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

Percentage Accurate: 85.1% → 91.4%

Time: 29.3s

Alternatives: 28

Speedup: 0.9×

• 51.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.5× speedup

Math

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.6%

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

   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 33.3%

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

   3. Taylor expanded in j around 0 45.8%

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

   4. Taylor expanded in a around 0 62.7%

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

4. Final simplification 92.5%

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

Alternative 2: 63.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - t_1\\ t_3 := b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ t_4 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+217}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t_1 \leq -8 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_1 \leq 10^{-68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_1\\ \end{array} \end{array} \]

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) t_1))
        (t_3 (+ (* b c) (* (+ (* t a) (* x i)) -4.0)))
        (t_4 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t_1 -1e+217)
     (+ (* j (* k -27.0)) (* (* x i) -4.0))
     (if (<= t_1 -8e+63)
       t_3
       (if (<= t_1 -2e+25)
         t_2
         (if (<= t_1 -5e-18)
           t_4
           (if (<= t_1 1e-68)
             t_3
             (if (<= t_1 2e+92)
               t_4
               (if (<= t_1 2e+164)
                 t_2
                 (if (<= t_1 2e+224)
                   (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
                   (- (* t (* a -4.0)) 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) - t_1;
	double t_3 = (b * c) + (((t * a) + (x * i)) * -4.0);
	double t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t_1 <= -1e+217) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (t_1 <= -8e+63) {
		tmp = t_3;
	} else if (t_1 <= -2e+25) {
		tmp = t_2;
	} else if (t_1 <= -5e-18) {
		tmp = t_4;
	} else if (t_1 <= 1e-68) {
		tmp = t_3;
	} else if (t_1 <= 2e+92) {
		tmp = t_4;
	} else if (t_1 <= 2e+164) {
		tmp = t_2;
	} else if (t_1 <= 2e+224) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (t * (a * -4.0)) - 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) - t_1
    t_3 = (b * c) + (((t * a) + (x * i)) * (-4.0d0))
    t_4 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t_1 <= (-1d+217)) then
        tmp = (j * (k * (-27.0d0))) + ((x * i) * (-4.0d0))
    else if (t_1 <= (-8d+63)) then
        tmp = t_3
    else if (t_1 <= (-2d+25)) then
        tmp = t_2
    else if (t_1 <= (-5d-18)) then
        tmp = t_4
    else if (t_1 <= 1d-68) then
        tmp = t_3
    else if (t_1 <= 2d+92) then
        tmp = t_4
    else if (t_1 <= 2d+164) then
        tmp = t_2
    else if (t_1 <= 2d+224) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else
        tmp = (t * (a * (-4.0d0))) - 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) - t_1;
	double t_3 = (b * c) + (((t * a) + (x * i)) * -4.0);
	double t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t_1 <= -1e+217) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (t_1 <= -8e+63) {
		tmp = t_3;
	} else if (t_1 <= -2e+25) {
		tmp = t_2;
	} else if (t_1 <= -5e-18) {
		tmp = t_4;
	} else if (t_1 <= 1e-68) {
		tmp = t_3;
	} else if (t_1 <= 2e+92) {
		tmp = t_4;
	} else if (t_1 <= 2e+164) {
		tmp = t_2;
	} else if (t_1 <= 2e+224) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else {
		tmp = (t * (a * -4.0)) - 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) - t_1
	t_3 = (b * c) + (((t * a) + (x * i)) * -4.0)
	t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t_1 <= -1e+217:
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0)
	elif t_1 <= -8e+63:
		tmp = t_3
	elif t_1 <= -2e+25:
		tmp = t_2
	elif t_1 <= -5e-18:
		tmp = t_4
	elif t_1 <= 1e-68:
		tmp = t_3
	elif t_1 <= 2e+92:
		tmp = t_4
	elif t_1 <= 2e+164:
		tmp = t_2
	elif t_1 <= 2e+224:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	else:
		tmp = (t * (a * -4.0)) - 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) - t_1)
	t_3 = Float64(Float64(b * c) + Float64(Float64(Float64(t * a) + Float64(x * i)) * -4.0))
	t_4 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t_1 <= -1e+217)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(x * i) * -4.0));
	elseif (t_1 <= -8e+63)
		tmp = t_3;
	elseif (t_1 <= -2e+25)
		tmp = t_2;
	elseif (t_1 <= -5e-18)
		tmp = t_4;
	elseif (t_1 <= 1e-68)
		tmp = t_3;
	elseif (t_1 <= 2e+92)
		tmp = t_4;
	elseif (t_1 <= 2e+164)
		tmp = t_2;
	elseif (t_1 <= 2e+224)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(t * Float64(a * -4.0)) - 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) - t_1;
	t_3 = (b * c) + (((t * a) + (x * i)) * -4.0);
	t_4 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t_1 <= -1e+217)
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	elseif (t_1 <= -8e+63)
		tmp = t_3;
	elseif (t_1 <= -2e+25)
		tmp = t_2;
	elseif (t_1 <= -5e-18)
		tmp = t_4;
	elseif (t_1 <= 1e-68)
		tmp = t_3;
	elseif (t_1 <= 2e+92)
		tmp = t_4;
	elseif (t_1 <= 2e+164)
		tmp = t_2;
	elseif (t_1 <= 2e+224)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	else
		tmp = (t * (a * -4.0)) - 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] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+217], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -8e+63], t$95$3, If[LessEqual[t$95$1, -2e+25], t$95$2, If[LessEqual[t$95$1, -5e-18], t$95$4, If[LessEqual[t$95$1, 1e-68], t$95$3, If[LessEqual[t$95$1, 2e+92], t$95$4, If[LessEqual[t$95$1, 2e+164], t$95$2, If[LessEqual[t$95$1, 2e+224], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e216

   1. Initial program 92.7%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in t around 0 93.0%

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

      1. associate-*r* 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-*r* 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-*r* 92.9%

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

      6. fma-udef 92.9%

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

      7. associate-*r* 93.0%

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

      8. *-commutative 93.0%

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

      9. associate-*r* 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in b around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-*r* 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*r* 92.9%

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

      5. distribute-neg-in 92.9%

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

      6. distribute-lft-neg-in 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-rgt-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. distribute-rgt-neg-in 92.9%

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

      11. metadata-eval 92.9%

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

   9. Simplified 92.9%

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

   if -9.9999999999999996e216 < (*.f64 (*.f64 j 27) k) < -8.00000000000000046e63 or -5.00000000000000036e-18 < (*.f64 (*.f64 j 27) k) < 1.00000000000000007e-68

   1. Initial program 89.9%

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

   2. Taylor expanded in y around 0 78.4%

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

      1. fma-neg 78.5%

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

      2. distribute-lft-out 78.5%

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

      3. distribute-lft-neg-in 78.5%

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

      4. metadata-eval 78.5%

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

      5. *-commutative 78.5%

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

      6. fma-def 79.3%

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

      7. *-commutative 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in j around 0 76.0%

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

   if -8.00000000000000046e63 < (*.f64 (*.f64 j 27) k) < -2.00000000000000018e25 or 2.0000000000000001e92 < (*.f64 (*.f64 j 27) k) < 2e164

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 95.8%

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

   3. Taylor expanded in b around inf 67.1%

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

   if -2.00000000000000018e25 < (*.f64 (*.f64 j 27) k) < -5.00000000000000036e-18 or 1.00000000000000007e-68 < (*.f64 (*.f64 j 27) k) < 2.0000000000000001e92

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0 78.3%

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

   3. Taylor expanded in t around inf 73.1%

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

   4. Taylor expanded in t around inf 70.9%

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

   if 2e164 < (*.f64 (*.f64 j 27) k) < 1.99999999999999994e224

   1. Initial program 79.8%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in x around inf 71.0%

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

   if 1.99999999999999994e224 < (*.f64 (*.f64 j 27) k)

   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 71.0%

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

   3. Taylor expanded in a around inf 90.3%

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

      1. associate-*r* 90.3%

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

   5. Simplified 90.3%

      \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+217}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -8 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-68}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+92}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+164}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 3: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+217}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t_1 \leq -8 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right)\right) - t_1\\ \end{array} \end{array} \]

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) (* (+ (* t a) (* x i)) -4.0)))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t_1 -1e+217)
     (+ (* j (* k -27.0)) (* (* x i) -4.0))
     (if (<= t_1 -8e+63)
       t_2
       (if (<= t_1 -2e+25)
         (- (* b c) t_1)
         (if (<= t_1 -5e-18)
           t_3
           (if (<= t_1 1e-68)
             t_2
             (if (<= t_1 5e+94)
               t_3
               (- (* t (* (* x y) (* 18.0 z))) 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) + (((t * a) + (x * i)) * -4.0);
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t_1 <= -1e+217) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (t_1 <= -8e+63) {
		tmp = t_2;
	} else if (t_1 <= -2e+25) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= -5e-18) {
		tmp = t_3;
	} else if (t_1 <= 1e-68) {
		tmp = t_2;
	} else if (t_1 <= 5e+94) {
		tmp = t_3;
	} else {
		tmp = (t * ((x * y) * (18.0 * z))) - 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) :: t_3
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (b * c) + (((t * a) + (x * i)) * (-4.0d0))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t_1 <= (-1d+217)) then
        tmp = (j * (k * (-27.0d0))) + ((x * i) * (-4.0d0))
    else if (t_1 <= (-8d+63)) then
        tmp = t_2
    else if (t_1 <= (-2d+25)) then
        tmp = (b * c) - t_1
    else if (t_1 <= (-5d-18)) then
        tmp = t_3
    else if (t_1 <= 1d-68) then
        tmp = t_2
    else if (t_1 <= 5d+94) then
        tmp = t_3
    else
        tmp = (t * ((x * y) * (18.0d0 * z))) - 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) + (((t * a) + (x * i)) * -4.0);
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t_1 <= -1e+217) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (t_1 <= -8e+63) {
		tmp = t_2;
	} else if (t_1 <= -2e+25) {
		tmp = (b * c) - t_1;
	} else if (t_1 <= -5e-18) {
		tmp = t_3;
	} else if (t_1 <= 1e-68) {
		tmp = t_2;
	} else if (t_1 <= 5e+94) {
		tmp = t_3;
	} else {
		tmp = (t * ((x * y) * (18.0 * z))) - 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) + (((t * a) + (x * i)) * -4.0)
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t_1 <= -1e+217:
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0)
	elif t_1 <= -8e+63:
		tmp = t_2
	elif t_1 <= -2e+25:
		tmp = (b * c) - t_1
	elif t_1 <= -5e-18:
		tmp = t_3
	elif t_1 <= 1e-68:
		tmp = t_2
	elif t_1 <= 5e+94:
		tmp = t_3
	else:
		tmp = (t * ((x * y) * (18.0 * z))) - 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(Float64(Float64(t * a) + Float64(x * i)) * -4.0))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t_1 <= -1e+217)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(x * i) * -4.0));
	elseif (t_1 <= -8e+63)
		tmp = t_2;
	elseif (t_1 <= -2e+25)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t_1 <= -5e-18)
		tmp = t_3;
	elseif (t_1 <= 1e-68)
		tmp = t_2;
	elseif (t_1 <= 5e+94)
		tmp = t_3;
	else
		tmp = Float64(Float64(t * Float64(Float64(x * y) * Float64(18.0 * z))) - 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) + (((t * a) + (x * i)) * -4.0);
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t_1 <= -1e+217)
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	elseif (t_1 <= -8e+63)
		tmp = t_2;
	elseif (t_1 <= -2e+25)
		tmp = (b * c) - t_1;
	elseif (t_1 <= -5e-18)
		tmp = t_3;
	elseif (t_1 <= 1e-68)
		tmp = t_2;
	elseif (t_1 <= 5e+94)
		tmp = t_3;
	else
		tmp = (t * ((x * y) * (18.0 * z))) - 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[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+217], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -8e+63], t$95$2, If[LessEqual[t$95$1, -2e+25], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -5e-18], t$95$3, If[LessEqual[t$95$1, 1e-68], t$95$2, If[LessEqual[t$95$1, 5e+94], t$95$3, N[(N[(t * N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.9999999999999996e216

   1. Initial program 92.7%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in t around 0 93.0%

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

      1. associate-*r* 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-*r* 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-*r* 92.9%

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

      6. fma-udef 92.9%

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

      7. associate-*r* 93.0%

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

      8. *-commutative 93.0%

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

      9. associate-*r* 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in b around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-*r* 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*r* 92.9%

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

      5. distribute-neg-in 92.9%

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

      6. distribute-lft-neg-in 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-rgt-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. distribute-rgt-neg-in 92.9%

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

      11. metadata-eval 92.9%

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

   9. Simplified 92.9%

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

   if -9.9999999999999996e216 < (*.f64 (*.f64 j 27) k) < -8.00000000000000046e63 or -5.00000000000000036e-18 < (*.f64 (*.f64 j 27) k) < 1.00000000000000007e-68

   1. Initial program 89.9%

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

   2. Taylor expanded in y around 0 78.4%

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

      1. fma-neg 78.5%

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

      2. distribute-lft-out 78.5%

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

      3. distribute-lft-neg-in 78.5%

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

      4. metadata-eval 78.5%

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

      5. *-commutative 78.5%

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

      6. fma-def 79.3%

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

      7. *-commutative 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in j around 0 76.0%

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

   if -8.00000000000000046e63 < (*.f64 (*.f64 j 27) k) < -2.00000000000000018e25

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in b around inf 69.3%

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

   if -2.00000000000000018e25 < (*.f64 (*.f64 j 27) k) < -5.00000000000000036e-18 or 1.00000000000000007e-68 < (*.f64 (*.f64 j 27) k) < 5.0000000000000001e94

   1. Initial program 80.9%

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

   2. Taylor expanded in x around 0 78.8%

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

   3. Taylor expanded in t around inf 71.3%

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

   4. Taylor expanded in t around inf 69.2%

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

   if 5.0000000000000001e94 < (*.f64 (*.f64 j 27) k)

   1. Initial program 78.3%

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

   2. Taylor expanded in x around 0 76.5%

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

   3. Taylor expanded in t around inf 77.8%

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

   4. Taylor expanded in x around inf 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*l* 75.9%

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

      3. associate-*r* 77.7%

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

      4. associate-*l* 75.7%

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

   6. Simplified 75.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+217}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -8 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-68}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 4: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-86}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right)\right) - t_1\\ \end{array} \end{array} \]

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 (<= t_1 -2e+20)
     (- (- (* b c) (* 4.0 (* x i))) t_1)
     (if (<= t_1 -5e-18)
       (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
       (if (<= t_1 5e-86)
         (+ (* b c) (* (+ (* t a) (* x i)) -4.0))
         (if (<= t_1 5e-18)
           (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
           (if (<= t_1 2e+102)
             (- (- (* b c) (* 4.0 (* t a))) t_1)
             (- (* t (* (* x y) (* 18.0 z))) 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 <= -2e+20) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t_1 <= -5e-18) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t_1 <= 5e-86) {
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0);
	} else if (t_1 <= 5e-18) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = (t * ((x * y) * (18.0 * z))) - 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 <= (-2d+20)) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (t_1 <= (-5d-18)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t_1 <= 5d-86) then
        tmp = (b * c) + (((t * a) + (x * i)) * (-4.0d0))
    else if (t_1 <= 5d-18) then
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    else if (t_1 <= 2d+102) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else
        tmp = (t * ((x * y) * (18.0d0 * z))) - 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 <= -2e+20) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t_1 <= -5e-18) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t_1 <= 5e-86) {
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0);
	} else if (t_1 <= 5e-18) {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = (t * ((x * y) * (18.0 * z))) - 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 <= -2e+20:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif t_1 <= -5e-18:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t_1 <= 5e-86:
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0)
	elif t_1 <= 5e-18:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	elif t_1 <= 2e+102:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	else:
		tmp = (t * ((x * y) * (18.0 * z))) - 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 <= -2e+20)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (t_1 <= -5e-18)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t_1 <= 5e-86)
		tmp = Float64(Float64(b * c) + Float64(Float64(Float64(t * a) + Float64(x * i)) * -4.0));
	elseif (t_1 <= 5e-18)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	elseif (t_1 <= 2e+102)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(Float64(t * Float64(Float64(x * y) * Float64(18.0 * z))) - 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 <= -2e+20)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (t_1 <= -5e-18)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t_1 <= 5e-86)
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0);
	elseif (t_1 <= 5e-18)
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	elseif (t_1 <= 2e+102)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	else
		tmp = (t * ((x * y) * (18.0 * z))) - 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, -2e+20], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, -5e-18], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-86], N[(N[(b * c), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-18], 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, 2e+102], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t * N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 j 27) k) < -2e20

   1. Initial program 87.8%

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

   2. Taylor expanded in t around 0 83.0%

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

   if -2e20 < (*.f64 (*.f64 j 27) k) < -5.00000000000000036e-18

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 74.2%

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

   3. Taylor expanded in t around inf 90.8%

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

   4. Taylor expanded in t around inf 90.8%

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

   if -5.00000000000000036e-18 < (*.f64 (*.f64 j 27) k) < 4.9999999999999999e-86

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 80.9%

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

      1. fma-neg 80.9%

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

      2. distribute-lft-out 80.9%

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

      3. distribute-lft-neg-in 80.9%

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

      4. metadata-eval 80.9%

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

      5. *-commutative 80.9%

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

      6. fma-def 81.0%

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

      7. *-commutative 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in j around 0 78.9%

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

   if 4.9999999999999999e-86 < (*.f64 (*.f64 j 27) k) < 5.00000000000000036e-18

   1. Initial program 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in x around inf 74.7%

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

   if 5.00000000000000036e-18 < (*.f64 (*.f64 j 27) k) < 1.99999999999999995e102

   1. Initial program 79.5%

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

   2. Taylor expanded in x around 0 65.4%

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

   if 1.99999999999999995e102 < (*.f64 (*.f64 j 27) k)

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in t around inf 79.4%

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

   4. Taylor expanded in x around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*l* 77.4%

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

      3. associate-*r* 79.2%

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

      4. associate-*l* 77.2%

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

   6. Simplified 77.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{-86}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 5: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := \left(b \cdot c + \left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\right) - \left(t_1 + j \cdot \left(27 \cdot k\right)\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - t_3\\ \end{array} \end{array} \]

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 (* 4.0 i)))
        (t_2
         (- (+ (* b c) (* (* 18.0 (* y z)) (* x t))) (+ t_1 (* j (* 27.0 k)))))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -5e+33)
     t_2
     (if (<= t_3 2e+92)
       (- (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))) t_1)
       (if (<= t_3 2e+232)
         t_2
         (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) t_3))))))

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 * (4.0 * i);
	double t_2 = ((b * c) + ((18.0 * (y * z)) * (x * t))) - (t_1 + (j * (27.0 * k)));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -5e+33) {
		tmp = t_2;
	} else if (t_3 <= 2e+92) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	} else if (t_3 <= 2e+232) {
		tmp = t_2;
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x * (4.0d0 * i)
    t_2 = ((b * c) + ((18.0d0 * (y * z)) * (x * t))) - (t_1 + (j * (27.0d0 * k)))
    t_3 = (j * 27.0d0) * k
    if (t_3 <= (-5d+33)) then
        tmp = t_2
    else if (t_3 <= 2d+92) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - t_1
    else if (t_3 <= 2d+232) then
        tmp = t_2
    else
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - t_3
    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 * (4.0 * i);
	double t_2 = ((b * c) + ((18.0 * (y * z)) * (x * t))) - (t_1 + (j * (27.0 * k)));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -5e+33) {
		tmp = t_2;
	} else if (t_3 <= 2e+92) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	} else if (t_3 <= 2e+232) {
		tmp = t_2;
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_3;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (4.0 * i)
	t_2 = ((b * c) + ((18.0 * (y * z)) * (x * t))) - (t_1 + (j * (27.0 * k)))
	t_3 = (j * 27.0) * k
	tmp = 0
	if t_3 <= -5e+33:
		tmp = t_2
	elif t_3 <= 2e+92:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1
	elif t_3 <= 2e+232:
		tmp = t_2
	else:
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_3
	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(4.0 * i))
	t_2 = Float64(Float64(Float64(b * c) + Float64(Float64(18.0 * Float64(y * z)) * Float64(x * t))) - Float64(t_1 + Float64(j * Float64(27.0 * k))))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -5e+33)
		tmp = t_2;
	elseif (t_3 <= 2e+92)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - t_1);
	elseif (t_3 <= 2e+232)
		tmp = t_2;
	else
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - t_3);
	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 * (4.0 * i);
	t_2 = ((b * c) + ((18.0 * (y * z)) * (x * t))) - (t_1 + (j * (27.0 * k)));
	t_3 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_3 <= -5e+33)
		tmp = t_2;
	elseif (t_3 <= 2e+92)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	elseif (t_3 <= 2e+232)
		tmp = t_2;
	else
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_3;
	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[(4.0 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+33], t$95$2, If[LessEqual[t$95$3, 2e+92], 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] - t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e+232], t$95$2, N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.99999999999999973e33 or 2.0000000000000001e92 < (*.f64 (*.f64 j 27) k) < 2.00000000000000011e232

   1. Initial program 89.4%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*r* 87.2%

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

      3. associate-*l* 87.2%

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

      4. *-commutative 87.2%

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

      5. *-commutative 87.2%

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

   6. Simplified 87.2%

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

   if -4.99999999999999973e33 < (*.f64 (*.f64 j 27) k) < 2.0000000000000001e92

   1. Initial program 88.5%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 90.1%

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

      1. associate-*r* 90.1%

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

      2. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   if 2.00000000000000011e232 < (*.f64 (*.f64 j 27) k)

   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 70.1%

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

   3. Taylor expanded in t around inf 90.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c + \left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+232}:\\ \;\;\;\;\left(b \cdot c + \left(18 \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 6: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := b \cdot c - t_2\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-18}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (- (* b c) (* 4.0 (* t a))))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (* b c) t_2)))
   (if (<= t_2 -2e+25)
     t_3
     (if (<= t_2 -5e-18)
       (* 18.0 (* t (* x (* y z))))
       (if (<= t_2 -1e-44)
         t_1
         (if (<= t_2 2e-57)
           (- (* b c) (* x (* 4.0 i)))
           (if (<= t_2 2e+92) t_1 t_3)))))))

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 = (b * c) - (4.0 * (t * a));
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) - t_2;
	double tmp;
	if (t_2 <= -2e+25) {
		tmp = t_3;
	} else if (t_2 <= -5e-18) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t_2 <= -1e-44) {
		tmp = t_1;
	} else if (t_2 <= 2e-57) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t_2 <= 2e+92) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (t * a))
    t_2 = (j * 27.0d0) * k
    t_3 = (b * c) - t_2
    if (t_2 <= (-2d+25)) then
        tmp = t_3
    else if (t_2 <= (-5d-18)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t_2 <= (-1d-44)) then
        tmp = t_1
    else if (t_2 <= 2d-57) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t_2 <= 2d+92) then
        tmp = t_1
    else
        tmp = t_3
    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 = (b * c) - (4.0 * (t * a));
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) - t_2;
	double tmp;
	if (t_2 <= -2e+25) {
		tmp = t_3;
	} else if (t_2 <= -5e-18) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t_2 <= -1e-44) {
		tmp = t_1;
	} else if (t_2 <= 2e-57) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t_2 <= 2e+92) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	t_2 = (j * 27.0) * k
	t_3 = (b * c) - t_2
	tmp = 0
	if t_2 <= -2e+25:
		tmp = t_3
	elif t_2 <= -5e-18:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t_2 <= -1e-44:
		tmp = t_1
	elif t_2 <= 2e-57:
		tmp = (b * c) - (x * (4.0 * i))
	elif t_2 <= 2e+92:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(b * c) - t_2)
	tmp = 0.0
	if (t_2 <= -2e+25)
		tmp = t_3;
	elseif (t_2 <= -5e-18)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t_2 <= -1e-44)
		tmp = t_1;
	elseif (t_2 <= 2e-57)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t_2 <= 2e+92)
		tmp = t_1;
	else
		tmp = t_3;
	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 = (b * c) - (4.0 * (t * a));
	t_2 = (j * 27.0) * k;
	t_3 = (b * c) - t_2;
	tmp = 0.0;
	if (t_2 <= -2e+25)
		tmp = t_3;
	elseif (t_2 <= -5e-18)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t_2 <= -1e-44)
		tmp = t_1;
	elseif (t_2 <= 2e-57)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t_2 <= 2e+92)
		tmp = t_1;
	else
		tmp = t_3;
	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[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+25], t$95$3, If[LessEqual[t$95$2, -5e-18], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-44], t$95$1, If[LessEqual[t$95$2, 2e-57], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+92], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -2.00000000000000018e25 or 2.0000000000000001e92 < (*.f64 (*.f64 j 27) k)

   1. Initial program 83.3%

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

   2. Taylor expanded in x around 0 81.7%

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

   3. Taylor expanded in b around inf 69.5%

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

   if -2.00000000000000018e25 < (*.f64 (*.f64 j 27) k) < -5.00000000000000036e-18

   1. Initial program 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 54.7%

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

   5. Taylor expanded in t around inf 64.0%

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

   if -5.00000000000000036e-18 < (*.f64 (*.f64 j 27) k) < -9.99999999999999953e-45 or 1.99999999999999991e-57 < (*.f64 (*.f64 j 27) k) < 2.0000000000000001e92

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0 83.6%

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

   3. Taylor expanded in j around 0 80.6%

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

   4. Taylor expanded in b around inf 58.3%

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

   if -9.99999999999999953e-45 < (*.f64 (*.f64 j 27) k) < 1.99999999999999991e-57

   1. Initial program 91.2%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around 0 55.7%

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

      1. associate-*r* 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*r* 55.7%

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

      4. *-commutative 55.7%

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

      5. associate-*r* 55.7%

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

      6. fma-udef 55.7%

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

      7. associate-*r* 55.7%

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

      8. *-commutative 55.7%

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

      9. associate-*r* 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in x around inf 53.7%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

      3. *-commutative 53.7%

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

   9. Simplified 53.7%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+25}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-18}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{-44}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+92}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 7: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \cdot 27 \leq -1 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;j \cdot 27 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= (* j 27.0) -1e-91)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (if (<= (* j 27.0) 2e+76)
     (-
      (-
       (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
       (* 4.0 (* t a)))
      (* (* j 27.0) k))
     (* j (* k -27.0)))))

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 ((j * 27.0) <= -1e-91) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else if ((j * 27.0) <= 2e+76) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = j * (k * -27.0);
	}
	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 ((j * 27.0d0) <= (-1d-91)) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else if ((j * 27.0d0) <= 2d+76) then
        tmp = (((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else
        tmp = j * (k * (-27.0d0))
    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 ((j * 27.0) <= -1e-91) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else if ((j * 27.0) <= 2e+76) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (j * 27.0) <= -1e-91:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	elif (j * 27.0) <= 2e+76:
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k)
	else:
		tmp = j * (k * -27.0)
	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(j * 27.0) <= -1e-91)
		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))));
	elseif (Float64(j * 27.0) <= 2e+76)
		tmp = 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));
	else
		tmp = Float64(j * Float64(k * -27.0));
	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 ((j * 27.0) <= -1e-91)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	elseif ((j * 27.0) <= 2e+76)
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - ((j * 27.0) * k);
	else
		tmp = j * (k * -27.0);
	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[(j * 27.0), $MachinePrecision], -1e-91], 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], If[LessEqual[N[(j * 27.0), $MachinePrecision], 2e+76], 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], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 j 27) < -1.00000000000000002e-91

   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 89.3%

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

   if -1.00000000000000002e-91 < (*.f64 j 27) < 2.0000000000000001e76

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 91.1%

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

   if 2.0000000000000001e76 < (*.f64 j 27)

   1. Initial program 76.4%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in j around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. associate-*l* 47.1%

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

   6. Simplified 47.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot 27 \leq -1 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;j \cdot 27 \leq 2 \cdot 10^{+76}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 8: 79.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \end{array} \end{array} \]

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 (<= t_1 -5e+33)
     (- (- (* b c) (* 4.0 (* x i))) t_1)
     (if (<= t_1 2e+102)
       (-
        (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
        (* 4.0 (* t a)))
       (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) 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+33) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a));
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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+33)) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (t_1 <= 2d+102) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))
    else
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - 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+33) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a));
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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+33:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif t_1 <= 2e+102:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))
	else:
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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+33)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (t_1 <= 2e+102)
		tmp = 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)));
	else
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - 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+33)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (t_1 <= 2e+102)
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a));
	else
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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+33], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], 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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.99999999999999973e33

   1. Initial program 88.9%

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

   2. Taylor expanded in t around 0 82.1%

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

   if -4.99999999999999973e33 < (*.f64 (*.f64 j 27) k) < 1.99999999999999995e102

   1. Initial program 88.6%

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

   2. Taylor expanded in x around 0 91.0%

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

   3. Taylor expanded in j around 0 88.6%

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

   if 1.99999999999999995e102 < (*.f64 (*.f64 j 27) k)

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in t around inf 79.4%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 9: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+224}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \end{array} \end{array} \]

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 (<= t_1 -4e+224)
     (* j (* k -27.0))
     (if (<= t_1 2e+102)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (* x (* 4.0 i)))
       (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) 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 <= -4e+224) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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 <= (-4d+224)) then
        tmp = j * (k * (-27.0d0))
    else if (t_1 <= 2d+102) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - (x * (4.0d0 * i))
    else
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - 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 <= -4e+224) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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 <= -4e+224:
		tmp = j * (k * -27.0)
	elif t_1 <= 2e+102:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i))
	else:
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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 <= -4e+224)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t_1 <= 2e+102)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	else
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - 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 <= -4e+224)
		tmp = j * (k * -27.0);
	elseif (t_1 <= 2e+102)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	else
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - 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, -4e+224], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], 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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -3.99999999999999988e224

   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 92.4%

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

   4. Taylor expanded in j around inf 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l* 96.0%

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

   6. Simplified 96.0%

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

   if -3.99999999999999988e224 < (*.f64 (*.f64 j 27) k) < 1.99999999999999995e102

   1. Initial program 88.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 86.5%

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

      1. associate-*r* 86.5%

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

      2. *-commutative 86.5%

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

   6. Simplified 86.5%

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

   if 1.99999999999999995e102 < (*.f64 (*.f64 j 27) k)

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in t around inf 79.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+224}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 10: 78.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+224}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(--18\right)\right) - t \cdot \left(a \cdot 4\right)\right) - t_1\\ \end{array} \end{array} \]

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 (<= t_1 -4e+224)
     (* j (* k -27.0))
     (if (<= t_1 2e+102)
       (-
        (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
        (* x (* 4.0 i)))
       (- (- (* t (* (* z (* x y)) (- -18.0))) (* t (* a 4.0))) 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 <= -4e+224) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = ((t * ((z * (x * y)) * -(-18.0))) - (t * (a * 4.0))) - 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 <= (-4d+224)) then
        tmp = j * (k * (-27.0d0))
    else if (t_1 <= 2d+102) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - (x * (4.0d0 * i))
    else
        tmp = ((t * ((z * (x * y)) * -(-18.0d0))) - (t * (a * 4.0d0))) - 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 <= -4e+224) {
		tmp = j * (k * -27.0);
	} else if (t_1 <= 2e+102) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	} else {
		tmp = ((t * ((z * (x * y)) * -(-18.0))) - (t * (a * 4.0))) - 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 <= -4e+224:
		tmp = j * (k * -27.0)
	elif t_1 <= 2e+102:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i))
	else:
		tmp = ((t * ((z * (x * y)) * -(-18.0))) - (t * (a * 4.0))) - 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 <= -4e+224)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t_1 <= 2e+102)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(x * Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(t * Float64(Float64(z * Float64(x * y)) * Float64(-(-18.0)))) - Float64(t * Float64(a * 4.0))) - 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 <= -4e+224)
		tmp = j * (k * -27.0);
	elseif (t_1 <= 2e+102)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - (x * (4.0 * i));
	else
		tmp = ((t * ((z * (x * y)) * -(-18.0))) - (t * (a * 4.0))) - 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, -4e+224], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+102], 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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] * (--18.0)), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -3.99999999999999988e224

   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 92.4%

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

   4. Taylor expanded in j around inf 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l* 96.0%

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

   6. Simplified 96.0%

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

   if -3.99999999999999988e224 < (*.f64 (*.f64 j 27) k) < 1.99999999999999995e102

   1. Initial program 88.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 86.5%

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

      1. associate-*r* 86.5%

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

      2. *-commutative 86.5%

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

   6. Simplified 86.5%

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

   if 1.99999999999999995e102 < (*.f64 (*.f64 j 27) k)

   1. Initial program 77.9%

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

   2. Taylor expanded in t around -inf 79.4%

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

      1. associate-*r* 79.4%

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

      2. neg-mul-1 79.4%

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

      3. cancel-sign-sub-inv 79.4%

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

      4. *-commutative 79.4%

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

      5. metadata-eval 79.4%

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

   4. Simplified 79.4%

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

      1. distribute-rgt-in 79.4%

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

      2. associate-*r* 81.2%

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

   6. Applied egg-rr 81.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+224}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(z \cdot \left(x \cdot y\right)\right) \cdot \left(--18\right)\right) - t \cdot \left(a \cdot 4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 11: 86.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= (* (* j 27.0) k) 2e+295)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* j (* k -27.0))))

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 (((j * 27.0) * k) <= 2e+295) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = j * (k * -27.0);
	}
	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 (((j * 27.0d0) * k) <= 2d+295) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = j * (k * (-27.0d0))
    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 (((j * 27.0) * k) <= 2e+295) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((j * 27.0) * k) <= 2e+295:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = j * (k * -27.0)
	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(Float64(j * 27.0) * k) <= 2e+295)
		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(j * Float64(k * -27.0));
	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 (((j * 27.0) * k) <= 2e+295)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = j * (k * -27.0);
	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[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision], 2e+295], 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < 2e295

   1. Initial program 89.1%

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

   3. Simplified 91.0%

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

   if 2e295 < (*.f64 (*.f64 j 27) k)

   1. Initial program 62.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in j around inf 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*l* 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 12: 32.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ t_4 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;j \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-306}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (* 18.0 (* t (* x (* y z)))))
        (t_2 (* t (* a -4.0)))
        (t_3 (* j (* k -27.0)))
        (t_4 (* (* x i) -4.0)))
   (if (<= j -1.4e+55)
     t_3
     (if (<= j -1.4e+29)
       t_2
       (if (<= j -1.85e-31)
         (* b c)
         (if (<= j -8.2e-126)
           t_1
           (if (<= j -1.35e-182)
             t_4
             (if (<= j -5.8e-207)
               t_2
               (if (<= j -8e-243)
                 t_1
                 (if (<= j 4e-306) t_4 (if (<= j 1.4e+85) t_1 t_3)))))))))))

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 = 18.0 * (t * (x * (y * z)));
	double t_2 = t * (a * -4.0);
	double t_3 = j * (k * -27.0);
	double t_4 = (x * i) * -4.0;
	double tmp;
	if (j <= -1.4e+55) {
		tmp = t_3;
	} else if (j <= -1.4e+29) {
		tmp = t_2;
	} else if (j <= -1.85e-31) {
		tmp = b * c;
	} else if (j <= -8.2e-126) {
		tmp = t_1;
	} else if (j <= -1.35e-182) {
		tmp = t_4;
	} else if (j <= -5.8e-207) {
		tmp = t_2;
	} else if (j <= -8e-243) {
		tmp = t_1;
	} else if (j <= 4e-306) {
		tmp = t_4;
	} else if (j <= 1.4e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    t_2 = t * (a * (-4.0d0))
    t_3 = j * (k * (-27.0d0))
    t_4 = (x * i) * (-4.0d0)
    if (j <= (-1.4d+55)) then
        tmp = t_3
    else if (j <= (-1.4d+29)) then
        tmp = t_2
    else if (j <= (-1.85d-31)) then
        tmp = b * c
    else if (j <= (-8.2d-126)) then
        tmp = t_1
    else if (j <= (-1.35d-182)) then
        tmp = t_4
    else if (j <= (-5.8d-207)) then
        tmp = t_2
    else if (j <= (-8d-243)) then
        tmp = t_1
    else if (j <= 4d-306) then
        tmp = t_4
    else if (j <= 1.4d+85) then
        tmp = t_1
    else
        tmp = t_3
    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 = 18.0 * (t * (x * (y * z)));
	double t_2 = t * (a * -4.0);
	double t_3 = j * (k * -27.0);
	double t_4 = (x * i) * -4.0;
	double tmp;
	if (j <= -1.4e+55) {
		tmp = t_3;
	} else if (j <= -1.4e+29) {
		tmp = t_2;
	} else if (j <= -1.85e-31) {
		tmp = b * c;
	} else if (j <= -8.2e-126) {
		tmp = t_1;
	} else if (j <= -1.35e-182) {
		tmp = t_4;
	} else if (j <= -5.8e-207) {
		tmp = t_2;
	} else if (j <= -8e-243) {
		tmp = t_1;
	} else if (j <= 4e-306) {
		tmp = t_4;
	} else if (j <= 1.4e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	t_2 = t * (a * -4.0)
	t_3 = j * (k * -27.0)
	t_4 = (x * i) * -4.0
	tmp = 0
	if j <= -1.4e+55:
		tmp = t_3
	elif j <= -1.4e+29:
		tmp = t_2
	elif j <= -1.85e-31:
		tmp = b * c
	elif j <= -8.2e-126:
		tmp = t_1
	elif j <= -1.35e-182:
		tmp = t_4
	elif j <= -5.8e-207:
		tmp = t_2
	elif j <= -8e-243:
		tmp = t_1
	elif j <= 4e-306:
		tmp = t_4
	elif j <= 1.4e+85:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_2 = Float64(t * Float64(a * -4.0))
	t_3 = Float64(j * Float64(k * -27.0))
	t_4 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (j <= -1.4e+55)
		tmp = t_3;
	elseif (j <= -1.4e+29)
		tmp = t_2;
	elseif (j <= -1.85e-31)
		tmp = Float64(b * c);
	elseif (j <= -8.2e-126)
		tmp = t_1;
	elseif (j <= -1.35e-182)
		tmp = t_4;
	elseif (j <= -5.8e-207)
		tmp = t_2;
	elseif (j <= -8e-243)
		tmp = t_1;
	elseif (j <= 4e-306)
		tmp = t_4;
	elseif (j <= 1.4e+85)
		tmp = t_1;
	else
		tmp = t_3;
	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 = 18.0 * (t * (x * (y * z)));
	t_2 = t * (a * -4.0);
	t_3 = j * (k * -27.0);
	t_4 = (x * i) * -4.0;
	tmp = 0.0;
	if (j <= -1.4e+55)
		tmp = t_3;
	elseif (j <= -1.4e+29)
		tmp = t_2;
	elseif (j <= -1.85e-31)
		tmp = b * c;
	elseif (j <= -8.2e-126)
		tmp = t_1;
	elseif (j <= -1.35e-182)
		tmp = t_4;
	elseif (j <= -5.8e-207)
		tmp = t_2;
	elseif (j <= -8e-243)
		tmp = t_1;
	elseif (j <= 4e-306)
		tmp = t_4;
	elseif (j <= 1.4e+85)
		tmp = t_1;
	else
		tmp = t_3;
	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[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[j, -1.4e+55], t$95$3, If[LessEqual[j, -1.4e+29], t$95$2, If[LessEqual[j, -1.85e-31], N[(b * c), $MachinePrecision], If[LessEqual[j, -8.2e-126], t$95$1, If[LessEqual[j, -1.35e-182], t$95$4, If[LessEqual[j, -5.8e-207], t$95$2, If[LessEqual[j, -8e-243], t$95$1, If[LessEqual[j, 4e-306], t$95$4, If[LessEqual[j, 1.4e+85], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.4e55 or 1.4e85 < j

   1. Initial program 84.1%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in j around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l* 51.6%

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

   6. Simplified 51.6%

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

   if -1.4e55 < j < -1.4e29 or -1.35e-182 < j < -5.80000000000000022e-207

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. fma-neg 90.3%

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

      2. distribute-lft-out 90.3%

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

      3. distribute-lft-neg-in 90.3%

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

      4. metadata-eval 90.3%

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

      5. *-commutative 90.3%

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

      6. fma-def 90.4%

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

      7. *-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. associate-*r* 56.9%

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

   7. Simplified 56.9%

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

   if -1.4e29 < j < -1.8499999999999999e-31

   1. Initial program 84.0%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in b around inf 26.9%

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

   if -1.8499999999999999e-31 < j < -8.1999999999999995e-126 or -5.80000000000000022e-207 < j < -7.99999999999999996e-243 or 4.00000000000000011e-306 < j < 1.4e85

   1. Initial program 88.1%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in x around inf 52.4%

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

   5. Taylor expanded in t around inf 37.3%

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

   if -8.1999999999999995e-126 < j < -1.35e-182 or -7.99999999999999996e-243 < j < 4.00000000000000011e-306

   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 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 i around inf 53.5%

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

      1. *-commutative 53.5%

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

   6. Simplified 53.5%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-126}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-182}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-243}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-306}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 13: 32.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ t_4 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-243}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-307}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (* 18.0 (* (* y z) (* x t))))
        (t_2 (* t (* a -4.0)))
        (t_3 (* j (* k -27.0)))
        (t_4 (* (* x i) -4.0)))
   (if (<= j -4.2e+50)
     t_3
     (if (<= j -3e+29)
       t_2
       (if (<= j -2.9e-31)
         (* b c)
         (if (<= j -9e-126)
           t_1
           (if (<= j -6.6e-183)
             t_4
             (if (<= j -6e-207)
               t_2
               (if (<= j -5.2e-243)
                 (* 18.0 (* t (* x (* y z))))
                 (if (<= j 6.3e-307) t_4 (if (<= j 2e+80) t_1 t_3)))))))))))

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 = 18.0 * ((y * z) * (x * t));
	double t_2 = t * (a * -4.0);
	double t_3 = j * (k * -27.0);
	double t_4 = (x * i) * -4.0;
	double tmp;
	if (j <= -4.2e+50) {
		tmp = t_3;
	} else if (j <= -3e+29) {
		tmp = t_2;
	} else if (j <= -2.9e-31) {
		tmp = b * c;
	} else if (j <= -9e-126) {
		tmp = t_1;
	} else if (j <= -6.6e-183) {
		tmp = t_4;
	} else if (j <= -6e-207) {
		tmp = t_2;
	} else if (j <= -5.2e-243) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 6.3e-307) {
		tmp = t_4;
	} else if (j <= 2e+80) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 18.0d0 * ((y * z) * (x * t))
    t_2 = t * (a * (-4.0d0))
    t_3 = j * (k * (-27.0d0))
    t_4 = (x * i) * (-4.0d0)
    if (j <= (-4.2d+50)) then
        tmp = t_3
    else if (j <= (-3d+29)) then
        tmp = t_2
    else if (j <= (-2.9d-31)) then
        tmp = b * c
    else if (j <= (-9d-126)) then
        tmp = t_1
    else if (j <= (-6.6d-183)) then
        tmp = t_4
    else if (j <= (-6d-207)) then
        tmp = t_2
    else if (j <= (-5.2d-243)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (j <= 6.3d-307) then
        tmp = t_4
    else if (j <= 2d+80) then
        tmp = t_1
    else
        tmp = t_3
    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 = 18.0 * ((y * z) * (x * t));
	double t_2 = t * (a * -4.0);
	double t_3 = j * (k * -27.0);
	double t_4 = (x * i) * -4.0;
	double tmp;
	if (j <= -4.2e+50) {
		tmp = t_3;
	} else if (j <= -3e+29) {
		tmp = t_2;
	} else if (j <= -2.9e-31) {
		tmp = b * c;
	} else if (j <= -9e-126) {
		tmp = t_1;
	} else if (j <= -6.6e-183) {
		tmp = t_4;
	} else if (j <= -6e-207) {
		tmp = t_2;
	} else if (j <= -5.2e-243) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 6.3e-307) {
		tmp = t_4;
	} else if (j <= 2e+80) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * ((y * z) * (x * t))
	t_2 = t * (a * -4.0)
	t_3 = j * (k * -27.0)
	t_4 = (x * i) * -4.0
	tmp = 0
	if j <= -4.2e+50:
		tmp = t_3
	elif j <= -3e+29:
		tmp = t_2
	elif j <= -2.9e-31:
		tmp = b * c
	elif j <= -9e-126:
		tmp = t_1
	elif j <= -6.6e-183:
		tmp = t_4
	elif j <= -6e-207:
		tmp = t_2
	elif j <= -5.2e-243:
		tmp = 18.0 * (t * (x * (y * z)))
	elif j <= 6.3e-307:
		tmp = t_4
	elif j <= 2e+80:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))
	t_2 = Float64(t * Float64(a * -4.0))
	t_3 = Float64(j * Float64(k * -27.0))
	t_4 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (j <= -4.2e+50)
		tmp = t_3;
	elseif (j <= -3e+29)
		tmp = t_2;
	elseif (j <= -2.9e-31)
		tmp = Float64(b * c);
	elseif (j <= -9e-126)
		tmp = t_1;
	elseif (j <= -6.6e-183)
		tmp = t_4;
	elseif (j <= -6e-207)
		tmp = t_2;
	elseif (j <= -5.2e-243)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (j <= 6.3e-307)
		tmp = t_4;
	elseif (j <= 2e+80)
		tmp = t_1;
	else
		tmp = t_3;
	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 = 18.0 * ((y * z) * (x * t));
	t_2 = t * (a * -4.0);
	t_3 = j * (k * -27.0);
	t_4 = (x * i) * -4.0;
	tmp = 0.0;
	if (j <= -4.2e+50)
		tmp = t_3;
	elseif (j <= -3e+29)
		tmp = t_2;
	elseif (j <= -2.9e-31)
		tmp = b * c;
	elseif (j <= -9e-126)
		tmp = t_1;
	elseif (j <= -6.6e-183)
		tmp = t_4;
	elseif (j <= -6e-207)
		tmp = t_2;
	elseif (j <= -5.2e-243)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (j <= 6.3e-307)
		tmp = t_4;
	elseif (j <= 2e+80)
		tmp = t_1;
	else
		tmp = t_3;
	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[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[j, -4.2e+50], t$95$3, If[LessEqual[j, -3e+29], t$95$2, If[LessEqual[j, -2.9e-31], N[(b * c), $MachinePrecision], If[LessEqual[j, -9e-126], t$95$1, If[LessEqual[j, -6.6e-183], t$95$4, If[LessEqual[j, -6e-207], t$95$2, If[LessEqual[j, -5.2e-243], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.3e-307], t$95$4, If[LessEqual[j, 2e+80], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -4.1999999999999999e50 or 2e80 < j

   1. Initial program 84.1%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in j around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l* 51.6%

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

   6. Simplified 51.6%

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

   if -4.1999999999999999e50 < j < -2.9999999999999999e29 or -6.5999999999999999e-183 < j < -5.9999999999999999e-207

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. fma-neg 90.3%

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

      2. distribute-lft-out 90.3%

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

      3. distribute-lft-neg-in 90.3%

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

      4. metadata-eval 90.3%

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

      5. *-commutative 90.3%

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

      6. fma-def 90.4%

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

      7. *-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. associate-*r* 56.9%

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

   7. Simplified 56.9%

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

   if -2.9999999999999999e29 < j < -2.9000000000000001e-31

   1. Initial program 84.0%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in b around inf 26.9%

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

   if -2.9000000000000001e-31 < j < -9.0000000000000005e-126 or 6.3000000000000003e-307 < j < 2e80

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 91.1%

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

   3. Taylor expanded in t around inf 62.3%

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

   4. Taylor expanded in t around inf 52.7%

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

   5. Taylor expanded in x around inf 35.0%

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

      1. associate-*r* 36.8%

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

   7. Simplified 36.8%

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

   if -9.0000000000000005e-126 < j < -6.5999999999999999e-183 or -5.1999999999999995e-243 < j < 6.3000000000000003e-307

   1. Initial program 85.2%

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

   3. Simplified 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 i around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if -5.9999999999999999e-207 < j < -5.1999999999999995e-243

   1. Initial program 80.1%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around inf 71.0%

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

   5. Taylor expanded in t around inf 57.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-126}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-243}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{-307}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+80}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 14: 32.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.9 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-243}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-306}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+76}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0))) (t_2 (* j (* k -27.0))) (t_3 (* (* x i) -4.0)))
   (if (<= j -4.2e+50)
     t_2
     (if (<= j -1.45e+29)
       t_1
       (if (<= j -2.3e-31)
         (* b c)
         (if (<= j -7.5e-126)
           (* t (* 18.0 (* y (* x z))))
           (if (<= j -3.1e-183)
             t_3
             (if (<= j -4.9e-207)
               t_1
               (if (<= j -5.5e-243)
                 (* 18.0 (* t (* x (* y z))))
                 (if (<= j 3.2e-306)
                   t_3
                   (if (<= j 5.8e+76)
                     (* 18.0 (* (* y z) (* x t)))
                     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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double t_3 = (x * i) * -4.0;
	double tmp;
	if (j <= -4.2e+50) {
		tmp = t_2;
	} else if (j <= -1.45e+29) {
		tmp = t_1;
	} else if (j <= -2.3e-31) {
		tmp = b * c;
	} else if (j <= -7.5e-126) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= -3.1e-183) {
		tmp = t_3;
	} else if (j <= -4.9e-207) {
		tmp = t_1;
	} else if (j <= -5.5e-243) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 3.2e-306) {
		tmp = t_3;
	} else if (j <= 5.8e+76) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = (x * i) * (-4.0d0)
    if (j <= (-4.2d+50)) then
        tmp = t_2
    else if (j <= (-1.45d+29)) then
        tmp = t_1
    else if (j <= (-2.3d-31)) then
        tmp = b * c
    else if (j <= (-7.5d-126)) then
        tmp = t * (18.0d0 * (y * (x * z)))
    else if (j <= (-3.1d-183)) then
        tmp = t_3
    else if (j <= (-4.9d-207)) then
        tmp = t_1
    else if (j <= (-5.5d-243)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (j <= 3.2d-306) then
        tmp = t_3
    else if (j <= 5.8d+76) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double t_3 = (x * i) * -4.0;
	double tmp;
	if (j <= -4.2e+50) {
		tmp = t_2;
	} else if (j <= -1.45e+29) {
		tmp = t_1;
	} else if (j <= -2.3e-31) {
		tmp = b * c;
	} else if (j <= -7.5e-126) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= -3.1e-183) {
		tmp = t_3;
	} else if (j <= -4.9e-207) {
		tmp = t_1;
	} else if (j <= -5.5e-243) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 3.2e-306) {
		tmp = t_3;
	} else if (j <= 5.8e+76) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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 = t * (a * -4.0)
	t_2 = j * (k * -27.0)
	t_3 = (x * i) * -4.0
	tmp = 0
	if j <= -4.2e+50:
		tmp = t_2
	elif j <= -1.45e+29:
		tmp = t_1
	elif j <= -2.3e-31:
		tmp = b * c
	elif j <= -7.5e-126:
		tmp = t * (18.0 * (y * (x * z)))
	elif j <= -3.1e-183:
		tmp = t_3
	elif j <= -4.9e-207:
		tmp = t_1
	elif j <= -5.5e-243:
		tmp = 18.0 * (t * (x * (y * z)))
	elif j <= 3.2e-306:
		tmp = t_3
	elif j <= 5.8e+76:
		tmp = 18.0 * ((y * z) * (x * t))
	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(t * Float64(a * -4.0))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (j <= -4.2e+50)
		tmp = t_2;
	elseif (j <= -1.45e+29)
		tmp = t_1;
	elseif (j <= -2.3e-31)
		tmp = Float64(b * c);
	elseif (j <= -7.5e-126)
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	elseif (j <= -3.1e-183)
		tmp = t_3;
	elseif (j <= -4.9e-207)
		tmp = t_1;
	elseif (j <= -5.5e-243)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (j <= 3.2e-306)
		tmp = t_3;
	elseif (j <= 5.8e+76)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	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 = t * (a * -4.0);
	t_2 = j * (k * -27.0);
	t_3 = (x * i) * -4.0;
	tmp = 0.0;
	if (j <= -4.2e+50)
		tmp = t_2;
	elseif (j <= -1.45e+29)
		tmp = t_1;
	elseif (j <= -2.3e-31)
		tmp = b * c;
	elseif (j <= -7.5e-126)
		tmp = t * (18.0 * (y * (x * z)));
	elseif (j <= -3.1e-183)
		tmp = t_3;
	elseif (j <= -4.9e-207)
		tmp = t_1;
	elseif (j <= -5.5e-243)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (j <= 3.2e-306)
		tmp = t_3;
	elseif (j <= 5.8e+76)
		tmp = 18.0 * ((y * z) * (x * t));
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[j, -4.2e+50], t$95$2, If[LessEqual[j, -1.45e+29], t$95$1, If[LessEqual[j, -2.3e-31], N[(b * c), $MachinePrecision], If[LessEqual[j, -7.5e-126], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.1e-183], t$95$3, If[LessEqual[j, -4.9e-207], t$95$1, If[LessEqual[j, -5.5e-243], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-306], t$95$3, If[LessEqual[j, 5.8e+76], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -4.1999999999999999e50 or 5.8000000000000003e76 < j

   1. Initial program 84.1%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in j around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l* 51.6%

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

   6. Simplified 51.6%

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

   if -4.1999999999999999e50 < j < -1.45e29 or -3.1e-183 < j < -4.9e-207

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. fma-neg 90.3%

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

      2. distribute-lft-out 90.3%

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

      3. distribute-lft-neg-in 90.3%

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

      4. metadata-eval 90.3%

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

      5. *-commutative 90.3%

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

      6. fma-def 90.4%

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

      7. *-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. associate-*r* 56.9%

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

   7. Simplified 56.9%

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

   if -1.45e29 < j < -2.2999999999999998e-31

   1. Initial program 84.0%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in b around inf 26.9%

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

   if -2.2999999999999998e-31 < j < -7.49999999999999976e-126

   1. Initial program 93.2%

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

   2. Taylor expanded in x around 0 74.1%

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

   3. Taylor expanded in t around inf 60.6%

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

   4. Taylor expanded in t around inf 54.6%

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

   5. Taylor expanded in x around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. associate-*l* 34.6%

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

   7. Simplified 34.6%

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

   if -7.49999999999999976e-126 < j < -3.1e-183 or -5.50000000000000004e-243 < j < 3.19999999999999971e-306

   1. Initial program 85.2%

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

   3. Simplified 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 i around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if -4.9e-207 < j < -5.50000000000000004e-243

   1. Initial program 80.1%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around inf 71.0%

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

   5. Taylor expanded in t around inf 57.6%

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

   if 3.19999999999999971e-306 < j < 5.8000000000000003e76

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 94.1%

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

   3. Taylor expanded in t around inf 62.5%

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

   4. Taylor expanded in t around inf 52.4%

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

   5. Taylor expanded in x around inf 35.0%

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

      1. associate-*r* 37.2%

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

   7. Simplified 37.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-183}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq -4.9 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-243}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-306}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+76}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 15: 32.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0))) (t_2 (* j (* k -27.0))) (t_3 (* (* x i) -4.0)))
   (if (<= j -1.8e+55)
     t_2
     (if (<= j -3e+29)
       t_1
       (if (<= j -2.5e-31)
         (* b c)
         (if (<= j -8.2e-126)
           (* t (* 18.0 (* y (* x z))))
           (if (<= j -2.3e-183)
             t_3
             (if (<= j -2.9e-207)
               t_1
               (if (<= j -5.2e-243)
                 (* (* x (* y z)) (* 18.0 t))
                 (if (<= j 6.2e-307)
                   t_3
                   (if (<= j 1.45e+77)
                     (* 18.0 (* (* y z) (* x t)))
                     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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double t_3 = (x * i) * -4.0;
	double tmp;
	if (j <= -1.8e+55) {
		tmp = t_2;
	} else if (j <= -3e+29) {
		tmp = t_1;
	} else if (j <= -2.5e-31) {
		tmp = b * c;
	} else if (j <= -8.2e-126) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= -2.3e-183) {
		tmp = t_3;
	} else if (j <= -2.9e-207) {
		tmp = t_1;
	} else if (j <= -5.2e-243) {
		tmp = (x * (y * z)) * (18.0 * t);
	} else if (j <= 6.2e-307) {
		tmp = t_3;
	} else if (j <= 1.45e+77) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = (x * i) * (-4.0d0)
    if (j <= (-1.8d+55)) then
        tmp = t_2
    else if (j <= (-3d+29)) then
        tmp = t_1
    else if (j <= (-2.5d-31)) then
        tmp = b * c
    else if (j <= (-8.2d-126)) then
        tmp = t * (18.0d0 * (y * (x * z)))
    else if (j <= (-2.3d-183)) then
        tmp = t_3
    else if (j <= (-2.9d-207)) then
        tmp = t_1
    else if (j <= (-5.2d-243)) then
        tmp = (x * (y * z)) * (18.0d0 * t)
    else if (j <= 6.2d-307) then
        tmp = t_3
    else if (j <= 1.45d+77) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double t_3 = (x * i) * -4.0;
	double tmp;
	if (j <= -1.8e+55) {
		tmp = t_2;
	} else if (j <= -3e+29) {
		tmp = t_1;
	} else if (j <= -2.5e-31) {
		tmp = b * c;
	} else if (j <= -8.2e-126) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= -2.3e-183) {
		tmp = t_3;
	} else if (j <= -2.9e-207) {
		tmp = t_1;
	} else if (j <= -5.2e-243) {
		tmp = (x * (y * z)) * (18.0 * t);
	} else if (j <= 6.2e-307) {
		tmp = t_3;
	} else if (j <= 1.45e+77) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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 = t * (a * -4.0)
	t_2 = j * (k * -27.0)
	t_3 = (x * i) * -4.0
	tmp = 0
	if j <= -1.8e+55:
		tmp = t_2
	elif j <= -3e+29:
		tmp = t_1
	elif j <= -2.5e-31:
		tmp = b * c
	elif j <= -8.2e-126:
		tmp = t * (18.0 * (y * (x * z)))
	elif j <= -2.3e-183:
		tmp = t_3
	elif j <= -2.9e-207:
		tmp = t_1
	elif j <= -5.2e-243:
		tmp = (x * (y * z)) * (18.0 * t)
	elif j <= 6.2e-307:
		tmp = t_3
	elif j <= 1.45e+77:
		tmp = 18.0 * ((y * z) * (x * t))
	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(t * Float64(a * -4.0))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (j <= -1.8e+55)
		tmp = t_2;
	elseif (j <= -3e+29)
		tmp = t_1;
	elseif (j <= -2.5e-31)
		tmp = Float64(b * c);
	elseif (j <= -8.2e-126)
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	elseif (j <= -2.3e-183)
		tmp = t_3;
	elseif (j <= -2.9e-207)
		tmp = t_1;
	elseif (j <= -5.2e-243)
		tmp = Float64(Float64(x * Float64(y * z)) * Float64(18.0 * t));
	elseif (j <= 6.2e-307)
		tmp = t_3;
	elseif (j <= 1.45e+77)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	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 = t * (a * -4.0);
	t_2 = j * (k * -27.0);
	t_3 = (x * i) * -4.0;
	tmp = 0.0;
	if (j <= -1.8e+55)
		tmp = t_2;
	elseif (j <= -3e+29)
		tmp = t_1;
	elseif (j <= -2.5e-31)
		tmp = b * c;
	elseif (j <= -8.2e-126)
		tmp = t * (18.0 * (y * (x * z)));
	elseif (j <= -2.3e-183)
		tmp = t_3;
	elseif (j <= -2.9e-207)
		tmp = t_1;
	elseif (j <= -5.2e-243)
		tmp = (x * (y * z)) * (18.0 * t);
	elseif (j <= 6.2e-307)
		tmp = t_3;
	elseif (j <= 1.45e+77)
		tmp = 18.0 * ((y * z) * (x * t));
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[j, -1.8e+55], t$95$2, If[LessEqual[j, -3e+29], t$95$1, If[LessEqual[j, -2.5e-31], N[(b * c), $MachinePrecision], If[LessEqual[j, -8.2e-126], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.3e-183], t$95$3, If[LessEqual[j, -2.9e-207], t$95$1, If[LessEqual[j, -5.2e-243], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-307], t$95$3, If[LessEqual[j, 1.45e+77], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.79999999999999994e55 or 1.4500000000000001e77 < j

   1. Initial program 84.1%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in j around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l* 51.6%

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

   6. Simplified 51.6%

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

   if -1.79999999999999994e55 < j < -2.9999999999999999e29 or -2.30000000000000016e-183 < j < -2.90000000000000011e-207

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. fma-neg 90.3%

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

      2. distribute-lft-out 90.3%

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

      3. distribute-lft-neg-in 90.3%

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

      4. metadata-eval 90.3%

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

      5. *-commutative 90.3%

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

      6. fma-def 90.4%

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

      7. *-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. associate-*r* 56.9%

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

   7. Simplified 56.9%

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

   if -2.9999999999999999e29 < j < -2.5e-31

   1. Initial program 84.0%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in b around inf 26.9%

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

   if -2.5e-31 < j < -8.1999999999999995e-126

   1. Initial program 93.2%

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

   2. Taylor expanded in x around 0 74.1%

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

   3. Taylor expanded in t around inf 60.6%

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

   4. Taylor expanded in t around inf 54.6%

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

   5. Taylor expanded in x around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. associate-*l* 34.6%

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

   7. Simplified 34.6%

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

   if -8.1999999999999995e-126 < j < -2.30000000000000016e-183 or -5.1999999999999995e-243 < j < 6.1999999999999996e-307

   1. Initial program 85.2%

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

   3. Simplified 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 i around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if -2.90000000000000011e-207 < j < -5.1999999999999995e-243

   1. Initial program 80.1%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around inf 71.0%

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

   5. Taylor expanded in t around inf 57.6%

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

      1. associate-*r* 57.8%

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

   7. Simplified 57.8%

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

   if 6.1999999999999996e-307 < j < 1.4500000000000001e77

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 94.1%

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

   3. Taylor expanded in t around inf 62.5%

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

   4. Taylor expanded in t around inf 52.4%

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

   5. Taylor expanded in x around inf 35.0%

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

      1. associate-*r* 37.2%

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

   7. Simplified 37.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-183}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-307}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 16: 32.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := \left(x \cdot i\right) \cdot -4\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.18 \cdot 10^{-306}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+79}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0))) (t_2 (* j (* k -27.0))) (t_3 (* (* x i) -4.0)))
   (if (<= j -7.5e+50)
     t_2
     (if (<= j -1.8e+29)
       t_1
       (if (<= j -2.7e-31)
         (* b c)
         (if (<= j -7.5e-126)
           (* t (* 18.0 (* y (* x z))))
           (if (<= j -3.8e-183)
             t_3
             (if (<= j -3.9e-207)
               t_1
               (if (<= j -6e-243)
                 (* (* x y) (* z (* 18.0 t)))
                 (if (<= j 1.18e-306)
                   t_3
                   (if (<= j 3.8e+79)
                     (* 18.0 (* (* y z) (* x t)))
                     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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double t_3 = (x * i) * -4.0;
	double tmp;
	if (j <= -7.5e+50) {
		tmp = t_2;
	} else if (j <= -1.8e+29) {
		tmp = t_1;
	} else if (j <= -2.7e-31) {
		tmp = b * c;
	} else if (j <= -7.5e-126) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= -3.8e-183) {
		tmp = t_3;
	} else if (j <= -3.9e-207) {
		tmp = t_1;
	} else if (j <= -6e-243) {
		tmp = (x * y) * (z * (18.0 * t));
	} else if (j <= 1.18e-306) {
		tmp = t_3;
	} else if (j <= 3.8e+79) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = j * (k * (-27.0d0))
    t_3 = (x * i) * (-4.0d0)
    if (j <= (-7.5d+50)) then
        tmp = t_2
    else if (j <= (-1.8d+29)) then
        tmp = t_1
    else if (j <= (-2.7d-31)) then
        tmp = b * c
    else if (j <= (-7.5d-126)) then
        tmp = t * (18.0d0 * (y * (x * z)))
    else if (j <= (-3.8d-183)) then
        tmp = t_3
    else if (j <= (-3.9d-207)) then
        tmp = t_1
    else if (j <= (-6d-243)) then
        tmp = (x * y) * (z * (18.0d0 * t))
    else if (j <= 1.18d-306) then
        tmp = t_3
    else if (j <= 3.8d+79) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double t_3 = (x * i) * -4.0;
	double tmp;
	if (j <= -7.5e+50) {
		tmp = t_2;
	} else if (j <= -1.8e+29) {
		tmp = t_1;
	} else if (j <= -2.7e-31) {
		tmp = b * c;
	} else if (j <= -7.5e-126) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= -3.8e-183) {
		tmp = t_3;
	} else if (j <= -3.9e-207) {
		tmp = t_1;
	} else if (j <= -6e-243) {
		tmp = (x * y) * (z * (18.0 * t));
	} else if (j <= 1.18e-306) {
		tmp = t_3;
	} else if (j <= 3.8e+79) {
		tmp = 18.0 * ((y * z) * (x * t));
	} 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 = t * (a * -4.0)
	t_2 = j * (k * -27.0)
	t_3 = (x * i) * -4.0
	tmp = 0
	if j <= -7.5e+50:
		tmp = t_2
	elif j <= -1.8e+29:
		tmp = t_1
	elif j <= -2.7e-31:
		tmp = b * c
	elif j <= -7.5e-126:
		tmp = t * (18.0 * (y * (x * z)))
	elif j <= -3.8e-183:
		tmp = t_3
	elif j <= -3.9e-207:
		tmp = t_1
	elif j <= -6e-243:
		tmp = (x * y) * (z * (18.0 * t))
	elif j <= 1.18e-306:
		tmp = t_3
	elif j <= 3.8e+79:
		tmp = 18.0 * ((y * z) * (x * t))
	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(t * Float64(a * -4.0))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(Float64(x * i) * -4.0)
	tmp = 0.0
	if (j <= -7.5e+50)
		tmp = t_2;
	elseif (j <= -1.8e+29)
		tmp = t_1;
	elseif (j <= -2.7e-31)
		tmp = Float64(b * c);
	elseif (j <= -7.5e-126)
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	elseif (j <= -3.8e-183)
		tmp = t_3;
	elseif (j <= -3.9e-207)
		tmp = t_1;
	elseif (j <= -6e-243)
		tmp = Float64(Float64(x * y) * Float64(z * Float64(18.0 * t)));
	elseif (j <= 1.18e-306)
		tmp = t_3;
	elseif (j <= 3.8e+79)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	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 = t * (a * -4.0);
	t_2 = j * (k * -27.0);
	t_3 = (x * i) * -4.0;
	tmp = 0.0;
	if (j <= -7.5e+50)
		tmp = t_2;
	elseif (j <= -1.8e+29)
		tmp = t_1;
	elseif (j <= -2.7e-31)
		tmp = b * c;
	elseif (j <= -7.5e-126)
		tmp = t * (18.0 * (y * (x * z)));
	elseif (j <= -3.8e-183)
		tmp = t_3;
	elseif (j <= -3.9e-207)
		tmp = t_1;
	elseif (j <= -6e-243)
		tmp = (x * y) * (z * (18.0 * t));
	elseif (j <= 1.18e-306)
		tmp = t_3;
	elseif (j <= 3.8e+79)
		tmp = 18.0 * ((y * z) * (x * t));
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[j, -7.5e+50], t$95$2, If[LessEqual[j, -1.8e+29], t$95$1, If[LessEqual[j, -2.7e-31], N[(b * c), $MachinePrecision], If[LessEqual[j, -7.5e-126], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.8e-183], t$95$3, If[LessEqual[j, -3.9e-207], t$95$1, If[LessEqual[j, -6e-243], N[(N[(x * y), $MachinePrecision] * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.18e-306], t$95$3, If[LessEqual[j, 3.8e+79], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -7.4999999999999999e50 or 3.8000000000000002e79 < j

   1. Initial program 84.1%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in j around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l* 51.6%

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

   6. Simplified 51.6%

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

   if -7.4999999999999999e50 < j < -1.79999999999999988e29 or -3.7999999999999996e-183 < j < -3.90000000000000021e-207

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. fma-neg 90.3%

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

      2. distribute-lft-out 90.3%

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

      3. distribute-lft-neg-in 90.3%

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

      4. metadata-eval 90.3%

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

      5. *-commutative 90.3%

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

      6. fma-def 90.4%

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

      7. *-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. associate-*r* 56.9%

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

   7. Simplified 56.9%

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

   if -1.79999999999999988e29 < j < -2.70000000000000014e-31

   1. Initial program 84.0%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in b around inf 26.9%

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

   if -2.70000000000000014e-31 < j < -7.49999999999999976e-126

   1. Initial program 93.2%

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

   2. Taylor expanded in x around 0 74.1%

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

   3. Taylor expanded in t around inf 60.6%

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

   4. Taylor expanded in t around inf 54.6%

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

   5. Taylor expanded in x around inf 34.6%

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

      1. *-commutative 34.6%

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

      2. associate-*l* 34.6%

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

   7. Simplified 34.6%

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

   if -7.49999999999999976e-126 < j < -3.7999999999999996e-183 or -6.0000000000000002e-243 < j < 1.17999999999999999e-306

   1. Initial program 85.2%

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

   3. Simplified 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 i around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if -3.90000000000000021e-207 < j < -6.0000000000000002e-243

   1. Initial program 80.1%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around inf 71.0%

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

   5. Taylor expanded in t around inf 57.6%

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

      1. associate-*r* 57.8%

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

      2. associate-*r* 57.6%

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

      3. *-commutative 57.6%

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

      4. associate-*l* 57.5%

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

   7. Simplified 57.5%

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

   if 1.17999999999999999e-306 < j < 3.8000000000000002e79

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 94.1%

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

   3. Taylor expanded in t around inf 62.5%

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

   4. Taylor expanded in t around inf 52.4%

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

   5. Taylor expanded in x around inf 35.0%

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

      1. associate-*r* 37.2%

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

   7. Simplified 37.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-31}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-183}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.18 \cdot 10^{-306}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+79}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 17: 43.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;j \leq -5.3 \cdot 10^{+131}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-158}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+78}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (- (* b c) (* x (* 4.0 i)))))
   (if (<= j -5.3e+131)
     (* -27.0 (* j k))
     (if (<= j -2.4e-55)
       t_1
       (if (<= j -1.15e-114)
         (* t (* 18.0 (* y (* x z))))
         (if (<= j 2.5e-208)
           t_1
           (if (<= j 2.15e-158)
             (* 18.0 (* (* y z) (* x t)))
             (if (<= j 3.6e-75)
               t_1
               (if (<= j 2.8e+78)
                 (* (* x y) (* z (* 18.0 t)))
                 (* j (* k -27.0)))))))))))

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 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (j <= -5.3e+131) {
		tmp = -27.0 * (j * k);
	} else if (j <= -2.4e-55) {
		tmp = t_1;
	} else if (j <= -1.15e-114) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= 2.5e-208) {
		tmp = t_1;
	} else if (j <= 2.15e-158) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 3.6e-75) {
		tmp = t_1;
	} else if (j <= 2.8e+78) {
		tmp = (x * y) * (z * (18.0 * t));
	} else {
		tmp = j * (k * -27.0);
	}
	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 = (b * c) - (x * (4.0d0 * i))
    if (j <= (-5.3d+131)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-2.4d-55)) then
        tmp = t_1
    else if (j <= (-1.15d-114)) then
        tmp = t * (18.0d0 * (y * (x * z)))
    else if (j <= 2.5d-208) then
        tmp = t_1
    else if (j <= 2.15d-158) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if (j <= 3.6d-75) then
        tmp = t_1
    else if (j <= 2.8d+78) then
        tmp = (x * y) * (z * (18.0d0 * t))
    else
        tmp = j * (k * (-27.0d0))
    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 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (j <= -5.3e+131) {
		tmp = -27.0 * (j * k);
	} else if (j <= -2.4e-55) {
		tmp = t_1;
	} else if (j <= -1.15e-114) {
		tmp = t * (18.0 * (y * (x * z)));
	} else if (j <= 2.5e-208) {
		tmp = t_1;
	} else if (j <= 2.15e-158) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 3.6e-75) {
		tmp = t_1;
	} else if (j <= 2.8e+78) {
		tmp = (x * y) * (z * (18.0 * t));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (x * (4.0 * i))
	tmp = 0
	if j <= -5.3e+131:
		tmp = -27.0 * (j * k)
	elif j <= -2.4e-55:
		tmp = t_1
	elif j <= -1.15e-114:
		tmp = t * (18.0 * (y * (x * z)))
	elif j <= 2.5e-208:
		tmp = t_1
	elif j <= 2.15e-158:
		tmp = 18.0 * ((y * z) * (x * t))
	elif j <= 3.6e-75:
		tmp = t_1
	elif j <= 2.8e+78:
		tmp = (x * y) * (z * (18.0 * t))
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (j <= -5.3e+131)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -2.4e-55)
		tmp = t_1;
	elseif (j <= -1.15e-114)
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	elseif (j <= 2.5e-208)
		tmp = t_1;
	elseif (j <= 2.15e-158)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (j <= 3.6e-75)
		tmp = t_1;
	elseif (j <= 2.8e+78)
		tmp = Float64(Float64(x * y) * Float64(z * Float64(18.0 * t)));
	else
		tmp = Float64(j * Float64(k * -27.0));
	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 = (b * c) - (x * (4.0 * i));
	tmp = 0.0;
	if (j <= -5.3e+131)
		tmp = -27.0 * (j * k);
	elseif (j <= -2.4e-55)
		tmp = t_1;
	elseif (j <= -1.15e-114)
		tmp = t * (18.0 * (y * (x * z)));
	elseif (j <= 2.5e-208)
		tmp = t_1;
	elseif (j <= 2.15e-158)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif (j <= 3.6e-75)
		tmp = t_1;
	elseif (j <= 2.8e+78)
		tmp = (x * y) * (z * (18.0 * t));
	else
		tmp = j * (k * -27.0);
	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[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.3e+131], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.4e-55], t$95$1, If[LessEqual[j, -1.15e-114], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-208], t$95$1, If[LessEqual[j, 2.15e-158], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e-75], t$95$1, If[LessEqual[j, 2.8e+78], N[(N[(x * y), $MachinePrecision] * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -5.2999999999999997e131

   1. Initial program 94.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in j around inf 61.6%

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

      1. *-commutative 61.6%

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

   6. Simplified 61.6%

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

   if -5.2999999999999997e131 < j < -2.39999999999999991e-55 or -1.15e-114 < j < 2.49999999999999981e-208 or 2.1499999999999998e-158 < j < 3.6e-75

   1. Initial program 87.0%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 57.3%

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

      1. associate-*r* 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-*r* 57.3%

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

      4. *-commutative 57.3%

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

      5. associate-*r* 56.4%

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

      6. fma-udef 56.4%

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

      7. associate-*r* 57.3%

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

      8. *-commutative 57.3%

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

      9. associate-*r* 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in x around inf 48.3%

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

      1. associate-*r* 48.3%

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

      2. *-commutative 48.3%

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

      3. *-commutative 48.3%

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

   9. Simplified 48.3%

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

   if -2.39999999999999991e-55 < j < -1.15e-114

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 75.6%

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

   3. Taylor expanded in t around inf 75.2%

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

   4. Taylor expanded in t around inf 63.5%

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

   5. Taylor expanded in x around inf 38.7%

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

      1. *-commutative 38.7%

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

      2. associate-*l* 38.7%

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

   7. Simplified 38.7%

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

   if 2.49999999999999981e-208 < j < 2.1499999999999998e-158

   1. Initial program 73.6%

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

   2. Taylor expanded in x around 0 93.2%

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

   3. Taylor expanded in t around inf 61.4%

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

   4. Taylor expanded in t around inf 48.9%

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

   5. Taylor expanded in x around inf 28.8%

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

      1. associate-*r* 34.9%

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

   7. Simplified 34.9%

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

   if 3.6e-75 < j < 2.8000000000000001e78

   1. Initial program 93.8%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around inf 44.9%

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

   5. Taylor expanded in t around inf 29.6%

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

      1. associate-*r* 29.6%

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

      2. associate-*r* 29.6%

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

      3. *-commutative 29.6%

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

      4. associate-*l* 32.5%

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

   7. Simplified 32.5%

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

   if 2.8000000000000001e78 < j

   1. Initial program 76.4%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in j around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. associate-*l* 47.1%

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

   6. Simplified 47.1%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.3 \cdot 10^{+131}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-55}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-158}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-75}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+78}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z \cdot \left(18 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 18: 72.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+187}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+78} \lor \neg \left(x \leq 2.5 \cdot 10^{+55}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))
   (if (<= x -3.6e+219)
     t_1
     (if (<= x -7e+187)
       (+ (* b c) (* (+ (* t a) (* x i)) -4.0))
       (if (or (<= x -1.9e+78) (not (<= x 2.5e+55)))
         t_1
         (- (- (* b c) (* 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) {
	double t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.6e+219) {
		tmp = t_1;
	} else if (x <= -7e+187) {
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0);
	} else if ((x <= -1.9e+78) || !(x <= 2.5e+55)) {
		tmp = t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((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) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    if (x <= (-3.6d+219)) then
        tmp = t_1
    else if (x <= (-7d+187)) then
        tmp = (b * c) + (((t * a) + (x * i)) * (-4.0d0))
    else if ((x <= (-1.9d+78)) .or. (.not. (x <= 2.5d+55))) then
        tmp = t_1
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((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 t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	double tmp;
	if (x <= -3.6e+219) {
		tmp = t_1;
	} else if (x <= -7e+187) {
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0);
	} else if ((x <= -1.9e+78) || !(x <= 2.5e+55)) {
		tmp = t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	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 x <= -3.6e+219:
		tmp = t_1
	elif x <= -7e+187:
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0)
	elif (x <= -1.9e+78) or not (x <= 2.5e+55):
		tmp = t_1
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	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 (x <= -3.6e+219)
		tmp = t_1;
	elseif (x <= -7e+187)
		tmp = Float64(Float64(b * c) + Float64(Float64(Float64(t * a) + Float64(x * i)) * -4.0));
	elseif ((x <= -1.9e+78) || !(x <= 2.5e+55))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - 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)
	t_1 = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -3.6e+219)
		tmp = t_1;
	elseif (x <= -7e+187)
		tmp = (b * c) + (((t * a) + (x * i)) * -4.0);
	elseif ((x <= -1.9e+78) || ~((x <= 2.5e+55)))
		tmp = t_1;
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((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_] := 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[x, -3.6e+219], t$95$1, If[LessEqual[x, -7e+187], N[(N[(b * c), $MachinePrecision] + N[(N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.9e+78], N[Not[LessEqual[x, 2.5e+55]], $MachinePrecision]], t$95$1, N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.60000000000000006e219 or -6.9999999999999995e187 < x < -1.9e78 or 2.50000000000000023e55 < x

   1. Initial program 77.5%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around inf 78.1%

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

   if -3.60000000000000006e219 < x < -6.9999999999999995e187

   1. Initial program 83.4%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. fma-neg 100.0%

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

      2. distribute-lft-out 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. *-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in j around 0 100.0%

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

   if -1.9e78 < x < 2.50000000000000023e55

   1. Initial program 91.7%

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

   2. Taylor expanded in x around 0 71.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+187}:\\ \;\;\;\;b \cdot c + \left(t \cdot a + x \cdot i\right) \cdot -4\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+78} \lor \neg \left(x \leq 2.5 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 19: 74.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-91} \lor \neg \left(t \leq 4.9 \cdot 10^{-59}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

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 (<= t -1.15e-91) (not (<= t 4.9e-59)))
     (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) t_1)
     (- (- (* b c) (* 4.0 (* x 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 ((t <= -1.15e-91) || !(t <= 4.9e-59)) {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.15d-91)) .or. (.not. (t <= 4.9d-59))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    end if
    code = tmp
end function

Java

assert 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 <= -1.15e-91) || !(t <= 4.9e-59)) {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (x * 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 (t <= -1.15e-91) or not (t <= 4.9e-59):
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (x * 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 ((t <= -1.15e-91) || !(t <= 4.9e-59))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * 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 ((t <= -1.15e-91) || ~((t <= 4.9e-59)))
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1;
	else
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: 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, -1.15e-91], N[Not[LessEqual[t, 4.9e-59]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.14999999999999998e-91 or 4.89999999999999977e-59 < t

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0 84.4%

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

   3. Taylor expanded in t around inf 77.3%

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

   if -1.14999999999999998e-91 < t < 4.89999999999999977e-59

   1. Initial program 88.6%

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

   2. Taylor expanded in t around 0 86.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-91} \lor \neg \left(t \leq 4.9 \cdot 10^{-59}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 20: 79.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -5 \cdot 10^{-38} \lor \neg \left(t \leq 1.95 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

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 (<= t -5e-38) (not (<= t 1.95e+34)))
     (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) t_1)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x 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 ((t <= -5e-38) || !(t <= 1.95e+34)) {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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 ((t <= (-5d-38)) .or. (.not. (t <= 1.95d+34))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * 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 ((t <= -5e-38) || !(t <= 1.95e+34)) {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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 (t <= -5e-38) or not (t <= 1.95e+34):
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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 ((t <= -5e-38) || !(t <= 1.95e+34))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * 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 ((t <= -5e-38) || ~((t <= 1.95e+34)))
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * 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[Or[LessEqual[t, -5e-38], N[Not[LessEqual[t, 1.95e+34]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], 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]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000033e-38 or 1.9500000000000001e34 < t

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0 81.8%

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

   3. Taylor expanded in t around inf 79.4%

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

   if -5.00000000000000033e-38 < t < 1.9500000000000001e34

   1. Initial program 87.9%

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

   2. Taylor expanded in y around 0 87.3%

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

      1. distribute-lft-out 87.3%

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

      2. *-commutative 87.3%

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

      3. *-commutative 87.3%

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

   4. Simplified 87.3%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-38} \lor \neg \left(t \leq 1.95 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 21: 76.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -750000000 \lor \neg \left(x \leq 2.7 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 -750000000.0) (not (<= x 2.7e+53)))
   (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
   (- (- (* b c) (* 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) {
	double tmp;
	if ((x <= -750000000.0) || !(x <= 2.7e+53)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((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 <= (-750000000.0d0)) .or. (.not. (x <= 2.7d+53))) then
        tmp = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((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 <= -750000000.0) || !(x <= 2.7e+53)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((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 <= -750000000.0) or not (x <= 2.7e+53):
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((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 <= -750000000.0) || !(x <= 2.7e+53))
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - 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 <= -750000000.0) || ~((x <= 2.7e+53)))
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((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, -750000000.0], N[Not[LessEqual[x, 2.7e+53]], $MachinePrecision]], 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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e8 or 2.70000000000000019e53 < x

   1. Initial program 80.4%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in j around 0 83.3%

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

   4. Taylor expanded in a around 0 81.1%

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

   if -7.5e8 < x < 2.70000000000000019e53

   1. Initial program 91.4%

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

   2. Taylor expanded in x around 0 74.1%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -750000000 \lor \neg \left(x \leq 2.7 \cdot 10^{+53}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 22: 59.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -3.3e-12)
     t_1
     (if (<= t 1.15e-210)
       (+ (* j (* k -27.0)) (* (* x i) -4.0))
       (if (<= t 1.15e+17) (- (* b c) (* (* j 27.0) 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -3.3e-12) {
		tmp = t_1;
	} else if (t <= 1.15e-210) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (t <= 1.15e+17) {
		tmp = (b * c) - ((j * 27.0) * 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 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-3.3d-12)) then
        tmp = t_1
    else if (t <= 1.15d-210) then
        tmp = (j * (k * (-27.0d0))) + ((x * i) * (-4.0d0))
    else if (t <= 1.15d+17) then
        tmp = (b * c) - ((j * 27.0d0) * 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -3.3e-12) {
		tmp = t_1;
	} else if (t <= 1.15e-210) {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	} else if (t <= 1.15e+17) {
		tmp = (b * c) - ((j * 27.0) * 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -3.3e-12:
		tmp = t_1
	elif t <= 1.15e-210:
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0)
	elif t <= 1.15e+17:
		tmp = (b * c) - ((j * 27.0) * 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(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -3.3e-12)
		tmp = t_1;
	elseif (t <= 1.15e-210)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(x * i) * -4.0));
	elseif (t <= 1.15e+17)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * 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 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -3.3e-12)
		tmp = t_1;
	elseif (t <= 1.15e-210)
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	elseif (t <= 1.15e+17)
		tmp = (b * c) - ((j * 27.0) * 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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-12], t$95$1, If[LessEqual[t, 1.15e-210], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+17], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3000000000000001e-12 or 1.15e17 < t

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 82.2%

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

   3. Taylor expanded in t around inf 78.8%

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

   4. Taylor expanded in t around inf 66.9%

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

   if -3.3000000000000001e-12 < t < 1.15e-210

   1. Initial program 84.4%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in t around 0 82.1%

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

      1. associate-*r* 82.1%

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

      2. *-commutative 82.1%

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

      3. associate-*r* 82.1%

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

      4. *-commutative 82.1%

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

      5. associate-*r* 82.1%

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

      6. fma-udef 84.6%

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

      7. associate-*r* 84.6%

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

      8. *-commutative 84.6%

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

      9. associate-*r* 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in b around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-*r* 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*r* 62.5%

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

      5. distribute-neg-in 62.5%

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

      6. distribute-lft-neg-in 62.5%

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

      7. metadata-eval 62.5%

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

      8. distribute-rgt-neg-in 62.5%

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

      9. *-commutative 62.5%

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

      10. distribute-rgt-neg-in 62.5%

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

      11. metadata-eval 62.5%

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

   9. Simplified 62.5%

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

   if 1.15e-210 < t < 1.15e17

   1. Initial program 94.1%

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

   2. Taylor expanded in x around 0 92.2%

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

   3. Taylor expanded in b around inf 68.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 23: 52.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.4 \cdot 10^{+135} \lor \neg \left(b \cdot c \leq 2.2 \cdot 10^{-65}\right):\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \end{array} \end{array} \]

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 (<= (* b c) -6.4e+135) (not (<= (* b c) 2.2e-65)))
   (- (* b c) (* (* j 27.0) k))
   (+ (* j (* k -27.0)) (* (* x i) -4.0))))

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) <= -6.4e+135) || !((b * c) <= 2.2e-65)) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	}
	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) <= (-6.4d+135)) .or. (.not. ((b * c) <= 2.2d-65))) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else
        tmp = (j * (k * (-27.0d0))) + ((x * i) * (-4.0d0))
    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) <= -6.4e+135) || !((b * c) <= 2.2e-65)) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	}
	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) <= -6.4e+135) or not ((b * c) <= 2.2e-65):
		tmp = (b * c) - ((j * 27.0) * k)
	else:
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0)
	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) <= -6.4e+135) || !(Float64(b * c) <= 2.2e-65))
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(Float64(x * i) * -4.0));
	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) <= -6.4e+135) || ~(((b * c) <= 2.2e-65)))
		tmp = (b * c) - ((j * 27.0) * k);
	else
		tmp = (j * (k * -27.0)) + ((x * i) * -4.0);
	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[N[(b * c), $MachinePrecision], -6.4e+135], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.2e-65]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -6.3999999999999995e135 or 2.20000000000000021e-65 < (*.f64 b c)

   1. Initial program 82.5%

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

   2. Taylor expanded in x around 0 86.7%

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

   3. Taylor expanded in b around inf 63.6%

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

   if -6.3999999999999995e135 < (*.f64 b c) < 2.20000000000000021e-65

   1. Initial program 89.1%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 59.0%

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

      1. associate-*r* 59.0%

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

      2. *-commutative 59.0%

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

      3. associate-*r* 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-*r* 58.3%

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

      6. fma-udef 59.0%

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

      7. associate-*r* 59.6%

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

      8. *-commutative 59.6%

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

      9. associate-*r* 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in b around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. associate-*r* 54.8%

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

      3. *-commutative 54.8%

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

      4. associate-*r* 54.2%

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

      5. distribute-neg-in 54.2%

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

      6. distribute-lft-neg-in 54.2%

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

      7. metadata-eval 54.2%

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

      8. distribute-rgt-neg-in 54.2%

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

      9. *-commutative 54.2%

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

      10. distribute-rgt-neg-in 54.2%

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

      11. metadata-eval 54.2%

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

   9. Simplified 54.2%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.4 \cdot 10^{+135} \lor \neg \left(b \cdot c \leq 2.2 \cdot 10^{-65}\right):\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + \left(x \cdot i\right) \cdot -4\\ \end{array} \]

Alternative 24: 31.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -4.7 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0))) (t_2 (* j (* k -27.0))))
   (if (<= j -4.7e+50)
     t_2
     (if (<= j -1.4e+29)
       t_1
       (if (<= j -1.85e-16)
         (* b c)
         (if (<= j -8e-126)
           t_1
           (if (<= j 2.4e-176)
             (* (* x i) -4.0)
             (if (<= j 2.2e+40) (* b c) 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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double tmp;
	if (j <= -4.7e+50) {
		tmp = t_2;
	} else if (j <= -1.4e+29) {
		tmp = t_1;
	} else if (j <= -1.85e-16) {
		tmp = b * c;
	} else if (j <= -8e-126) {
		tmp = t_1;
	} else if (j <= 2.4e-176) {
		tmp = (x * i) * -4.0;
	} else if (j <= 2.2e+40) {
		tmp = b * c;
	} 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 = t * (a * (-4.0d0))
    t_2 = j * (k * (-27.0d0))
    if (j <= (-4.7d+50)) then
        tmp = t_2
    else if (j <= (-1.4d+29)) then
        tmp = t_1
    else if (j <= (-1.85d-16)) then
        tmp = b * c
    else if (j <= (-8d-126)) then
        tmp = t_1
    else if (j <= 2.4d-176) then
        tmp = (x * i) * (-4.0d0)
    else if (j <= 2.2d+40) then
        tmp = b * c
    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 = t * (a * -4.0);
	double t_2 = j * (k * -27.0);
	double tmp;
	if (j <= -4.7e+50) {
		tmp = t_2;
	} else if (j <= -1.4e+29) {
		tmp = t_1;
	} else if (j <= -1.85e-16) {
		tmp = b * c;
	} else if (j <= -8e-126) {
		tmp = t_1;
	} else if (j <= 2.4e-176) {
		tmp = (x * i) * -4.0;
	} else if (j <= 2.2e+40) {
		tmp = b * c;
	} 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 = t * (a * -4.0)
	t_2 = j * (k * -27.0)
	tmp = 0
	if j <= -4.7e+50:
		tmp = t_2
	elif j <= -1.4e+29:
		tmp = t_1
	elif j <= -1.85e-16:
		tmp = b * c
	elif j <= -8e-126:
		tmp = t_1
	elif j <= 2.4e-176:
		tmp = (x * i) * -4.0
	elif j <= 2.2e+40:
		tmp = b * c
	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(t * Float64(a * -4.0))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (j <= -4.7e+50)
		tmp = t_2;
	elseif (j <= -1.4e+29)
		tmp = t_1;
	elseif (j <= -1.85e-16)
		tmp = Float64(b * c);
	elseif (j <= -8e-126)
		tmp = t_1;
	elseif (j <= 2.4e-176)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (j <= 2.2e+40)
		tmp = Float64(b * c);
	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 = t * (a * -4.0);
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if (j <= -4.7e+50)
		tmp = t_2;
	elseif (j <= -1.4e+29)
		tmp = t_1;
	elseif (j <= -1.85e-16)
		tmp = b * c;
	elseif (j <= -8e-126)
		tmp = t_1;
	elseif (j <= 2.4e-176)
		tmp = (x * i) * -4.0;
	elseif (j <= 2.2e+40)
		tmp = b * c;
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.7e+50], t$95$2, If[LessEqual[j, -1.4e+29], t$95$1, If[LessEqual[j, -1.85e-16], N[(b * c), $MachinePrecision], If[LessEqual[j, -8e-126], t$95$1, If[LessEqual[j, 2.4e-176], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[j, 2.2e+40], N[(b * c), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.69999999999999974e50 or 2.1999999999999999e40 < j

   1. Initial program 84.3%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in j around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-*l* 48.5%

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

   6. Simplified 48.5%

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

   if -4.69999999999999974e50 < j < -1.4e29 or -1.85e-16 < j < -7.9999999999999996e-126

   1. Initial program 95.6%

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

   2. Taylor expanded in y around 0 79.6%

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

      1. fma-neg 79.6%

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

      2. distribute-lft-out 79.6%

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

      3. distribute-lft-neg-in 79.6%

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

      4. metadata-eval 79.6%

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

      5. *-commutative 79.6%

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

      6. fma-def 79.7%

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

      7. *-commutative 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in t around inf 37.4%

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

      1. associate-*r* 37.4%

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

   7. Simplified 37.4%

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

   if -1.4e29 < j < -1.85e-16 or 2.40000000000000006e-176 < j < 2.1999999999999999e40

   1. Initial program 89.6%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in b around inf 26.6%

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

   if -7.9999999999999996e-126 < j < 2.40000000000000006e-176

   1. Initial program 84.5%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in i around inf 32.0%

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

      1. *-commutative 32.0%

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

   6. Simplified 32.0%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.7 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-16}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 25: 45.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+112}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-158}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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 (- (* b c) (* 4.0 (* t a)))))
   (if (<= j -1.8e+112)
     (* -27.0 (* j k))
     (if (<= j 3.25e-208)
       t_1
       (if (<= j 2.15e-158)
         (* 18.0 (* (* y z) (* x t)))
         (if (<= j 8.2e+42) t_1 (* j (* k -27.0))))))))

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 = (b * c) - (4.0 * (t * a));
	double tmp;
	if (j <= -1.8e+112) {
		tmp = -27.0 * (j * k);
	} else if (j <= 3.25e-208) {
		tmp = t_1;
	} else if (j <= 2.15e-158) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 8.2e+42) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	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 = (b * c) - (4.0d0 * (t * a))
    if (j <= (-1.8d+112)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= 3.25d-208) then
        tmp = t_1
    else if (j <= 2.15d-158) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if (j <= 8.2d+42) then
        tmp = t_1
    else
        tmp = j * (k * (-27.0d0))
    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 = (b * c) - (4.0 * (t * a));
	double tmp;
	if (j <= -1.8e+112) {
		tmp = -27.0 * (j * k);
	} else if (j <= 3.25e-208) {
		tmp = t_1;
	} else if (j <= 2.15e-158) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (j <= 8.2e+42) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (t * a))
	tmp = 0
	if j <= -1.8e+112:
		tmp = -27.0 * (j * k)
	elif j <= 3.25e-208:
		tmp = t_1
	elif j <= 2.15e-158:
		tmp = 18.0 * ((y * z) * (x * t))
	elif j <= 8.2e+42:
		tmp = t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(t * a)))
	tmp = 0.0
	if (j <= -1.8e+112)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= 3.25e-208)
		tmp = t_1;
	elseif (j <= 2.15e-158)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (j <= 8.2e+42)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(k * -27.0));
	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 = (b * c) - (4.0 * (t * a));
	tmp = 0.0;
	if (j <= -1.8e+112)
		tmp = -27.0 * (j * k);
	elseif (j <= 3.25e-208)
		tmp = t_1;
	elseif (j <= 2.15e-158)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif (j <= 8.2e+42)
		tmp = t_1;
	else
		tmp = j * (k * -27.0);
	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[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+112], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.25e-208], t$95$1, If[LessEqual[j, 2.15e-158], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+42], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.8e112

   1. Initial program 92.7%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in j around inf 56.7%

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

      1. *-commutative 56.7%

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

   6. Simplified 56.7%

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

   if -1.8e112 < j < 3.2499999999999999e-208 or 2.1499999999999998e-158 < j < 8.2000000000000001e42

   1. Initial program 89.8%

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

   2. Taylor expanded in x around 0 89.2%

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

   3. Taylor expanded in j around 0 79.3%

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

   4. Taylor expanded in b around inf 40.6%

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

   if 3.2499999999999999e-208 < j < 2.1499999999999998e-158

   1. Initial program 73.6%

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

   2. Taylor expanded in x around 0 93.2%

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

   3. Taylor expanded in t around inf 61.4%

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

   4. Taylor expanded in t around inf 48.9%

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

   5. Taylor expanded in x around inf 28.8%

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

      1. associate-*r* 34.9%

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

   7. Simplified 34.9%

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

   if 8.2000000000000001e42 < j

   1. Initial program 77.6%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in j around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-*l* 41.6%

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

   6. Simplified 41.6%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+112}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{-208}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-158}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 26: 31.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-14}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* j (* k -27.0))))
   (if (<= j -9.2e+51)
     t_1
     (if (<= j -1.16e-14)
       (* b c)
       (if (<= j 1.5e-176)
         (* (* x i) -4.0)
         (if (<= j 4.8e+50) (* 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 * (k * -27.0);
	double tmp;
	if (j <= -9.2e+51) {
		tmp = t_1;
	} else if (j <= -1.16e-14) {
		tmp = b * c;
	} else if (j <= 1.5e-176) {
		tmp = (x * i) * -4.0;
	} else if (j <= 4.8e+50) {
		tmp = b * c;
	} 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 = j * (k * (-27.0d0))
    if (j <= (-9.2d+51)) then
        tmp = t_1
    else if (j <= (-1.16d-14)) then
        tmp = b * c
    else if (j <= 1.5d-176) then
        tmp = (x * i) * (-4.0d0)
    else if (j <= 4.8d+50) then
        tmp = b * c
    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 = j * (k * -27.0);
	double tmp;
	if (j <= -9.2e+51) {
		tmp = t_1;
	} else if (j <= -1.16e-14) {
		tmp = b * c;
	} else if (j <= 1.5e-176) {
		tmp = (x * i) * -4.0;
	} else if (j <= 4.8e+50) {
		tmp = b * c;
	} 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 = j * (k * -27.0)
	tmp = 0
	if j <= -9.2e+51:
		tmp = t_1
	elif j <= -1.16e-14:
		tmp = b * c
	elif j <= 1.5e-176:
		tmp = (x * i) * -4.0
	elif j <= 4.8e+50:
		tmp = b * c
	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(j * Float64(k * -27.0))
	tmp = 0.0
	if (j <= -9.2e+51)
		tmp = t_1;
	elseif (j <= -1.16e-14)
		tmp = Float64(b * c);
	elseif (j <= 1.5e-176)
		tmp = Float64(Float64(x * i) * -4.0);
	elseif (j <= 4.8e+50)
		tmp = Float64(b * c);
	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 = j * (k * -27.0);
	tmp = 0.0;
	if (j <= -9.2e+51)
		tmp = t_1;
	elseif (j <= -1.16e-14)
		tmp = b * c;
	elseif (j <= 1.5e-176)
		tmp = (x * i) * -4.0;
	elseif (j <= 4.8e+50)
		tmp = b * c;
	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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.2e+51], t$95$1, If[LessEqual[j, -1.16e-14], N[(b * c), $MachinePrecision], If[LessEqual[j, 1.5e-176], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[j, 4.8e+50], N[(b * c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.2000000000000002e51 or 4.8000000000000004e50 < j

   1. Initial program 84.1%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in j around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-*l* 48.9%

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

   6. Simplified 48.9%

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

   if -9.2000000000000002e51 < j < -1.16000000000000007e-14 or 1.5e-176 < j < 4.8000000000000004e50

   1. Initial program 90.5%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in b around inf 24.3%

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

   if -1.16000000000000007e-14 < j < 1.5e-176

   1. Initial program 86.9%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in i around inf 32.3%

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

      1. *-commutative 32.3%

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

   6. Simplified 32.3%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-14}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-176}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 27: 34.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 10^{+71}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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) -2.7e+135)
   (* b c)
   (if (<= (* b c) 1e+71) (* (* x i) -4.0) (* 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) <= -2.7e+135) {
		tmp = b * c;
	} else if ((b * c) <= 1e+71) {
		tmp = (x * i) * -4.0;
	} 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) <= (-2.7d+135)) then
        tmp = b * c
    else if ((b * c) <= 1d+71) then
        tmp = (x * i) * (-4.0d0)
    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) <= -2.7e+135) {
		tmp = b * c;
	} else if ((b * c) <= 1e+71) {
		tmp = (x * i) * -4.0;
	} 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) <= -2.7e+135:
		tmp = b * c
	elif (b * c) <= 1e+71:
		tmp = (x * i) * -4.0
	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) <= -2.7e+135)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1e+71)
		tmp = Float64(Float64(x * i) * -4.0);
	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) <= -2.7e+135)
		tmp = b * c;
	elseif ((b * c) <= 1e+71)
		tmp = (x * i) * -4.0;
	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], -2.7e+135], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+71], N[(N[(x * i), $MachinePrecision] * -4.0), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.69999999999999985e135 or 1e71 < (*.f64 b c)

   1. Initial program 83.2%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in b around inf 46.2%

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

   if -2.69999999999999985e135 < (*.f64 b c) < 1e71

   1. Initial program 88.2%

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

   3. Simplified 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 i around inf 29.5%

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

      1. *-commutative 29.5%

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

   6. Simplified 29.5%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 10^{+71}:\\ \;\;\;\;\left(x \cdot i\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 28: 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 86.6%

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

3. Simplified 88.7%

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

4. Taylor expanded in b around inf 19.5%

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

5. Final simplification 19.5%

   \[\leadsto b \cdot c \]

Developer target: 88.7% 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 2023271 
(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)))