial program 79.1%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in b around inf 65.1%

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

   if -1.7499999999999999e199 < (*.f64 b c) < -1.60000000000000004e-231 or -1.1e-301 < (*.f64 b c) < 6.19999999999999946e-101 or 1.60000000000000001e42 < (*.f64 b c) < 1e92

   1. Initial program 79.4%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in j around inf 35.6%

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

   if -1.60000000000000004e-231 < (*.f64 b c) < -1.1e-301 or 6.19999999999999946e-101 < (*.f64 b c) < 1.60000000000000001e42

   1. Initial program 83.6%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in a around inf 40.4%

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

      1. *-commutative 40.4%

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

      2. *-commutative 40.4%

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

      3. associate-*r* 40.4%

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

   6. Simplified 40.4%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.75 \cdot 10^{+199}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-231}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -1.1 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+92}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 8: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+289}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -9.5 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -5.3 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (+ (* x (* y (* 18.0 z))) (* a -4.0)))))
   (if (<= (* b c) -6.2e+289)
     (* b c)
     (if (<= (* b c) -9.5e-6)
       t_1
       (if (<= (* b c) -5.3e-46)
         (* k (* j -27.0))
         (if (<= (* b c) 3.6e+125) t_1 (* 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 t_1 = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	double tmp;
	if ((b * c) <= -6.2e+289) {
		tmp = b * c;
	} else if ((b * c) <= -9.5e-6) {
		tmp = t_1;
	} else if ((b * c) <= -5.3e-46) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.6e+125) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((x * (y * (18.0d0 * z))) + (a * (-4.0d0)))
    if ((b * c) <= (-6.2d+289)) then
        tmp = b * c
    else if ((b * c) <= (-9.5d-6)) then
        tmp = t_1
    else if ((b * c) <= (-5.3d-46)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 3.6d+125) then
        tmp = t_1
    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 t_1 = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	double tmp;
	if ((b * c) <= -6.2e+289) {
		tmp = b * c;
	} else if ((b * c) <= -9.5e-6) {
		tmp = t_1;
	} else if ((b * c) <= -5.3e-46) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 3.6e+125) {
		tmp = t_1;
	} 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):
	t_1 = t * ((x * (y * (18.0 * z))) + (a * -4.0))
	tmp = 0
	if (b * c) <= -6.2e+289:
		tmp = b * c
	elif (b * c) <= -9.5e-6:
		tmp = t_1
	elif (b * c) <= -5.3e-46:
		tmp = k * (j * -27.0)
	elif (b * c) <= 3.6e+125:
		tmp = t_1
	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)
	t_1 = Float64(t * Float64(Float64(x * Float64(y * Float64(18.0 * z))) + Float64(a * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -6.2e+289)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -9.5e-6)
		tmp = t_1;
	elseif (Float64(b * c) <= -5.3e-46)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 3.6e+125)
		tmp = t_1;
	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)
	t_1 = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	tmp = 0.0;
	if ((b * c) <= -6.2e+289)
		tmp = b * c;
	elseif ((b * c) <= -9.5e-6)
		tmp = t_1;
	elseif ((b * c) <= -5.3e-46)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 3.6e+125)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(t * N[(N[(x * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.2e+289], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -9.5e-6], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5.3e-46], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.6e+125], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -6.2000000000000002e289 or 3.6000000000000003e125 < (*.f64 b c)

   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 81.0%

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

   4. Taylor expanded in b around inf 76.1%

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

   if -6.2000000000000002e289 < (*.f64 b c) < -9.5000000000000005e-6 or -5.30000000000000018e-46 < (*.f64 b c) < 3.6000000000000003e125

   1. Initial program 79.8%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in t around inf 55.3%

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

      1. cancel-sign-sub-inv 55.3%

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

      2. *-commutative 55.3%

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

      3. associate-*r* 53.1%

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

      4. associate-*r* 53.1%

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

      5. associate-*l* 55.3%

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

      6. metadata-eval 55.3%

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

   6. Applied egg-rr 55.3%

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

   if -9.5000000000000005e-6 < (*.f64 b c) < -5.30000000000000018e-46

   1. Initial program 67.4%

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

   3. Simplified 59.1%

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

   4. Taylor expanded in j around inf 67.0%

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

      1. associate-*r* 67.0%

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

   6. Simplified 67.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+289}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -9.5 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -5.3 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 9: 75.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(b \cdot c - t_1\right) - \left(j \cdot 27\right) \cdot k\\ t_3 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-78}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (* 4.0 (* x i)))
        (t_2 (- (- (* b c) t_1) (* (* j 27.0) k)))
        (t_3 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))
   (if (<= t -2.7e+87)
     t_3
     (if (<= t -2.55e-14)
       t_2
       (if (<= t -1.65e-51)
         t_3
         (if (<= t -2e-78)
           (- (+ (* b c) (* (* t a) -4.0)) t_1)
           (if (<= t 1.05e-9) t_2 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 = 4.0 * (x * i);
	double t_2 = ((b * c) - t_1) - ((j * 27.0) * k);
	double t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -2.7e+87) {
		tmp = t_3;
	} else if (t <= -2.55e-14) {
		tmp = t_2;
	} else if (t <= -1.65e-51) {
		tmp = t_3;
	} else if (t <= -2e-78) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (t <= 1.05e-9) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 * (x * i)
    t_2 = ((b * c) - t_1) - ((j * 27.0d0) * k)
    t_3 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    if (t <= (-2.7d+87)) then
        tmp = t_3
    else if (t <= (-2.55d-14)) then
        tmp = t_2
    else if (t <= (-1.65d-51)) then
        tmp = t_3
    else if (t <= (-2d-78)) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - t_1
    else if (t <= 1.05d-9) then
        tmp = t_2
    else
        tmp = t_3
    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 = ((b * c) - t_1) - ((j * 27.0) * k);
	double t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double tmp;
	if (t <= -2.7e+87) {
		tmp = t_3;
	} else if (t <= -2.55e-14) {
		tmp = t_2;
	} else if (t <= -1.65e-51) {
		tmp = t_3;
	} else if (t <= -2e-78) {
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	} else if (t <= 1.05e-9) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = ((b * c) - t_1) - ((j * 27.0) * k)
	t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	tmp = 0
	if t <= -2.7e+87:
		tmp = t_3
	elif t <= -2.55e-14:
		tmp = t_2
	elif t <= -1.65e-51:
		tmp = t_3
	elif t <= -2e-78:
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1
	elif t <= 1.05e-9:
		tmp = t_2
	else:
		tmp = 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(4.0 * Float64(x * i))
	t_2 = Float64(Float64(Float64(b * c) - t_1) - Float64(Float64(j * 27.0) * k))
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -2.7e+87)
		tmp = t_3;
	elseif (t <= -2.55e-14)
		tmp = t_2;
	elseif (t <= -1.65e-51)
		tmp = t_3;
	elseif (t <= -2e-78)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - t_1);
	elseif (t <= 1.05e-9)
		tmp = t_2;
	else
		tmp = t_3;
	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 = ((b * c) - t_1) - ((j * 27.0) * k);
	t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -2.7e+87)
		tmp = t_3;
	elseif (t <= -2.55e-14)
		tmp = t_2;
	elseif (t <= -1.65e-51)
		tmp = t_3;
	elseif (t <= -2e-78)
		tmp = ((b * c) + ((t * a) * -4.0)) - t_1;
	elseif (t <= 1.05e-9)
		tmp = t_2;
	else
		tmp = t_3;
	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[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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]}, If[LessEqual[t, -2.7e+87], t$95$3, If[LessEqual[t, -2.55e-14], t$95$2, If[LessEqual[t, -1.65e-51], t$95$3, If[LessEqual[t, -2e-78], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.05e-9], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.70000000000000007e87 or -2.5499999999999999e-14 < t < -1.64999999999999986e-51 or 1.0500000000000001e-9 < t

   1. Initial program 77.6%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in x around inf 84.1%

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

      1. associate-*r* 84.1%

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

      2. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in i around 0 85.2%

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

   if -2.70000000000000007e87 < t < -2.5499999999999999e-14 or -2e-78 < t < 1.0500000000000001e-9

   1. Initial program 82.3%

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

   2. Taylor expanded in t around 0 80.0%

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

   if -1.64999999999999986e-51 < t < -2e-78

   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 88.9%

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

   4. Taylor expanded in x around inf 92.0%

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

      1. associate-*r* 92.0%

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

      2. *-commutative 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in y around 0 92.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-14}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-78}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 10: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;b \cdot c \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.32 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (+ (* b c) (* t (* (* x 18.0) (* y z))))))
   (if (<= (* b c) -9.2e+14)
     t_1
     (if (<= (* b c) -5.5e-46)
       (* k (* j -27.0))
       (if (<= (* b c) 1.32e+73)
         (* t (+ (* x (* y (* 18.0 z))) (* a -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 = (b * c) + (t * ((x * 18.0) * (y * z)));
	double tmp;
	if ((b * c) <= -9.2e+14) {
		tmp = t_1;
	} else if ((b * c) <= -5.5e-46) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.32e+73) {
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	} else {
		tmp = 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 = (b * c) + (t * ((x * 18.0d0) * (y * z)))
    if ((b * c) <= (-9.2d+14)) then
        tmp = t_1
    else if ((b * c) <= (-5.5d-46)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= 1.32d+73) then
        tmp = t * ((x * (y * (18.0d0 * z))) + (a * (-4.0d0)))
    else
        tmp = 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 = (b * c) + (t * ((x * 18.0) * (y * z)));
	double tmp;
	if ((b * c) <= -9.2e+14) {
		tmp = t_1;
	} else if ((b * c) <= -5.5e-46) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= 1.32e+73) {
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	} else {
		tmp = 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 = (b * c) + (t * ((x * 18.0) * (y * z)))
	tmp = 0
	if (b * c) <= -9.2e+14:
		tmp = t_1
	elif (b * c) <= -5.5e-46:
		tmp = k * (j * -27.0)
	elif (b * c) <= 1.32e+73:
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0))
	else:
		tmp = 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(b * c) + Float64(t * Float64(Float64(x * 18.0) * Float64(y * z))))
	tmp = 0.0
	if (Float64(b * c) <= -9.2e+14)
		tmp = t_1;
	elseif (Float64(b * c) <= -5.5e-46)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= 1.32e+73)
		tmp = Float64(t * Float64(Float64(x * Float64(y * Float64(18.0 * z))) + Float64(a * -4.0)));
	else
		tmp = 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 = (b * c) + (t * ((x * 18.0) * (y * z)));
	tmp = 0.0;
	if ((b * c) <= -9.2e+14)
		tmp = t_1;
	elseif ((b * c) <= -5.5e-46)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= 1.32e+73)
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	else
		tmp = 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[(b * c), $MachinePrecision] + N[(t * N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -9.2e+14], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -5.5e-46], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.32e+73], N[(t * N[(N[(x * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.2e14 or 1.32e73 < (*.f64 b c)

   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 80.7%

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

   4. Taylor expanded in x around inf 75.1%

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

      1. associate-*r* 75.1%

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

      2. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in i around 0 72.6%

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

   8. Taylor expanded in x around inf 69.9%

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

      1. associate-*r* 69.9%

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

      2. *-commutative 69.9%

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

   10. Simplified 69.9%

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

   if -9.2e14 < (*.f64 b c) < -5.49999999999999983e-46

   1. Initial program 73.9%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in j around inf 60.4%

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

      1. associate-*r* 60.4%

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

   6. Simplified 60.4%

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

   if -5.49999999999999983e-46 < (*.f64 b c) < 1.32e73

   1. Initial program 82.8%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. cancel-sign-sub-inv 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*r* 56.8%

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

      4. associate-*r* 56.8%

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

      5. associate-*l* 58.4%

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

      6. metadata-eval 58.4%

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

   6. Applied egg-rr 58.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 1.32 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 11: 80.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+136} \lor \neg \left(t \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 (<= t -1.55e+136) (not (<= t 1.35e-9)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (- (* b c) (* 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 ((t <= -1.55e+136) || !(t <= 1.35e-9)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (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 ((t <= (-1.55d+136)) .or. (.not. (t <= 1.35d-9))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = ((b * c) - (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 ((t <= -1.55e+136) || !(t <= 1.35e-9)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (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 (t <= -1.55e+136) or not (t <= 1.35e-9):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = ((b * c) - (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 ((t <= -1.55e+136) || !(t <= 1.35e-9))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - 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 ((t <= -1.55e+136) || ~((t <= 1.35e-9)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = ((b * c) - (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[t, -1.55e+136], N[Not[LessEqual[t, 1.35e-9]], $MachinePrecision]], 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[(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]]

Derivation

1. Split input into 2 regimes

2. if t < -1.54999999999999992e136 or 1.3500000000000001e-9 < t

   1. Initial program 75.8%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in x around inf 84.3%

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

      1. associate-*r* 84.3%

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

      2. *-commutative 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in i around 0 86.3%

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

   if -1.54999999999999992e136 < t < 1.3500000000000001e-9

   1. Initial program 82.9%

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

   2. Taylor expanded in y around 0 81.5%

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

      1. distribute-lft-out 81.5%

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

      2. *-commutative 81.5%

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

      3. *-commutative 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+136} \lor \neg \left(t \leq 1.35 \cdot 10^{-9}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 12: 62.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+172} \lor \neg \left(y \leq 3.4 \cdot 10^{-74}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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 (<= y -1.32e+172) (not (<= y 3.4e-74)))
   (+ (* b c) (* t (* (* x 18.0) (* y z))))
   (- (+ (* b c) (* (* t a) -4.0)) (* 4.0 (* x i)))))

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 ((y <= -1.32e+172) || !(y <= 3.4e-74)) {
		tmp = (b * c) + (t * ((x * 18.0) * (y * z)));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i));
	}
	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 ((y <= (-1.32d+172)) .or. (.not. (y <= 3.4d-74))) then
        tmp = (b * c) + (t * ((x * 18.0d0) * (y * z)))
    else
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - (4.0d0 * (x * i))
    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 ((y <= -1.32e+172) || !(y <= 3.4e-74)) {
		tmp = (b * c) + (t * ((x * 18.0) * (y * z)));
	} else {
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i));
	}
	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 (y <= -1.32e+172) or not (y <= 3.4e-74):
		tmp = (b * c) + (t * ((x * 18.0) * (y * z)))
	else:
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i))
	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 ((y <= -1.32e+172) || !(y <= 3.4e-74))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(x * 18.0) * Float64(y * z))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(4.0 * Float64(x * i)));
	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 ((y <= -1.32e+172) || ~((y <= 3.4e-74)))
		tmp = (b * c) + (t * ((x * 18.0) * (y * z)));
	else
		tmp = ((b * c) + ((t * a) * -4.0)) - (4.0 * (x * i));
	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[y, -1.32e+172], N[Not[LessEqual[y, 3.4e-74]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.31999999999999996e172 or 3.4000000000000001e-74 < y

   1. Initial program 74.4%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in x around inf 71.3%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in i around 0 72.3%

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

   8. Taylor expanded in x around inf 64.8%

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

      1. associate-*r* 64.7%

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

      2. *-commutative 64.7%

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

   10. Simplified 64.7%

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

   if -1.31999999999999996e172 < y < 3.4000000000000001e-74

   1. Initial program 84.4%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in x around inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in y around 0 60.7%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+172} \lor \neg \left(y \leq 3.4 \cdot 10^{-74}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 13: 71.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \end{array} \]

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 (<= t -6.5e+136)
   (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
   (if (<= t 2.25e-9)
     (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))
     (* t (+ (* x (* y (* 18.0 z))) (* a -4.0))))))

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 (t <= -6.5e+136) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 2.25e-9) {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	} else {
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	}
	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 (t <= (-6.5d+136)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 2.25d-9) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    else
        tmp = t * ((x * (y * (18.0d0 * z))) + (a * (-4.0d0)))
    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 (t <= -6.5e+136) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 2.25e-9) {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	} else {
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	}
	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 t <= -6.5e+136:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 2.25e-9:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	else:
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0))
	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 (t <= -6.5e+136)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 2.25e-9)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(t * Float64(Float64(x * Float64(y * Float64(18.0 * z))) + Float64(a * -4.0)));
	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 (t <= -6.5e+136)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 2.25e-9)
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	else
		tmp = t * ((x * (y * (18.0 * z))) + (a * -4.0));
	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[t, -6.5e+136], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e-9], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999998e136

   1. Initial program 75.9%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 83.2%

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

   if -6.4999999999999998e136 < t < 2.24999999999999988e-9

   1. Initial program 82.9%

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

   2. Taylor expanded in t around 0 76.3%

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

   if 2.24999999999999988e-9 < t

   1. Initial program 75.7%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in t around inf 65.8%

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

      1. cancel-sign-sub-inv 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r* 66.9%

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

      4. associate-*r* 66.9%

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

      5. associate-*l* 65.8%

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

      6. metadata-eval 65.8%

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

   6. Applied egg-rr 65.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-9}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 14: 36.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.4 \cdot 10^{+200}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+88}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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) -1.4e+200)
   (* b c)
   (if (<= (* b c) 9.5e+88) (* -27.0 (* j k)) (* 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) <= -1.4e+200) {
		tmp = b * c;
	} else if ((b * c) <= 9.5e+88) {
		tmp = -27.0 * (j * k);
	} 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) <= (-1.4d+200)) then
        tmp = b * c
    else if ((b * c) <= 9.5d+88) then
        tmp = (-27.0d0) * (j * k)
    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) <= -1.4e+200) {
		tmp = b * c;
	} else if ((b * c) <= 9.5e+88) {
		tmp = -27.0 * (j * k);
	} 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) <= -1.4e+200:
		tmp = b * c
	elif (b * c) <= 9.5e+88:
		tmp = -27.0 * (j * k)
	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) <= -1.4e+200)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 9.5e+88)
		tmp = Float64(-27.0 * Float64(j * k));
	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) <= -1.4e+200)
		tmp = b * c;
	elseif ((b * c) <= 9.5e+88)
		tmp = -27.0 * (j * k);
	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], -1.4e+200], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+88], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.39999999999999992e200 or 9.50000000000000059e88 < (*.f64 b c)

   1. Initial program 79.1%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in b around inf 65.1%

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

   if -1.39999999999999992e200 < (*.f64 b c) < 9.50000000000000059e88

   1. Initial program 80.3%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in j around inf 31.0%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.4 \cdot 10^{+200}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+88}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 15: 23.3% 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 79.9%

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

3. Simplified 83.8%

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

4. Taylor expanded in b around inf 25.8%

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

5. Final simplification 25.8%

   \[\leadsto b \cdot c \]

Developer target: 89.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023275 
(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)))