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

Percentage Accurate: 85.5% → 89.8%

Time: 22.4s

Alternatives: 20

Speedup: 1.1×

• 49.6% 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: 89.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1) <= math.inf:
		tmp = (((b * c) + t_2) - (4.0 * (t * a))) - t_1
	else:
		tmp = t_2 - t_1
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.4%

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

   2. Taylor expanded in x around 0 95.3%

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

      1. pow1 95.3%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 95.3%

      \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. unpow1 95.3%

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

      2. associate-*r* 98.6%

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

   6. Simplified 98.6%

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

   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%

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

   2. Taylor expanded in x around 0 43.8%

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

   3. Taylor expanded in x around inf 59.6%

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

      1. pow1 43.8%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied egg-rr 59.6%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. unpow1 43.8%

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

      2. associate-*r* 46.9%

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

   7. Simplified 62.8%

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

4. Final simplification 94.1%

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

Alternative 2: 88.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -27000000:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+156}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -27000000.0)
     (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) t_1)
     (if (<= x 1.45e+156)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
       (- (* x (- (* 18.0 (* z (* y t))) (* 4.0 i))) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -27000000.0) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else if (x <= 1.45e+156) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (x <= (-27000000.0d0)) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - t_1
    else if (x <= 1.45d+156) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))) - t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= -27000000.0) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else if (x <= 1.45e+156) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -27000000.0:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1
	elif x <= 1.45e+156:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -27000000.0)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - t_1);
	elseif (x <= 1.45e+156)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i))) - t_1);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -27000000.0)
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	elseif (x <= 1.45e+156)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -27000000.0], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.45e+156], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e7

   1. Initial program 71.2%

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

   2. Taylor expanded in x around 0 87.0%

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

   3. Taylor expanded in a around 0 87.6%

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

   if -2.7e7 < x < 1.45000000000000005e156

   1. Initial program 92.8%

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

   3. Simplified 92.2%

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

   if 1.45000000000000005e156 < x

   1. Initial program 61.5%

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

   2. Taylor expanded in x around 0 83.3%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. pow1 83.3%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied egg-rr 79.0%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. unpow1 83.3%

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

      2. associate-*r* 86.0%

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

   7. Simplified 81.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -27000000:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+156}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 3: 36.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.2 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -6.4 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 2.2 \cdot 10^{-109}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 7900:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

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 (* i -4.0))))
   (if (<= (* b c) -2.3e+63)
     (* b c)
     (if (<= (* b c) -6.2e-148)
       (* j (* k -27.0))
       (if (<= (* b c) -6.4e-282)
         t_1
         (if (<= (* b c) 2.2e-109)
           (* (* j k) -27.0)
           (if (<= (* b c) 7900.0)
             (* t (* 18.0 (* z (* x y))))
             (if (<= (* b c) 1.05e+42) t_1 (* b c)))))))))

C

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 * (i * -4.0);
	double tmp;
	if ((b * c) <= -2.3e+63) {
		tmp = b * c;
	} else if ((b * c) <= -6.2e-148) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -6.4e-282) {
		tmp = t_1;
	} else if ((b * c) <= 2.2e-109) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 7900.0) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if ((b * c) <= 1.05e+42) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

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 = x * (i * (-4.0d0))
    if ((b * c) <= (-2.3d+63)) then
        tmp = b * c
    else if ((b * c) <= (-6.2d-148)) then
        tmp = j * (k * (-27.0d0))
    else if ((b * c) <= (-6.4d-282)) then
        tmp = t_1
    else if ((b * c) <= 2.2d-109) then
        tmp = (j * k) * (-27.0d0)
    else if ((b * c) <= 7900.0d0) then
        tmp = t * (18.0d0 * (z * (x * y)))
    else if ((b * c) <= 1.05d+42) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

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 * (i * -4.0);
	double tmp;
	if ((b * c) <= -2.3e+63) {
		tmp = b * c;
	} else if ((b * c) <= -6.2e-148) {
		tmp = j * (k * -27.0);
	} else if ((b * c) <= -6.4e-282) {
		tmp = t_1;
	} else if ((b * c) <= 2.2e-109) {
		tmp = (j * k) * -27.0;
	} else if ((b * c) <= 7900.0) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if ((b * c) <= 1.05e+42) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -2.3e+63:
		tmp = b * c
	elif (b * c) <= -6.2e-148:
		tmp = j * (k * -27.0)
	elif (b * c) <= -6.4e-282:
		tmp = t_1
	elif (b * c) <= 2.2e-109:
		tmp = (j * k) * -27.0
	elif (b * c) <= 7900.0:
		tmp = t * (18.0 * (z * (x * y)))
	elif (b * c) <= 1.05e+42:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -2.3e+63)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -6.2e-148)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (Float64(b * c) <= -6.4e-282)
		tmp = t_1;
	elseif (Float64(b * c) <= 2.2e-109)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (Float64(b * c) <= 7900.0)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	elseif (Float64(b * c) <= 1.05e+42)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -2.3e+63)
		tmp = b * c;
	elseif ((b * c) <= -6.2e-148)
		tmp = j * (k * -27.0);
	elseif ((b * c) <= -6.4e-282)
		tmp = t_1;
	elseif ((b * c) <= 2.2e-109)
		tmp = (j * k) * -27.0;
	elseif ((b * c) <= 7900.0)
		tmp = t * (18.0 * (z * (x * y)));
	elseif ((b * c) <= 1.05e+42)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2.3e+63], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.2e-148], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.4e-282], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 2.2e-109], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 7900.0], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.05e+42], t$95$1, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -2.29999999999999993e63 or 1.04999999999999998e42 < (*.f64 b c)

   1. Initial program 76.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in b around inf 54.7%

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

   if -2.29999999999999993e63 < (*.f64 b c) < -6.2000000000000003e-148

   1. Initial program 77.7%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in j around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. associate-*l* 39.1%

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

   6. Simplified 39.1%

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

   if -6.2000000000000003e-148 < (*.f64 b c) < -6.39999999999999966e-282 or 7900 < (*.f64 b c) < 1.04999999999999998e42

   1. Initial program 88.9%

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

   3. Simplified 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 i around inf 49.2%

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

      1. associate-*r* 49.2%

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

      2. *-commutative 49.2%

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

   6. Simplified 49.2%

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

   if -6.39999999999999966e-282 < (*.f64 b c) < 2.1999999999999999e-109

   1. Initial program 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in j around inf 40.1%

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

      1. *-commutative 40.1%

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

   6. Simplified 40.1%

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

   if 2.1999999999999999e-109 < (*.f64 b c) < 7900

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in a around 0 80.4%

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

   4. Taylor expanded in t around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l* 46.6%

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

      3. associate-*r* 46.7%

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

      4. *-commutative 46.7%

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

   6. Simplified 46.7%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -6.2 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -6.4 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.2 \cdot 10^{-109}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;b \cdot c \leq 7900:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 4: 87.0% accurate, 1.1× speedup

Math

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

FPCore

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) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) (* 4.0 (* t a)))
  (* (* j 27.0) k)))

C

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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
}

Fortran

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) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
end function

Java

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) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

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

2. Taylor expanded in x around 0 88.8%

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

3. Final simplification 88.8%

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

Alternative 5: 54.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - t_1\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t_1 \leq 0.01:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (* b c) t_1)))
   (if (<= t_1 -2e+120)
     t_2
     (if (<= t_1 -5e-30)
       (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
       (if (<= t_1 0.01) (- (* b c) (* 4.0 (* t a))) t_2)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -2e+120) {
		tmp = t_2;
	} else if (t_1 <= -5e-30) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t_1 <= 0.01) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) - t_1
    if (t_1 <= (-2d+120)) then
        tmp = t_2
    else if (t_1 <= (-5d-30)) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t_1 <= 0.01d0) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) - t_1;
	double tmp;
	if (t_1 <= -2e+120) {
		tmp = t_2;
	} else if (t_1 <= -5e-30) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t_1 <= 0.01) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) - t_1
	tmp = 0
	if t_1 <= -2e+120:
		tmp = t_2
	elif t_1 <= -5e-30:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t_1 <= 0.01:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = t_2
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) - t_1)
	tmp = 0.0
	if (t_1 <= -2e+120)
		tmp = t_2;
	elseif (t_1 <= -5e-30)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t_1 <= 0.01)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (t_1 <= -2e+120)
		tmp = t_2;
	elseif (t_1 <= -5e-30)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t_1 <= 0.01)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+120], t$95$2, If[LessEqual[t$95$1, -5e-30], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.01], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e120 or 0.0100000000000000002 < (*.f64 (*.f64 j 27) k)

   1. Initial program 80.0%

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

   2. Taylor expanded in x around 0 84.8%

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

   3. Taylor expanded in b around inf 68.7%

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

   if -2e120 < (*.f64 (*.f64 j 27) k) < -4.99999999999999972e-30

   1. Initial program 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 59.3%

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

   if -4.99999999999999972e-30 < (*.f64 (*.f64 j 27) k) < 0.0100000000000000002

   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 x around 0 56.8%

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

      1. sub-neg 56.8%

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

      2. associate-*r* 56.8%

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

      3. associate-*r* 56.8%

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

   4. Applied egg-rr 56.8%

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

   5. Taylor expanded in j around 0 55.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 0.01:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 6: 70.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+14} \lor \neg \left(t_1 \leq 0.01\right):\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+14) (not (<= t_1 0.01)))
     (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (- (+ (* b c) (* t (* a -4.0))) (* x (* 4.0 i))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+14) || !(t_1 <= 0.01)) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (a * -4.0))) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+14)) .or. (.not. (t_1 <= 0.01d0))) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * (a * (-4.0d0)))) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+14) || !(t_1 <= 0.01)) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (a * -4.0))) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+14) or not (t_1 <= 0.01):
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * (a * -4.0))) - (x * (4.0 * i))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+14) || !(t_1 <= 0.01))
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(a * -4.0))) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+14) || ~((t_1 <= 0.01)))
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * (a * -4.0))) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+14], N[Not[LessEqual[t$95$1, 0.01]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e14 or 0.0100000000000000002 < (*.f64 (*.f64 j 27) k)

   1. Initial program 81.7%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in t around 0 72.8%

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

   if -2e14 < (*.f64 (*.f64 j 27) k) < 0.0100000000000000002

   1. Initial program 83.5%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. *-commutative 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in x around inf 74.6%

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

      1. associate-*r* 74.6%

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

      2. *-commutative 74.6%

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

   9. Simplified 74.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+14} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 0.01\right):\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \end{array} \]

Alternative 7: 84.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-10} \lor \neg \left(x \leq 1.2 \cdot 10^{+73}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -5.7e-10) (not (<= x 1.2e+73)))
   (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) (* (* j 27.0) k))
   (- (+ (* b c) (* t (* a -4.0))) (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

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 <= -5.7e-10) || !(x <= 1.2e+73)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

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 <= (-5.7d-10)) .or. (.not. (x <= 1.2d+73))) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * (a * (-4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

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 <= -5.7e-10) || !(x <= 1.2e+73)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -5.7e-10) or not (x <= 1.2e+73):
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -5.7e-10) || !(x <= 1.2e+73))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(a * -4.0))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

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 <= -5.7e-10) || ~((x <= 1.2e+73)))
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

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[x, -5.7e-10], N[Not[LessEqual[x, 1.2e+73]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $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 < -5.69999999999999996e-10 or 1.20000000000000001e73 < x

   1. Initial program 70.8%

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

   2. Taylor expanded in x around 0 87.3%

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

   3. Taylor expanded in a around 0 85.5%

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

   if -5.69999999999999996e-10 < x < 1.20000000000000001e73

   1. Initial program 93.9%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-*r* 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-10} \lor \neg \left(x \leq 1.2 \cdot 10^{+73}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 8: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - t_1\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-108}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (- (* x (- (* 18.0 (* z (* y t))) (* 4.0 i))) t_1)))
   (if (<= x -3.5e+49)
     t_2
     (if (<= x -5.4e-108)
       (-
        (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (* 4.0 (* x i)))
       (if (<= x 6.8e+74)
         (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
         t_2)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	double tmp;
	if (x <= -3.5e+49) {
		tmp = t_2;
	} else if (x <= -5.4e-108) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else if (x <= 6.8e+74) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))) - t_1
    if (x <= (-3.5d+49)) then
        tmp = t_2
    else if (x <= (-5.4d-108)) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    else if (x <= 6.8d+74) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	double tmp;
	if (x <= -3.5e+49) {
		tmp = t_2;
	} else if (x <= -5.4e-108) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	} else if (x <= 6.8e+74) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1
	tmp = 0
	if x <= -3.5e+49:
		tmp = t_2
	elif x <= -5.4e-108:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	elif x <= 6.8e+74:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i))) - t_1)
	tmp = 0.0
	if (x <= -3.5e+49)
		tmp = t_2;
	elseif (x <= -5.4e-108)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	elseif (x <= 6.8e+74)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	tmp = 0.0;
	if (x <= -3.5e+49)
		tmp = t_2;
	elseif (x <= -5.4e-108)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	elseif (x <= 6.8e+74)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -3.5e+49], t$95$2, If[LessEqual[x, -5.4e-108], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+74], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.49999999999999975e49 or 6.7999999999999998e74 < x

   1. Initial program 71.6%

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

   2. Taylor expanded in x around 0 89.8%

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

   3. Taylor expanded in x around inf 78.1%

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

      1. pow1 89.8%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied egg-rr 78.1%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. unpow1 89.8%

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

      2. associate-*r* 90.6%

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

   7. Simplified 78.9%

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

   if -3.49999999999999975e49 < x < -5.4000000000000001e-108

   1. Initial program 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in j around 0 80.3%

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

   if -5.4000000000000001e-108 < x < 6.7999999999999998e74

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 92.7%

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

      1. distribute-lft-out 92.7%

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

      2. *-commutative 92.7%

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

      3. *-commutative 92.7%

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

   4. Simplified 92.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-108}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 9: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (* x (* i -4.0))))
   (if (<= (* b c) -1.95e+63)
     (* b c)
     (if (<= (* b c) -2.7e-147)
       t_1
       (if (<= (* b c) -2.9e-275)
         t_2
         (if (<= (* b c) 2.9e-68)
           t_1
           (if (<= (* b c) 9.5e+41) t_2 (* b c))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -1.95e+63) {
		tmp = b * c;
	} else if ((b * c) <= -2.7e-147) {
		tmp = t_1;
	} else if ((b * c) <= -2.9e-275) {
		tmp = t_2;
	} else if ((b * c) <= 2.9e-68) {
		tmp = t_1;
	} else if ((b * c) <= 9.5e+41) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = x * (i * (-4.0d0))
    if ((b * c) <= (-1.95d+63)) then
        tmp = b * c
    else if ((b * c) <= (-2.7d-147)) then
        tmp = t_1
    else if ((b * c) <= (-2.9d-275)) then
        tmp = t_2
    else if ((b * c) <= 2.9d-68) then
        tmp = t_1
    else if ((b * c) <= 9.5d+41) then
        tmp = t_2
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = x * (i * -4.0);
	double tmp;
	if ((b * c) <= -1.95e+63) {
		tmp = b * c;
	} else if ((b * c) <= -2.7e-147) {
		tmp = t_1;
	} else if ((b * c) <= -2.9e-275) {
		tmp = t_2;
	} else if ((b * c) <= 2.9e-68) {
		tmp = t_1;
	} else if ((b * c) <= 9.5e+41) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = x * (i * -4.0)
	tmp = 0
	if (b * c) <= -1.95e+63:
		tmp = b * c
	elif (b * c) <= -2.7e-147:
		tmp = t_1
	elif (b * c) <= -2.9e-275:
		tmp = t_2
	elif (b * c) <= 2.9e-68:
		tmp = t_1
	elif (b * c) <= 9.5e+41:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (Float64(b * c) <= -1.95e+63)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -2.7e-147)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.9e-275)
		tmp = t_2;
	elseif (Float64(b * c) <= 2.9e-68)
		tmp = t_1;
	elseif (Float64(b * c) <= 9.5e+41)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if ((b * c) <= -1.95e+63)
		tmp = b * c;
	elseif ((b * c) <= -2.7e-147)
		tmp = t_1;
	elseif ((b * c) <= -2.9e-275)
		tmp = t_2;
	elseif ((b * c) <= 2.9e-68)
		tmp = t_1;
	elseif ((b * c) <= 9.5e+41)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.95e+63], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.7e-147], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.9e-275], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 2.9e-68], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+41], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.95e63 or 9.4999999999999996e41 < (*.f64 b c)

   1. Initial program 76.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in b around inf 54.7%

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

   if -1.95e63 < (*.f64 b c) < -2.6999999999999999e-147 or -2.9e-275 < (*.f64 b c) < 2.9e-68

   1. Initial program 85.5%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in j around inf 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-*l* 38.1%

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

   6. Simplified 38.1%

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

   if -2.6999999999999999e-147 < (*.f64 b c) < -2.9e-275 or 2.9e-68 < (*.f64 b c) < 9.4999999999999996e41

   1. Initial program 89.9%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in i around inf 43.7%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

   6. Simplified 43.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.95 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -2.9 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2.9 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 10: 72.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -3.05 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+68}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) - t_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-75} \lor \neg \left(x \leq 4.3 \cdot 10^{+73}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))
   (if (<= x -3.05e+203)
     t_2
     (if (<= x -5.2e+68)
       (- (* 18.0 (* x (* z (* y t)))) t_1)
       (if (or (<= x -1.85e-75) (not (<= x 4.3e+73)))
         t_2
         (- (- (* b c) (* 4.0 (* t a))) t_1))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -3.05e+203) {
		tmp = t_2;
	} else if (x <= -5.2e+68) {
		tmp = (18.0 * (x * (z * (y * t)))) - t_1;
	} else if ((x <= -1.85e-75) || !(x <= 4.3e+73)) {
		tmp = t_2;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    if (x <= (-3.05d+203)) then
        tmp = t_2
    else if (x <= (-5.2d+68)) then
        tmp = (18.0d0 * (x * (z * (y * t)))) - t_1
    else if ((x <= (-1.85d-75)) .or. (.not. (x <= 4.3d+73))) then
        tmp = t_2
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	double tmp;
	if (x <= -3.05e+203) {
		tmp = t_2;
	} else if (x <= -5.2e+68) {
		tmp = (18.0 * (x * (z * (y * t)))) - t_1;
	} else if ((x <= -1.85e-75) || !(x <= 4.3e+73)) {
		tmp = t_2;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	tmp = 0
	if x <= -3.05e+203:
		tmp = t_2
	elif x <= -5.2e+68:
		tmp = (18.0 * (x * (z * (y * t)))) - t_1
	elif (x <= -1.85e-75) or not (x <= 4.3e+73):
		tmp = t_2
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))))
	tmp = 0.0
	if (x <= -3.05e+203)
		tmp = t_2;
	elseif (x <= -5.2e+68)
		tmp = Float64(Float64(18.0 * Float64(x * Float64(z * Float64(y * t)))) - t_1);
	elseif ((x <= -1.85e-75) || !(x <= 4.3e+73))
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	tmp = 0.0;
	if (x <= -3.05e+203)
		tmp = t_2;
	elseif (x <= -5.2e+68)
		tmp = (18.0 * (x * (z * (y * t)))) - t_1;
	elseif ((x <= -1.85e-75) || ~((x <= 4.3e+73)))
		tmp = t_2;
	else
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.05e+203], t$95$2, If[LessEqual[x, -5.2e+68], N[(N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[Or[LessEqual[x, -1.85e-75], N[Not[LessEqual[x, 4.3e+73]], $MachinePrecision]], t$95$2, N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.05000000000000007e203 or -5.1999999999999996e68 < x < -1.85000000000000012e-75 or 4.30000000000000013e73 < x

   1. Initial program 74.0%

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

   2. Taylor expanded in x around 0 87.8%

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

   3. Taylor expanded in a around 0 82.6%

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

   4. Taylor expanded in j around 0 78.9%

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

   if -3.05000000000000007e203 < x < -5.1999999999999996e68

   1. Initial program 74.0%

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

   2. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. associate-*r* 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in t around 0 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-*l* 76.9%

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

      3. *-commutative 76.9%

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

      4. associate-*r* 79.8%

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

      5. *-commutative 79.8%

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

   8. Simplified 79.8%

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

   if -1.85000000000000012e-75 < x < 4.30000000000000013e73

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 81.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+203}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+68}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-75} \lor \neg \left(x \leq 4.3 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 11: 76.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{-10} \lor \neg \left(x \leq 5.5 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= x -2.15e-10) (not (<= x 5.5e+24)))
     (- (* x (- (* 18.0 (* z (* y t))) (* 4.0 i))) t_1)
     (- (- (* b c) (* 4.0 (* t a))) t_1))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -2.15e-10) || !(x <= 5.5e+24)) {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((x <= (-2.15d-10)) .or. (.not. (x <= 5.5d+24))) then
        tmp = (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -2.15e-10) || !(x <= 5.5e+24)) {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (x <= -2.15e-10) or not (x <= 5.5e+24):
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((x <= -2.15e-10) || !(x <= 5.5e+24))
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((x <= -2.15e-10) || ~((x <= 5.5e+24)))
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	else
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[x, -2.15e-10], N[Not[LessEqual[x, 5.5e+24]], $MachinePrecision]], N[(N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15000000000000007e-10 or 5.5000000000000002e24 < x

   1. Initial program 71.0%

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

   2. Taylor expanded in x around 0 86.2%

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

   3. Taylor expanded in x around inf 73.4%

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

      1. pow1 86.2%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied egg-rr 73.4%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. unpow1 86.2%

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

      2. associate-*r* 89.6%

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

   7. Simplified 76.8%

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

   if -2.15000000000000007e-10 < x < 5.5000000000000002e24

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 81.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-10} \lor \neg \left(x \leq 5.5 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 12: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1.92 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+24}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_2\\ \end{array} \end{array} \]

FPCore

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 (* t (* y z))) (* 4.0 i))))
        (t_2 (* (* j 27.0) k)))
   (if (<= x -1.92e-75)
     (+ (* b c) t_1)
     (if (<= x 6e+24) (- (- (* b c) (* 4.0 (* t a))) t_2) (- t_1 t_2)))))

C

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 * (t * (y * z))) - (4.0 * i));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -1.92e-75) {
		tmp = (b * c) + t_1;
	} else if (x <= 6e+24) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Fortran

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 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    t_2 = (j * 27.0d0) * k
    if (x <= (-1.92d-75)) then
        tmp = (b * c) + t_1
    else if (x <= 6d+24) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_2
    else
        tmp = t_1 - t_2
    end if
    code = tmp
end function

Java

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 * (t * (y * z))) - (4.0 * i));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -1.92e-75) {
		tmp = (b * c) + t_1;
	} else if (x <= 6e+24) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	t_2 = (j * 27.0) * k
	tmp = 0
	if x <= -1.92e-75:
		tmp = (b * c) + t_1
	elif x <= 6e+24:
		tmp = ((b * c) - (4.0 * (t * a))) - t_2
	else:
		tmp = t_1 - t_2
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -1.92e-75)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (x <= 6e+24)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_2);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

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 * (t * (y * z))) - (4.0 * i));
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -1.92e-75)
		tmp = (b * c) + t_1;
	elseif (x <= 6e+24)
		tmp = ((b * c) - (4.0 * (t * a))) - t_2;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -1.92e-75], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 6e+24], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.92000000000000011e-75

   1. Initial program 76.0%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in a around 0 85.5%

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

   4. Taylor expanded in j around 0 73.6%

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

   if -1.92000000000000011e-75 < x < 5.9999999999999999e24

   1. Initial program 95.1%

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

   2. Taylor expanded in x around 0 83.4%

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

   if 5.9999999999999999e24 < x

   1. Initial program 72.2%

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

   2. Taylor expanded in x around 0 87.5%

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

   3. Taylor expanded in x around inf 76.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.92 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+24}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 13: 79.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 4.3 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

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 4.3e+74)
   (- (+ (* b c) (* t (* a -4.0))) (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (- (* x (- (* 18.0 (* z (* y t))) (* 4.0 i))) (* (* j 27.0) k))))

C

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 <= 4.3e+74) {
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

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 <= 4.3d+74) then
        tmp = ((b * c) + (t * (a * (-4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

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 <= 4.3e+74) {
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 4.3e+74:
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - ((j * 27.0) * k)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 4.3e+74)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(a * -4.0))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

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 <= 4.3e+74)
		tmp = ((b * c) + (t * (a * -4.0))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

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, 4.3e+74], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.30000000000000001e74

   1. Initial program 85.9%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 83.9%

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

      1. *-commutative 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 83.9%

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

   6. Simplified 83.9%

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

   if 4.30000000000000001e74 < x

   1. Initial program 70.1%

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

   2. Taylor expanded in x around 0 88.6%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. pow1 88.6%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied egg-rr 79.0%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. unpow1 88.6%

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

      2. associate-*r* 90.4%

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

   7. Simplified 80.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.3 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 14: 65.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

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 (* t (* y z))) (* 4.0 i)))))
   (if (<= t -4.5e+230)
     t_1
     (if (<= t -3.3e+124)
       (- (* t (* a -4.0)) (* (* j 27.0) k))
       (if (<= t 1.36e+84)
         (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
         t_1)))))

C

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 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (t <= -4.5e+230) {
		tmp = t_1;
	} else if (t <= -3.3e+124) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else if (t <= 1.36e+84) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (t <= (-4.5d+230)) then
        tmp = t_1
    else if (t <= (-3.3d+124)) then
        tmp = (t * (a * (-4.0d0))) - ((j * 27.0d0) * k)
    else if (t <= 1.36d+84) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (t <= -4.5e+230) {
		tmp = t_1;
	} else if (t <= -3.3e+124) {
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	} else if (t <= 1.36e+84) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	tmp = 0
	if t <= -4.5e+230:
		tmp = t_1
	elif t <= -3.3e+124:
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k)
	elif t <= 1.36e+84:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))
	tmp = 0.0
	if (t <= -4.5e+230)
		tmp = t_1;
	elseif (t <= -3.3e+124)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 1.36e+84)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (t <= -4.5e+230)
		tmp = t_1;
	elseif (t <= -3.3e+124)
		tmp = (t * (a * -4.0)) - ((j * 27.0) * k);
	elseif (t <= 1.36e+84)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+230], t$95$1, If[LessEqual[t, -3.3e+124], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e+84], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4999999999999999e230 or 1.3599999999999999e84 < t

   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 83.4%

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

   4. Taylor expanded in x around inf 58.0%

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

   if -4.4999999999999999e230 < t < -3.30000000000000015e124

   1. Initial program 94.3%

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

   2. Taylor expanded in x around 0 94.3%

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

   3. Taylor expanded in a around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*r* 88.9%

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

   5. Simplified 88.9%

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

   if -3.30000000000000015e124 < t < 1.3599999999999999e84

   1. Initial program 83.5%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around 0 74.6%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 15: 53.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+14} \lor \neg \left(t_1 \leq 0.01\right):\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+14) (not (<= t_1 0.01)))
     (- (* b c) t_1)
     (- (* b c) (* 4.0 (* t a))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+14) || !(t_1 <= 0.01)) {
		tmp = (b * c) - t_1;
	} else {
		tmp = (b * c) - (4.0 * (t * a));
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+14)) .or. (.not. (t_1 <= 0.01d0))) then
        tmp = (b * c) - t_1
    else
        tmp = (b * c) - (4.0d0 * (t * a))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+14) || !(t_1 <= 0.01)) {
		tmp = (b * c) - t_1;
	} else {
		tmp = (b * c) - (4.0 * (t * a));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+14) or not (t_1 <= 0.01):
		tmp = (b * c) - t_1
	else:
		tmp = (b * c) - (4.0 * (t * a))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+14) || !(t_1 <= 0.01))
		tmp = Float64(Float64(b * c) - t_1);
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+14) || ~((t_1 <= 0.01)))
		tmp = (b * c) - t_1;
	else
		tmp = (b * c) - (4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+14], N[Not[LessEqual[t$95$1, 0.01]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e14 or 0.0100000000000000002 < (*.f64 (*.f64 j 27) k)

   1. Initial program 81.7%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in b around inf 64.9%

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

   if -2e14 < (*.f64 (*.f64 j 27) k) < 0.0100000000000000002

   1. Initial program 83.5%

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

   2. Taylor expanded in x around 0 55.1%

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

      1. sub-neg 55.1%

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

      2. associate-*r* 55.1%

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

      3. associate-*r* 55.2%

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

   4. Applied egg-rr 55.2%

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

   5. Taylor expanded in j around 0 53.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+14} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 0.01\right):\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 16: 53.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-30}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) - t_1\\ \mathbf{elif}\;t_1 \leq 0.01:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -5e-30)
     (- (* 18.0 (* x (* z (* y t)))) t_1)
     (if (<= t_1 0.01) (- (* b c) (* 4.0 (* t a))) (- (* b c) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e-30) {
		tmp = (18.0 * (x * (z * (y * t)))) - t_1;
	} else if (t_1 <= 0.01) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-5d-30)) then
        tmp = (18.0d0 * (x * (z * (y * t)))) - t_1
    else if (t_1 <= 0.01d0) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = (b * c) - t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -5e-30) {
		tmp = (18.0 * (x * (z * (y * t)))) - t_1;
	} else if (t_1 <= 0.01) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (b * c) - t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -5e-30:
		tmp = (18.0 * (x * (z * (y * t)))) - t_1
	elif t_1 <= 0.01:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = (b * c) - t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -5e-30)
		tmp = Float64(Float64(18.0 * Float64(x * Float64(z * Float64(y * t)))) - t_1);
	elseif (t_1 <= 0.01)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - t_1);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -5e-30)
		tmp = (18.0 * (x * (z * (y * t)))) - t_1;
	elseif (t_1 <= 0.01)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = (b * c) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-30], N[(N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 0.01], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.99999999999999972e-30

   1. Initial program 78.8%

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

   2. Taylor expanded in x around 0 86.4%

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

   3. Taylor expanded in y around inf 62.7%

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

      1. associate-*r* 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in t around 0 62.7%

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

      1. *-commutative 62.7%

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

      2. associate-*l* 66.3%

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

      3. *-commutative 66.3%

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

      4. associate-*r* 67.8%

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

      5. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -4.99999999999999972e-30 < (*.f64 (*.f64 j 27) k) < 0.0100000000000000002

   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 x around 0 56.8%

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

      1. sub-neg 56.8%

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

      2. associate-*r* 56.8%

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

      3. associate-*r* 56.8%

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

   4. Applied egg-rr 56.8%

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

   5. Taylor expanded in j around 0 55.0%

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

   if 0.0100000000000000002 < (*.f64 (*.f64 j 27) k)

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 87.6%

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

   3. Taylor expanded in b around inf 67.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-30}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 0.01:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 17: 79.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x 8.5e+74)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
     (- (* x (- (* 18.0 (* z (* y t))) (* 4.0 i))) t_1))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= 8.5e+74) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (x <= 8.5d+74) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = (x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))) - t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (x <= 8.5e+74) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= 8.5e+74:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= 8.5e+74)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i))) - t_1);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= 8.5e+74)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = (x * ((18.0 * (z * (y * t))) - (4.0 * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, 8.5e+74], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 8.50000000000000028e74

   1. Initial program 85.9%

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

   2. Taylor expanded in y around 0 83.9%

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

      1. distribute-lft-out 83.9%

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

      2. *-commutative 83.9%

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

      3. *-commutative 83.9%

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

   4. Simplified 83.9%

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

   if 8.50000000000000028e74 < x

   1. Initial program 70.1%

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

   2. Taylor expanded in x around 0 88.6%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. pow1 88.6%

         \[\leadsto \left(\left(b \cdot c + x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right)\right) - 4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k \]

   5. Applied egg-rr 79.0%

      \[\leadsto x \cdot \left(18 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. unpow1 88.6%

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

      2. associate-*r* 90.4%

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

   7. Simplified 80.8%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 18: 46.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+170}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.05e+203)
   (* x (* i -4.0))
   (if (<= x -4.3e+170)
     (* j (* k -27.0))
     (if (<= x -4.5e+103)
       (* t (* 18.0 (* z (* x y))))
       (if (<= x 9.2e+80)
         (- (* b c) (* 4.0 (* t a)))
         (* (* x (* y z)) (* 18.0 t)))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.05e+203) {
		tmp = x * (i * -4.0);
	} else if (x <= -4.3e+170) {
		tmp = j * (k * -27.0);
	} else if (x <= -4.5e+103) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if (x <= 9.2e+80) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (x * (y * z)) * (18.0 * t);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-3.05d+203)) then
        tmp = x * (i * (-4.0d0))
    else if (x <= (-4.3d+170)) then
        tmp = j * (k * (-27.0d0))
    else if (x <= (-4.5d+103)) then
        tmp = t * (18.0d0 * (z * (x * y)))
    else if (x <= 9.2d+80) then
        tmp = (b * c) - (4.0d0 * (t * a))
    else
        tmp = (x * (y * z)) * (18.0d0 * t)
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -3.05e+203) {
		tmp = x * (i * -4.0);
	} else if (x <= -4.3e+170) {
		tmp = j * (k * -27.0);
	} else if (x <= -4.5e+103) {
		tmp = t * (18.0 * (z * (x * y)));
	} else if (x <= 9.2e+80) {
		tmp = (b * c) - (4.0 * (t * a));
	} else {
		tmp = (x * (y * z)) * (18.0 * t);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -3.05e+203:
		tmp = x * (i * -4.0)
	elif x <= -4.3e+170:
		tmp = j * (k * -27.0)
	elif x <= -4.5e+103:
		tmp = t * (18.0 * (z * (x * y)))
	elif x <= 9.2e+80:
		tmp = (b * c) - (4.0 * (t * a))
	else:
		tmp = (x * (y * z)) * (18.0 * t)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -3.05e+203)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (x <= -4.3e+170)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= -4.5e+103)
		tmp = Float64(t * Float64(18.0 * Float64(z * Float64(x * y))));
	elseif (x <= 9.2e+80)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(x * Float64(y * z)) * Float64(18.0 * t));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.05e+203)
		tmp = x * (i * -4.0);
	elseif (x <= -4.3e+170)
		tmp = j * (k * -27.0);
	elseif (x <= -4.5e+103)
		tmp = t * (18.0 * (z * (x * y)));
	elseif (x <= 9.2e+80)
		tmp = (b * c) - (4.0 * (t * a));
	else
		tmp = (x * (y * z)) * (18.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -3.05e+203], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e+170], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e+103], N[(t * N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.2e+80], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.05000000000000007e203

   1. Initial program 72.8%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in i around inf 56.4%

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

      1. associate-*r* 56.4%

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

      2. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if -3.05000000000000007e203 < x < -4.2999999999999999e170

   1. Initial program 75.1%

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

   3. Simplified 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 j around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*l* 59.3%

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

   6. Simplified 59.3%

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

   if -4.2999999999999999e170 < x < -4.50000000000000001e103

   1. Initial program 77.6%

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

   2. Taylor expanded in x around 0 92.3%

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

   3. Taylor expanded in a around 0 92.6%

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

   4. Taylor expanded in t around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-*l* 48.4%

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

      3. associate-*r* 48.4%

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

      4. *-commutative 48.4%

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

   6. Simplified 48.4%

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

   if -4.50000000000000001e103 < x < 9.20000000000000016e80

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 74.8%

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

      1. sub-neg 74.8%

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

      2. associate-*r* 74.8%

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

      3. associate-*r* 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in j around 0 53.1%

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

   if 9.20000000000000016e80 < x

   1. Initial program 69.5%

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

   2. Taylor expanded in x around 0 88.4%

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

   3. Taylor expanded in a around 0 83.2%

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

   4. Taylor expanded in t around inf 52.3%

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

      1. associate-*r* 52.4%

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

   6. Simplified 52.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+170}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \end{array} \]

Alternative 19: 37.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

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) -2.3e+63)
   (* b c)
   (if (<= (* b c) 3.5e+42) (* j (* k -27.0)) (* b c))))

C

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) <= -2.3e+63) {
		tmp = b * c;
	} else if ((b * c) <= 3.5e+42) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

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) <= (-2.3d+63)) then
        tmp = b * c
    else if ((b * c) <= 3.5d+42) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

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) <= -2.3e+63) {
		tmp = b * c;
	} else if ((b * c) <= 3.5e+42) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2.3e+63:
		tmp = b * c
	elif (b * c) <= 3.5e+42:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2.3e+63)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 3.5e+42)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

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) <= -2.3e+63)
		tmp = b * c;
	elseif ((b * c) <= 3.5e+42)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

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], -2.3e+63], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.5e+42], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.29999999999999993e63 or 3.50000000000000023e42 < (*.f64 b c)

   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 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 b around inf 55.2%

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

   if -2.29999999999999993e63 < (*.f64 b c) < 3.50000000000000023e42

   1. Initial program 86.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in j around inf 32.4%

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

      1. *-commutative 32.4%

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

      2. associate-*l* 33.0%

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

   6. Simplified 33.0%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.3 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3.5 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20: 23.6% accurate, 10.3× speedup

Math

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

FPCore

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(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: 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 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

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

Julia

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

MATLAB

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: 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 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 85.4%

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

4. Taylor expanded in b around inf 25.3%

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

5. Final simplification 25.3%

   \[\leadsto b \cdot c \]

Developer target: 89.5% 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 2023293 
(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)))