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

Percentage Accurate: 85.4% → 91.9%

Time: 26.2s

Alternatives: 20

Speedup: 1.0×

• 50.5% 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: 85.4% 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: 91.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (((((z * ((x * 18.0) * y)) * 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 = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	return tmp

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]), $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[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $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 96.9%

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

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

   1. Initial program 0.0%

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

   3. Simplified 16.1%

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

   4. Taylor expanded in x around inf 68.0%

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

      1. expm1-log1p-u 42.2%

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

      2. expm1-udef 42.2%

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

   6. Applied egg-rr 42.2%

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

      1. expm1-def 42.2%

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

      2. expm1-log1p 68.0%

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

      3. associate-*r* 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 94.2%

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

Alternative 2: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-82}:\\ \;\;\;\;\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(\left(x \cdot 18\right) \cdot y\right) - t \cdot \left(a \cdot 4\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (<= x -2.1e+99)
     (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
     (if (<= x 5e-82)
       (- (+ (* b c) (- (* (* z t) (* (* x 18.0) y)) (* t (* a 4.0)))) t_1)
       (- (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if (x <= -2.1e+99) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (x <= 5e-82) {
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (4.0d0 * i)) + (j * (27.0d0 * k))
    if (x <= (-2.1d+99)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (x <= 5d-82) then
        tmp = ((b * c) + (((z * t) * ((x * 18.0d0) * y)) - (t * (a * 4.0d0)))) - t_1
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if (x <= -2.1e+99) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (x <= 5e-82) {
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if x <= -2.1e+99:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif x <= 5e-82:
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - t_1
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if (x <= -2.1e+99)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (x <= 5e-82)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(Float64(z * t) * Float64(Float64(x * 18.0) * y)) - Float64(t * Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if (x <= -2.1e+99)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (x <= 5e-82)
		tmp = ((b * c) + (((z * t) * ((x * 18.0) * y)) - (t * (a * 4.0)))) - t_1;
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+99], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-82], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1000000000000001e99

   1. Initial program 58.8%

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

   3. Simplified 63.4%

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

   4. Taylor expanded in x around inf 78.9%

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

      1. expm1-log1p-u 49.6%

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

      2. expm1-udef 47.0%

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

   6. Applied egg-rr 47.0%

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

      1. expm1-def 49.6%

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

      2. expm1-log1p 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*l* 81.3%

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

      5. *-commutative 81.3%

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

   8. Simplified 81.3%

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

   if -2.1000000000000001e99 < x < 4.9999999999999998e-82

   1. Initial program 92.0%

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

   3. Simplified 87.1%

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

      1. associate-*r* 93.5%

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

      2. distribute-rgt-out-- 92.0%

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

      3. associate-*l* 89.0%

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

      4. *-commutative 89.0%

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

      5. *-commutative 89.0%

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

   5. Applied egg-rr 89.0%

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

   if 4.9999999999999998e-82 < x

   1. Initial program 87.2%

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

   3. Simplified 93.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-82}:\\ \;\;\;\;\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(\left(x \cdot 18\right) \cdot y\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 3: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_4 := x \cdot \left(i \cdot -4\right) + t_2\\ \mathbf{if}\;t \leq -400000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-267}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-251}:\\ \;\;\;\;b \cdot c + t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-184}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (+ (* b c) (* 18.0 (* (* y z) (* x t)))) (* 27.0 (* j k))))
        (t_2 (* j (* k -27.0)))
        (t_3 (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
        (t_4 (+ (* x (* i -4.0)) t_2)))
   (if (<= t -400000.0)
     t_3
     (if (<= t -6.8e-198)
       t_1
       (if (<= t -7.5e-267)
         t_4
         (if (<= t 5.2e-251)
           (+ (* b c) t_2)
           (if (<= t 6e-184) t_4 (if (<= t 1e+22) t_1 t_3))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) + (18.0 * ((y * z) * (x * t)))) - (27.0 * (j * k));
	double t_2 = j * (k * -27.0);
	double t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_4 = (x * (i * -4.0)) + t_2;
	double tmp;
	if (t <= -400000.0) {
		tmp = t_3;
	} else if (t <= -6.8e-198) {
		tmp = t_1;
	} else if (t <= -7.5e-267) {
		tmp = t_4;
	} else if (t <= 5.2e-251) {
		tmp = (b * c) + t_2;
	} else if (t <= 6e-184) {
		tmp = t_4;
	} else if (t <= 1e+22) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = ((b * c) + (18.0d0 * ((y * z) * (x * t)))) - (27.0d0 * (j * k))
    t_2 = j * (k * (-27.0d0))
    t_3 = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    t_4 = (x * (i * (-4.0d0))) + t_2
    if (t <= (-400000.0d0)) then
        tmp = t_3
    else if (t <= (-6.8d-198)) then
        tmp = t_1
    else if (t <= (-7.5d-267)) then
        tmp = t_4
    else if (t <= 5.2d-251) then
        tmp = (b * c) + t_2
    else if (t <= 6d-184) then
        tmp = t_4
    else if (t <= 1d+22) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) + (18.0 * ((y * z) * (x * t)))) - (27.0 * (j * k));
	double t_2 = j * (k * -27.0);
	double t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	double t_4 = (x * (i * -4.0)) + t_2;
	double tmp;
	if (t <= -400000.0) {
		tmp = t_3;
	} else if (t <= -6.8e-198) {
		tmp = t_1;
	} else if (t <= -7.5e-267) {
		tmp = t_4;
	} else if (t <= 5.2e-251) {
		tmp = (b * c) + t_2;
	} else if (t <= 6e-184) {
		tmp = t_4;
	} else if (t <= 1e+22) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) + (18.0 * ((y * z) * (x * t)))) - (27.0 * (j * k))
	t_2 = j * (k * -27.0)
	t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	t_4 = (x * (i * -4.0)) + t_2
	tmp = 0
	if t <= -400000.0:
		tmp = t_3
	elif t <= -6.8e-198:
		tmp = t_1
	elif t <= -7.5e-267:
		tmp = t_4
	elif t <= 5.2e-251:
		tmp = (b * c) + t_2
	elif t <= 6e-184:
		tmp = t_4
	elif t <= 1e+22:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(j * Float64(k * -27.0))
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))))
	t_4 = Float64(Float64(x * Float64(i * -4.0)) + t_2)
	tmp = 0.0
	if (t <= -400000.0)
		tmp = t_3;
	elseif (t <= -6.8e-198)
		tmp = t_1;
	elseif (t <= -7.5e-267)
		tmp = t_4;
	elseif (t <= 5.2e-251)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (t <= 6e-184)
		tmp = t_4;
	elseif (t <= 1e+22)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) + (18.0 * ((y * z) * (x * t)))) - (27.0 * (j * k));
	t_2 = j * (k * -27.0);
	t_3 = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	t_4 = (x * (i * -4.0)) + t_2;
	tmp = 0.0;
	if (t <= -400000.0)
		tmp = t_3;
	elseif (t <= -6.8e-198)
		tmp = t_1;
	elseif (t <= -7.5e-267)
		tmp = t_4;
	elseif (t <= 5.2e-251)
		tmp = (b * c) + t_2;
	elseif (t <= 6e-184)
		tmp = t_4;
	elseif (t <= 1e+22)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t, -400000.0], t$95$3, If[LessEqual[t, -6.8e-198], t$95$1, If[LessEqual[t, -7.5e-267], t$95$4, If[LessEqual[t, 5.2e-251], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, 6e-184], t$95$4, If[LessEqual[t, 1e+22], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4e5 or 1e22 < t

   1. Initial program 83.9%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in i around 0 88.9%

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

   5. Taylor expanded in j around 0 84.3%

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

   if -4e5 < t < -6.7999999999999996e-198 or 5.99999999999999982e-184 < t < 1e22

   1. Initial program 83.6%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in i around 0 72.6%

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

   5. Taylor expanded in x around inf 67.8%

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

      1. associate-*r* 48.2%

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

   7. Simplified 67.9%

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

   if -6.7999999999999996e-198 < t < -7.4999999999999999e-267 or 5.1999999999999998e-251 < t < 5.99999999999999982e-184

   1. Initial program 89.5%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in i around inf 93.3%

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

      1. associate-*r* 93.3%

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

      2. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   if -7.4999999999999999e-267 < t < 5.1999999999999998e-251

   1. Initial program 94.4%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in b around inf 73.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -400000:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-198}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-251}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 10^{+22}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 4: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.25e+161)
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.25e+161) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-1.25d+161)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.25e+161) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -1.25e+161:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.25e+161)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -1.25e+161)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.25e+161], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2499999999999999e161

   1. Initial program 51.8%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in x around inf 78.1%

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

      1. expm1-log1p-u 52.3%

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

      2. expm1-udef 49.1%

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

   6. Applied egg-rr 49.1%

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

      1. expm1-def 52.3%

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

      2. expm1-log1p 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   if -1.2499999999999999e161 < x

   1. Initial program 89.8%

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

   3. Simplified 89.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 5: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4\right) + t_1\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-252}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-70}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 180000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* x (* i -4.0)) t_1))
        (t_3 (+ (* b c) t_1)))
   (if (<= t -3.9e-42)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t 6.7e-252)
       t_3
       (if (<= t 2.7e-96)
         t_2
         (if (<= t 3e-70)
           (+ (* b c) (* 18.0 (* (* y z) (* x t))))
           (if (<= t 5.6e-24)
             t_2
             (if (<= t 180000.0)
               t_3
               (* t (+ (* a -4.0) (* 18.0 (* y (* x z)))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (x * (i * -4.0)) + t_1;
	double t_3 = (b * c) + t_1;
	double tmp;
	if (t <= -3.9e-42) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 6.7e-252) {
		tmp = t_3;
	} else if (t <= 2.7e-96) {
		tmp = t_2;
	} else if (t <= 3e-70) {
		tmp = (b * c) + (18.0 * ((y * z) * (x * t)));
	} else if (t <= 5.6e-24) {
		tmp = t_2;
	} else if (t <= 180000.0) {
		tmp = t_3;
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (x * (i * (-4.0d0))) + t_1
    t_3 = (b * c) + t_1
    if (t <= (-3.9d-42)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 6.7d-252) then
        tmp = t_3
    else if (t <= 2.7d-96) then
        tmp = t_2
    else if (t <= 3d-70) then
        tmp = (b * c) + (18.0d0 * ((y * z) * (x * t)))
    else if (t <= 5.6d-24) then
        tmp = t_2
    else if (t <= 180000.0d0) then
        tmp = t_3
    else
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (y * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (x * (i * -4.0)) + t_1;
	double t_3 = (b * c) + t_1;
	double tmp;
	if (t <= -3.9e-42) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 6.7e-252) {
		tmp = t_3;
	} else if (t <= 2.7e-96) {
		tmp = t_2;
	} else if (t <= 3e-70) {
		tmp = (b * c) + (18.0 * ((y * z) * (x * t)));
	} else if (t <= 5.6e-24) {
		tmp = t_2;
	} else if (t <= 180000.0) {
		tmp = t_3;
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (x * (i * -4.0)) + t_1
	t_3 = (b * c) + t_1
	tmp = 0
	if t <= -3.9e-42:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 6.7e-252:
		tmp = t_3
	elif t <= 2.7e-96:
		tmp = t_2
	elif t <= 3e-70:
		tmp = (b * c) + (18.0 * ((y * z) * (x * t)))
	elif t <= 5.6e-24:
		tmp = t_2
	elif t <= 180000.0:
		tmp = t_3
	else:
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(x * Float64(i * -4.0)) + t_1)
	t_3 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -3.9e-42)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 6.7e-252)
		tmp = t_3;
	elseif (t <= 2.7e-96)
		tmp = t_2;
	elseif (t <= 3e-70)
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))));
	elseif (t <= 5.6e-24)
		tmp = t_2;
	elseif (t <= 180000.0)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(y * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (x * (i * -4.0)) + t_1;
	t_3 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -3.9e-42)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 6.7e-252)
		tmp = t_3;
	elseif (t <= 2.7e-96)
		tmp = t_2;
	elseif (t <= 3e-70)
		tmp = (b * c) + (18.0 * ((y * z) * (x * t)));
	elseif (t <= 5.6e-24)
		tmp = t_2;
	elseif (t <= 180000.0)
		tmp = t_3;
	else
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -3.9e-42], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.7e-252], t$95$3, If[LessEqual[t, 2.7e-96], t$95$2, If[LessEqual[t, 3e-70], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-24], t$95$2, If[LessEqual[t, 180000.0], t$95$3, N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.9000000000000002e-42

   1. Initial program 87.1%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -3.9000000000000002e-42 < t < 6.69999999999999958e-252 or 5.6000000000000003e-24 < t < 1.8e5

   1. Initial program 87.6%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in b around inf 68.7%

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

   if 6.69999999999999958e-252 < t < 2.7e-96 or 3.0000000000000001e-70 < t < 5.6000000000000003e-24

   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 83.6%

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

   4. Taylor expanded in i around inf 74.8%

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

      1. associate-*r* 74.8%

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

      2. *-commutative 74.8%

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

   6. Simplified 74.8%

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

   if 2.7e-96 < t < 3.0000000000000001e-70

   1. Initial program 81.8%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in i around 0 81.8%

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

   5. Taylor expanded in j around 0 82.1%

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

   6. Taylor expanded in x around inf 82.1%

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

      1. associate-*r* 81.9%

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

   8. Simplified 81.9%

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

   if 1.8e5 < t

   1. Initial program 80.3%

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

   3. Simplified 80.6%

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

      1. associate-*r* 85.2%

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

      2. distribute-rgt-out-- 80.3%

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

      3. associate-*l* 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in t around -inf 68.9%

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

      1. associate-*r* 68.9%

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

      2. neg-mul-1 68.9%

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

      3. cancel-sign-sub-inv 68.9%

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

      4. associate-*r* 68.9%

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

      5. metadata-eval 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in t around 0 68.9%

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

       1. associate-*r* 68.9%

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

       2. neg-mul-1 68.9%

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

       3. *-commutative 68.9%

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

       4. *-commutative 68.9%

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

       5. *-commutative 68.9%

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

       6. associate-*r* 68.9%

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

       7. fma-udef 68.9%

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

       8. distribute-lft-neg-in 68.9%

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

       9. distribute-rgt-neg-in 68.9%

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

       10. fma-udef 68.9%

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

       11. +-commutative 68.9%

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

       12. distribute-neg-in 68.9%

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

       13. *-commutative 68.9%

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

       14. distribute-lft-neg-in 68.9%

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

       15. metadata-eval 68.9%

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

       16. associate-*r* 68.9%

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

       17. *-commutative 68.9%

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

       18. *-commutative 68.9%

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

       19. distribute-lft-neg-in 68.9%

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

       20. metadata-eval 68.9%

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

       21. *-commutative 68.9%

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

       22. associate-*l* 74.6%

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

   11. Simplified 74.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-252}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-70}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 180000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 6: 59.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4\right) + t_1\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-248}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-66}:\\ \;\;\;\;b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 132000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* x (* i -4.0)) t_1))
        (t_3 (+ (* b c) t_1)))
   (if (<= t -3.8e-45)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t 1.9e-248)
       t_3
       (if (<= t 2.8e-96)
         t_2
         (if (<= t 1.85e-66)
           (+ (* b c) (* t (* x (* z (* 18.0 y)))))
           (if (<= t 2.05e-23)
             t_2
             (if (<= t 132000000.0)
               t_3
               (* t (+ (* a -4.0) (* 18.0 (* y (* x z)))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (x * (i * -4.0)) + t_1;
	double t_3 = (b * c) + t_1;
	double tmp;
	if (t <= -3.8e-45) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 1.9e-248) {
		tmp = t_3;
	} else if (t <= 2.8e-96) {
		tmp = t_2;
	} else if (t <= 1.85e-66) {
		tmp = (b * c) + (t * (x * (z * (18.0 * y))));
	} else if (t <= 2.05e-23) {
		tmp = t_2;
	} else if (t <= 132000000.0) {
		tmp = t_3;
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (x * (i * (-4.0d0))) + t_1
    t_3 = (b * c) + t_1
    if (t <= (-3.8d-45)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 1.9d-248) then
        tmp = t_3
    else if (t <= 2.8d-96) then
        tmp = t_2
    else if (t <= 1.85d-66) then
        tmp = (b * c) + (t * (x * (z * (18.0d0 * y))))
    else if (t <= 2.05d-23) then
        tmp = t_2
    else if (t <= 132000000.0d0) then
        tmp = t_3
    else
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (y * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (x * (i * -4.0)) + t_1;
	double t_3 = (b * c) + t_1;
	double tmp;
	if (t <= -3.8e-45) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 1.9e-248) {
		tmp = t_3;
	} else if (t <= 2.8e-96) {
		tmp = t_2;
	} else if (t <= 1.85e-66) {
		tmp = (b * c) + (t * (x * (z * (18.0 * y))));
	} else if (t <= 2.05e-23) {
		tmp = t_2;
	} else if (t <= 132000000.0) {
		tmp = t_3;
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (x * (i * -4.0)) + t_1
	t_3 = (b * c) + t_1
	tmp = 0
	if t <= -3.8e-45:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 1.9e-248:
		tmp = t_3
	elif t <= 2.8e-96:
		tmp = t_2
	elif t <= 1.85e-66:
		tmp = (b * c) + (t * (x * (z * (18.0 * y))))
	elif t <= 2.05e-23:
		tmp = t_2
	elif t <= 132000000.0:
		tmp = t_3
	else:
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(x * Float64(i * -4.0)) + t_1)
	t_3 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -3.8e-45)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 1.9e-248)
		tmp = t_3;
	elseif (t <= 2.8e-96)
		tmp = t_2;
	elseif (t <= 1.85e-66)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(x * Float64(z * Float64(18.0 * y)))));
	elseif (t <= 2.05e-23)
		tmp = t_2;
	elseif (t <= 132000000.0)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(y * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (x * (i * -4.0)) + t_1;
	t_3 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -3.8e-45)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 1.9e-248)
		tmp = t_3;
	elseif (t <= 2.8e-96)
		tmp = t_2;
	elseif (t <= 1.85e-66)
		tmp = (b * c) + (t * (x * (z * (18.0 * y))));
	elseif (t <= 2.05e-23)
		tmp = t_2;
	elseif (t <= 132000000.0)
		tmp = t_3;
	else
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -3.8e-45], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-248], t$95$3, If[LessEqual[t, 2.8e-96], t$95$2, If[LessEqual[t, 1.85e-66], N[(N[(b * c), $MachinePrecision] + N[(t * N[(x * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-23], t$95$2, If[LessEqual[t, 132000000.0], t$95$3, N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.79999999999999997e-45

   1. Initial program 87.1%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -3.79999999999999997e-45 < t < 1.8999999999999999e-248 or 2.05000000000000015e-23 < t < 1.32e8

   1. Initial program 87.6%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in b around inf 68.7%

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

   if 1.8999999999999999e-248 < t < 2.80000000000000015e-96 or 1.8500000000000001e-66 < t < 2.05000000000000015e-23

   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 83.6%

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

   4. Taylor expanded in i around inf 74.8%

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

      1. associate-*r* 74.8%

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

      2. *-commutative 74.8%

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

   6. Simplified 74.8%

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

   if 2.80000000000000015e-96 < t < 1.8500000000000001e-66

   1. Initial program 81.8%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in i around 0 81.8%

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

   5. Taylor expanded in j around 0 82.1%

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

   6. Taylor expanded in x around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*l* 82.1%

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

      3. associate-*l* 82.1%

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

      4. associate-*r* 82.1%

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

      5. *-commutative 82.1%

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

      6. associate-*l* 82.1%

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

   8. Simplified 82.1%

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

   if 1.32e8 < t

   1. Initial program 80.3%

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

   3. Simplified 80.6%

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

      1. associate-*r* 85.2%

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

      2. distribute-rgt-out-- 80.3%

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

      3. associate-*l* 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in t around -inf 68.9%

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

      1. associate-*r* 68.9%

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

      2. neg-mul-1 68.9%

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

      3. cancel-sign-sub-inv 68.9%

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

      4. associate-*r* 68.9%

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

      5. metadata-eval 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in t around 0 68.9%

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

       1. associate-*r* 68.9%

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

       2. neg-mul-1 68.9%

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

       3. *-commutative 68.9%

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

       4. *-commutative 68.9%

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

       5. *-commutative 68.9%

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

       6. associate-*r* 68.9%

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

       7. fma-udef 68.9%

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

       8. distribute-lft-neg-in 68.9%

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

       9. distribute-rgt-neg-in 68.9%

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

       10. fma-udef 68.9%

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

       11. +-commutative 68.9%

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

       12. distribute-neg-in 68.9%

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

       13. *-commutative 68.9%

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

       14. distribute-lft-neg-in 68.9%

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

       15. metadata-eval 68.9%

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

       16. associate-*r* 68.9%

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

       17. *-commutative 68.9%

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

       18. *-commutative 68.9%

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

       19. distribute-lft-neg-in 68.9%

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

       20. metadata-eval 68.9%

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

       21. *-commutative 68.9%

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

       22. associate-*l* 74.6%

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

   11. Simplified 74.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-248}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-66}:\\ \;\;\;\;b \cdot c + t \cdot \left(x \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 132000000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.6e+131)
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (-
    (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
    (* 27.0 (* j k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.6e+131) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= (-2.6d+131)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.6e+131) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -2.6e+131:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.6e+131)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -2.6e+131)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.6e+131], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e131

   1. Initial program 55.8%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in x around inf 78.5%

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

      1. expm1-log1p-u 50.8%

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

      2. expm1-udef 47.8%

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

   6. Applied egg-rr 47.8%

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

      1. expm1-def 50.8%

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

      2. expm1-log1p 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   if -2.6e131 < x

   1. Initial program 90.0%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in i around 0 81.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 8: 34.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-260}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+35}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))))
   (if (<= t -5e-42)
     t_1
     (if (<= t -4.5e-187)
       (* b c)
       (if (<= t -1.05e-260)
         (* (* j k) -27.0)
         (if (<= t 6e-290)
           (* b c)
           (if (<= t 5.8e+35)
             (* k (* j -27.0))
             (if (<= t 1.45e+210) t_1 (* t (* a -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -5e-42) {
		tmp = t_1;
	} else if (t <= -4.5e-187) {
		tmp = b * c;
	} else if (t <= -1.05e-260) {
		tmp = (j * k) * -27.0;
	} else if (t <= 6e-290) {
		tmp = b * c;
	} else if (t <= 5.8e+35) {
		tmp = k * (j * -27.0);
	} else if (t <= 1.45e+210) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (x * (y * z)))
    if (t <= (-5d-42)) then
        tmp = t_1
    else if (t <= (-4.5d-187)) then
        tmp = b * c
    else if (t <= (-1.05d-260)) then
        tmp = (j * k) * (-27.0d0)
    else if (t <= 6d-290) then
        tmp = b * c
    else if (t <= 5.8d+35) then
        tmp = k * (j * (-27.0d0))
    else if (t <= 1.45d+210) then
        tmp = t_1
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double tmp;
	if (t <= -5e-42) {
		tmp = t_1;
	} else if (t <= -4.5e-187) {
		tmp = b * c;
	} else if (t <= -1.05e-260) {
		tmp = (j * k) * -27.0;
	} else if (t <= 6e-290) {
		tmp = b * c;
	} else if (t <= 5.8e+35) {
		tmp = k * (j * -27.0);
	} else if (t <= 1.45e+210) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if t <= -5e-42:
		tmp = t_1
	elif t <= -4.5e-187:
		tmp = b * c
	elif t <= -1.05e-260:
		tmp = (j * k) * -27.0
	elif t <= 6e-290:
		tmp = b * c
	elif t <= 5.8e+35:
		tmp = k * (j * -27.0)
	elif t <= 1.45e+210:
		tmp = t_1
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (t <= -5e-42)
		tmp = t_1;
	elseif (t <= -4.5e-187)
		tmp = Float64(b * c);
	elseif (t <= -1.05e-260)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (t <= 6e-290)
		tmp = Float64(b * c);
	elseif (t <= 5.8e+35)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (t <= 1.45e+210)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (t <= -5e-42)
		tmp = t_1;
	elseif (t <= -4.5e-187)
		tmp = b * c;
	elseif (t <= -1.05e-260)
		tmp = (j * k) * -27.0;
	elseif (t <= 6e-290)
		tmp = b * c;
	elseif (t <= 5.8e+35)
		tmp = k * (j * -27.0);
	elseif (t <= 1.45e+210)
		tmp = t_1;
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-42], t$95$1, If[LessEqual[t, -4.5e-187], N[(b * c), $MachinePrecision], If[LessEqual[t, -1.05e-260], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t, 6e-290], N[(b * c), $MachinePrecision], If[LessEqual[t, 5.8e+35], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+210], t$95$1, N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.00000000000000003e-42 or 5.79999999999999989e35 < t < 1.44999999999999996e210

   1. Initial program 87.2%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around inf 57.2%

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

      1. expm1-log1p-u 27.7%

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

      2. expm1-udef 27.6%

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

   6. Applied egg-rr 27.6%

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

      1. expm1-def 27.7%

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

      2. expm1-log1p 57.2%

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

      3. associate-*r* 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in t around inf 48.0%

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

   if -5.00000000000000003e-42 < t < -4.4999999999999998e-187 or -1.05000000000000002e-260 < t < 5.99999999999999985e-290

   1. Initial program 92.3%

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

   3. Simplified 90.0%

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

      1. associate-*r* 92.4%

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

      2. distribute-rgt-out-- 92.3%

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

      3. associate-*l* 92.3%

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

      4. *-commutative 92.3%

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

      5. *-commutative 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in b around inf 46.8%

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

   if -4.4999999999999998e-187 < t < -1.05000000000000002e-260

   1. Initial program 74.8%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in j around inf 63.4%

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

   if 5.99999999999999985e-290 < t < 5.79999999999999989e35

   1. Initial program 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in i around 0 72.0%

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

   5. Taylor expanded in j around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-commutative 40.2%

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

      3. associate-*l* 40.2%

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

   7. Simplified 40.2%

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

   if 1.44999999999999996e210 < t

   1. Initial program 68.4%

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

   3. Simplified 73.7%

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

      1. associate-*r* 84.2%

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

      2. distribute-rgt-out-- 68.4%

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

      3. associate-*l* 52.9%

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

      4. *-commutative 52.9%

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

      5. *-commutative 52.9%

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

   5. Applied egg-rr 52.9%

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

   6. Taylor expanded in a around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-*r* 59.2%

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

   8. Simplified 59.2%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-42}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-260}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+35}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+210}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 9: 34.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-42}:\\ \;\;\;\;t_1 \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-259}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+214}:\\ \;\;\;\;18 \cdot \left(t \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= t -1.2e-42)
     (* t_1 (* 18.0 t))
     (if (<= t -5.4e-195)
       (* b c)
       (if (<= t -1e-259)
         (* (* j k) -27.0)
         (if (<= t 3.4e-290)
           (* b c)
           (if (<= t 4e+37)
             (* k (* j -27.0))
             (if (<= t 7e+214) (* 18.0 (* t t_1)) (* t (* a -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double tmp;
	if (t <= -1.2e-42) {
		tmp = t_1 * (18.0 * t);
	} else if (t <= -5.4e-195) {
		tmp = b * c;
	} else if (t <= -1e-259) {
		tmp = (j * k) * -27.0;
	} else if (t <= 3.4e-290) {
		tmp = b * c;
	} else if (t <= 4e+37) {
		tmp = k * (j * -27.0);
	} else if (t <= 7e+214) {
		tmp = 18.0 * (t * t_1);
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (t <= (-1.2d-42)) then
        tmp = t_1 * (18.0d0 * t)
    else if (t <= (-5.4d-195)) then
        tmp = b * c
    else if (t <= (-1d-259)) then
        tmp = (j * k) * (-27.0d0)
    else if (t <= 3.4d-290) then
        tmp = b * c
    else if (t <= 4d+37) then
        tmp = k * (j * (-27.0d0))
    else if (t <= 7d+214) then
        tmp = 18.0d0 * (t * t_1)
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double tmp;
	if (t <= -1.2e-42) {
		tmp = t_1 * (18.0 * t);
	} else if (t <= -5.4e-195) {
		tmp = b * c;
	} else if (t <= -1e-259) {
		tmp = (j * k) * -27.0;
	} else if (t <= 3.4e-290) {
		tmp = b * c;
	} else if (t <= 4e+37) {
		tmp = k * (j * -27.0);
	} else if (t <= 7e+214) {
		tmp = 18.0 * (t * t_1);
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	tmp = 0
	if t <= -1.2e-42:
		tmp = t_1 * (18.0 * t)
	elif t <= -5.4e-195:
		tmp = b * c
	elif t <= -1e-259:
		tmp = (j * k) * -27.0
	elif t <= 3.4e-290:
		tmp = b * c
	elif t <= 4e+37:
		tmp = k * (j * -27.0)
	elif t <= 7e+214:
		tmp = 18.0 * (t * t_1)
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (t <= -1.2e-42)
		tmp = Float64(t_1 * Float64(18.0 * t));
	elseif (t <= -5.4e-195)
		tmp = Float64(b * c);
	elseif (t <= -1e-259)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (t <= 3.4e-290)
		tmp = Float64(b * c);
	elseif (t <= 4e+37)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (t <= 7e+214)
		tmp = Float64(18.0 * Float64(t * t_1));
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (t <= -1.2e-42)
		tmp = t_1 * (18.0 * t);
	elseif (t <= -5.4e-195)
		tmp = b * c;
	elseif (t <= -1e-259)
		tmp = (j * k) * -27.0;
	elseif (t <= 3.4e-290)
		tmp = b * c;
	elseif (t <= 4e+37)
		tmp = k * (j * -27.0);
	elseif (t <= 7e+214)
		tmp = 18.0 * (t * t_1);
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e-42], N[(t$95$1 * N[(18.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e-195], N[(b * c), $MachinePrecision], If[LessEqual[t, -1e-259], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t, 3.4e-290], N[(b * c), $MachinePrecision], If[LessEqual[t, 4e+37], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+214], N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.20000000000000001e-42

   1. Initial program 87.1%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. expm1-log1p-u 32.5%

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

      2. expm1-udef 32.4%

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

   6. Applied egg-rr 32.4%

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

      1. expm1-def 32.5%

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

      2. expm1-log1p 61.4%

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

      3. associate-*r* 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in t around inf 49.8%

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

       1. associate-*r* 49.9%

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

       2. *-commutative 49.9%

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

   11. Simplified 49.9%

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

   if -1.20000000000000001e-42 < t < -5.4e-195 or -1.0000000000000001e-259 < t < 3.39999999999999984e-290

   1. Initial program 92.3%

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

   3. Simplified 90.0%

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

      1. associate-*r* 92.4%

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

      2. distribute-rgt-out-- 92.3%

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

      3. associate-*l* 92.3%

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

      4. *-commutative 92.3%

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

      5. *-commutative 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in b around inf 46.8%

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

   if -5.4e-195 < t < -1.0000000000000001e-259

   1. Initial program 74.8%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in j around inf 63.4%

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

   if 3.39999999999999984e-290 < t < 3.99999999999999982e37

   1. Initial program 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in i around 0 72.0%

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

   5. Taylor expanded in j around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-commutative 40.2%

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

      3. associate-*l* 40.2%

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

   7. Simplified 40.2%

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

   if 3.99999999999999982e37 < t < 6.9999999999999999e214

   1. Initial program 87.4%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in x around inf 47.3%

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

      1. expm1-log1p-u 16.1%

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

      2. expm1-udef 16.1%

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

   6. Applied egg-rr 16.1%

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

      1. expm1-def 16.1%

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

      2. expm1-log1p 47.3%

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

      3. associate-*r* 45.6%

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

   8. Simplified 45.6%

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

   9. Taylor expanded in t around inf 43.6%

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

   if 6.9999999999999999e214 < t

   1. Initial program 68.4%

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

   3. Simplified 73.7%

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

      1. associate-*r* 84.2%

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

      2. distribute-rgt-out-- 68.4%

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

      3. associate-*l* 52.9%

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

      4. *-commutative 52.9%

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

      5. *-commutative 52.9%

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

   5. Applied egg-rr 52.9%

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

   6. Taylor expanded in a around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-*r* 59.2%

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

   8. Simplified 59.2%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-42}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(18 \cdot t\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-259}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+214}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 10: 34.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-260}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-289}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 425000000:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* z (* (* x y) (* 18.0 t)))))
   (if (<= t -1.02e-46)
     t_1
     (if (<= t -5.8e-187)
       (* b c)
       (if (<= t -1.25e-260)
         (* (* j k) -27.0)
         (if (<= t 1.25e-289)
           (* b c)
           (if (<= t 425000000.0)
             (* k (* j -27.0))
             (if (<= t 1.05e+173) t_1 (* t (* a -4.0))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * ((x * y) * (18.0 * t));
	double tmp;
	if (t <= -1.02e-46) {
		tmp = t_1;
	} else if (t <= -5.8e-187) {
		tmp = b * c;
	} else if (t <= -1.25e-260) {
		tmp = (j * k) * -27.0;
	} else if (t <= 1.25e-289) {
		tmp = b * c;
	} else if (t <= 425000000.0) {
		tmp = k * (j * -27.0);
	} else if (t <= 1.05e+173) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) * (18.0d0 * t))
    if (t <= (-1.02d-46)) then
        tmp = t_1
    else if (t <= (-5.8d-187)) then
        tmp = b * c
    else if (t <= (-1.25d-260)) then
        tmp = (j * k) * (-27.0d0)
    else if (t <= 1.25d-289) then
        tmp = b * c
    else if (t <= 425000000.0d0) then
        tmp = k * (j * (-27.0d0))
    else if (t <= 1.05d+173) then
        tmp = t_1
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * ((x * y) * (18.0 * t));
	double tmp;
	if (t <= -1.02e-46) {
		tmp = t_1;
	} else if (t <= -5.8e-187) {
		tmp = b * c;
	} else if (t <= -1.25e-260) {
		tmp = (j * k) * -27.0;
	} else if (t <= 1.25e-289) {
		tmp = b * c;
	} else if (t <= 425000000.0) {
		tmp = k * (j * -27.0);
	} else if (t <= 1.05e+173) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = z * ((x * y) * (18.0 * t))
	tmp = 0
	if t <= -1.02e-46:
		tmp = t_1
	elif t <= -5.8e-187:
		tmp = b * c
	elif t <= -1.25e-260:
		tmp = (j * k) * -27.0
	elif t <= 1.25e-289:
		tmp = b * c
	elif t <= 425000000.0:
		tmp = k * (j * -27.0)
	elif t <= 1.05e+173:
		tmp = t_1
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(z * Float64(Float64(x * y) * Float64(18.0 * t)))
	tmp = 0.0
	if (t <= -1.02e-46)
		tmp = t_1;
	elseif (t <= -5.8e-187)
		tmp = Float64(b * c);
	elseif (t <= -1.25e-260)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (t <= 1.25e-289)
		tmp = Float64(b * c);
	elseif (t <= 425000000.0)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (t <= 1.05e+173)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = z * ((x * y) * (18.0 * t));
	tmp = 0.0;
	if (t <= -1.02e-46)
		tmp = t_1;
	elseif (t <= -5.8e-187)
		tmp = b * c;
	elseif (t <= -1.25e-260)
		tmp = (j * k) * -27.0;
	elseif (t <= 1.25e-289)
		tmp = b * c;
	elseif (t <= 425000000.0)
		tmp = k * (j * -27.0);
	elseif (t <= 1.05e+173)
		tmp = t_1;
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e-46], t$95$1, If[LessEqual[t, -5.8e-187], N[(b * c), $MachinePrecision], If[LessEqual[t, -1.25e-260], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t, 1.25e-289], N[(b * c), $MachinePrecision], If[LessEqual[t, 425000000.0], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+173], t$95$1, N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.02e-46 or 4.25e8 < t < 1.05e173

   1. Initial program 86.0%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around inf 58.2%

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

      1. expm1-log1p-u 27.4%

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

      2. expm1-udef 27.3%

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

   6. Applied egg-rr 27.3%

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

      1. expm1-def 27.4%

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

      2. expm1-log1p 58.2%

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

      3. associate-*r* 56.9%

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

   8. Simplified 56.9%

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

   9. Taylor expanded in t around inf 47.3%

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

       1. associate-*r* 47.3%

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

       2. associate-*r* 48.1%

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

       3. associate-*r* 48.9%

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

       4. *-commutative 48.9%

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

       5. *-commutative 48.9%

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

   11. Simplified 48.9%

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

   if -1.02e-46 < t < -5.79999999999999977e-187 or -1.2500000000000001e-260 < t < 1.25000000000000007e-289

   1. Initial program 92.3%

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

   3. Simplified 90.0%

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

      1. associate-*r* 92.4%

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

      2. distribute-rgt-out-- 92.3%

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

      3. associate-*l* 92.3%

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

      4. *-commutative 92.3%

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

      5. *-commutative 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in b around inf 46.8%

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

   if -5.79999999999999977e-187 < t < -1.2500000000000001e-260

   1. Initial program 74.8%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in j around inf 63.4%

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

   if 1.25000000000000007e-289 < t < 4.25e8

   1. Initial program 85.7%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in i around 0 71.5%

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

   5. Taylor expanded in j around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. *-commutative 41.5%

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

      3. associate-*l* 41.6%

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

   7. Simplified 41.6%

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

   if 1.05e173 < t

   1. Initial program 75.0%

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

   3. Simplified 79.2%

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

      1. associate-*r* 87.5%

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

      2. distribute-rgt-out-- 75.0%

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

      3. associate-*l* 62.7%

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

      4. *-commutative 62.7%

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

      5. *-commutative 62.7%

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

   5. Applied egg-rr 62.7%

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

   6. Taylor expanded in a around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-*r* 51.5%

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

   8. Simplified 51.5%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-260}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-289}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 425000000:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 11: 60.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_1\\ \mathbf{elif}\;t \leq 6800000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (+ (* a -4.0) (* 18.0 (* y (* x z)))))))
   (if (<= t -1.55e-43)
     t_3
     (if (<= t 1.9e-250)
       t_2
       (if (<= t 9.5e-185)
         (+ (* x (* i -4.0)) t_1)
         (if (<= t 6800000000.0) t_2 t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	double tmp;
	if (t <= -1.55e-43) {
		tmp = t_3;
	} else if (t <= 1.9e-250) {
		tmp = t_2;
	} else if (t <= 9.5e-185) {
		tmp = (x * (i * -4.0)) + t_1;
	} else if (t <= 6800000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = t * ((a * (-4.0d0)) + (18.0d0 * (y * (x * z))))
    if (t <= (-1.55d-43)) then
        tmp = t_3
    else if (t <= 1.9d-250) then
        tmp = t_2
    else if (t <= 9.5d-185) then
        tmp = (x * (i * (-4.0d0))) + t_1
    else if (t <= 6800000000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	double tmp;
	if (t <= -1.55e-43) {
		tmp = t_3;
	} else if (t <= 1.9e-250) {
		tmp = t_2;
	} else if (t <= 9.5e-185) {
		tmp = (x * (i * -4.0)) + t_1;
	} else if (t <= 6800000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t * ((a * -4.0) + (18.0 * (y * (x * z))))
	tmp = 0
	if t <= -1.55e-43:
		tmp = t_3
	elif t <= 1.9e-250:
		tmp = t_2
	elif t <= 9.5e-185:
		tmp = (x * (i * -4.0)) + t_1
	elif t <= 6800000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(y * Float64(x * z)))))
	tmp = 0.0
	if (t <= -1.55e-43)
		tmp = t_3;
	elseif (t <= 1.9e-250)
		tmp = t_2;
	elseif (t <= 9.5e-185)
		tmp = Float64(Float64(x * Float64(i * -4.0)) + t_1);
	elseif (t <= 6800000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	tmp = 0.0;
	if (t <= -1.55e-43)
		tmp = t_3;
	elseif (t <= 1.9e-250)
		tmp = t_2;
	elseif (t <= 9.5e-185)
		tmp = (x * (i * -4.0)) + t_1;
	elseif (t <= 6800000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e-43], t$95$3, If[LessEqual[t, 1.9e-250], t$95$2, If[LessEqual[t, 9.5e-185], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6800000000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e-43 or 6.8e9 < t

   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 86.4%

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

      1. associate-*r* 88.4%

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

      2. distribute-rgt-out-- 84.1%

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

      3. associate-*l* 79.2%

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

      4. *-commutative 79.2%

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

      5. *-commutative 79.2%

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

   5. Applied egg-rr 79.2%

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

   6. Taylor expanded in t around -inf 73.8%

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

      1. associate-*r* 73.8%

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

      2. neg-mul-1 73.8%

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

      3. cancel-sign-sub-inv 73.8%

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

      4. associate-*r* 73.8%

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

      5. metadata-eval 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in t around 0 73.8%

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

       1. associate-*r* 73.8%

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

       2. neg-mul-1 73.8%

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

       3. *-commutative 73.8%

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

       4. *-commutative 73.8%

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

       5. *-commutative 73.8%

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

       6. associate-*r* 73.8%

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

       7. fma-udef 73.8%

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

       8. distribute-lft-neg-in 73.8%

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

       9. distribute-rgt-neg-in 73.8%

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

       10. fma-udef 73.8%

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

       11. +-commutative 73.8%

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

       12. distribute-neg-in 73.8%

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

       13. *-commutative 73.8%

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

       14. distribute-lft-neg-in 73.8%

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

       15. metadata-eval 73.8%

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

       16. associate-*r* 73.8%

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

       17. *-commutative 73.8%

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

       18. *-commutative 73.8%

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

       19. distribute-lft-neg-in 73.8%

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

       20. metadata-eval 73.8%

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

       21. *-commutative 73.8%

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

       22. associate-*l* 76.2%

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

   11. Simplified 76.2%

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

   if -1.55e-43 < t < 1.89999999999999985e-250 or 9.50000000000000042e-185 < t < 6.8e9

   1. Initial program 85.6%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in b around inf 64.4%

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

   if 1.89999999999999985e-250 < t < 9.50000000000000042e-185

   1. Initial program 92.9%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in i around inf 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-250}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6800000000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 12: 60.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_1\\ \mathbf{elif}\;t \leq 6500000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ (* b c) t_1)))
   (if (<= t -4.2e-43)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t 1.75e-249)
       t_2
       (if (<= t 1.5e-185)
         (+ (* x (* i -4.0)) t_1)
         (if (<= t 6500000000.0)
           t_2
           (* t (+ (* a -4.0) (* 18.0 (* y (* x z)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (t <= -4.2e-43) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 1.75e-249) {
		tmp = t_2;
	} else if (t <= 1.5e-185) {
		tmp = (x * (i * -4.0)) + t_1;
	} else if (t <= 6500000000.0) {
		tmp = t_2;
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    if (t <= (-4.2d-43)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= 1.75d-249) then
        tmp = t_2
    else if (t <= 1.5d-185) then
        tmp = (x * (i * (-4.0d0))) + t_1
    else if (t <= 6500000000.0d0) then
        tmp = t_2
    else
        tmp = t * ((a * (-4.0d0)) + (18.0d0 * (y * (x * z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (t <= -4.2e-43) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= 1.75e-249) {
		tmp = t_2;
	} else if (t <= 1.5e-185) {
		tmp = (x * (i * -4.0)) + t_1;
	} else if (t <= 6500000000.0) {
		tmp = t_2;
	} else {
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	tmp = 0
	if t <= -4.2e-43:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= 1.75e-249:
		tmp = t_2
	elif t <= 1.5e-185:
		tmp = (x * (i * -4.0)) + t_1
	elif t <= 6500000000.0:
		tmp = t_2
	else:
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (t <= -4.2e-43)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= 1.75e-249)
		tmp = t_2;
	elseif (t <= 1.5e-185)
		tmp = Float64(Float64(x * Float64(i * -4.0)) + t_1);
	elseif (t <= 6500000000.0)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) + Float64(18.0 * Float64(y * Float64(x * z)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if (t <= -4.2e-43)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= 1.75e-249)
		tmp = t_2;
	elseif (t <= 1.5e-185)
		tmp = (x * (i * -4.0)) + t_1;
	elseif (t <= 6500000000.0)
		tmp = t_2;
	else
		tmp = t * ((a * -4.0) + (18.0 * (y * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t, -4.2e-43], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-249], t$95$2, If[LessEqual[t, 1.5e-185], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6500000000.0], t$95$2, N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.2000000000000001e-43

   1. Initial program 87.1%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -4.2000000000000001e-43 < t < 1.75000000000000006e-249 or 1.50000000000000015e-185 < t < 6.5e9

   1. Initial program 85.6%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in b around inf 64.4%

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

   if 1.75000000000000006e-249 < t < 1.50000000000000015e-185

   1. Initial program 92.9%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in i around inf 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   if 6.5e9 < t

   1. Initial program 80.3%

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

   3. Simplified 80.6%

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

      1. associate-*r* 85.2%

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

      2. distribute-rgt-out-- 80.3%

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

      3. associate-*l* 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in t around -inf 68.9%

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

      1. associate-*r* 68.9%

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

      2. neg-mul-1 68.9%

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

      3. cancel-sign-sub-inv 68.9%

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

      4. associate-*r* 68.9%

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

      5. metadata-eval 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in t around 0 68.9%

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

       1. associate-*r* 68.9%

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

       2. neg-mul-1 68.9%

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

       3. *-commutative 68.9%

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

       4. *-commutative 68.9%

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

       5. *-commutative 68.9%

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

       6. associate-*r* 68.9%

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

       7. fma-udef 68.9%

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

       8. distribute-lft-neg-in 68.9%

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

       9. distribute-rgt-neg-in 68.9%

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

       10. fma-udef 68.9%

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

       11. +-commutative 68.9%

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

       12. distribute-neg-in 68.9%

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

       13. *-commutative 68.9%

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

       14. distribute-lft-neg-in 68.9%

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

       15. metadata-eval 68.9%

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

       16. associate-*r* 68.9%

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

       17. *-commutative 68.9%

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

       18. *-commutative 68.9%

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

       19. distribute-lft-neg-in 68.9%

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

       20. metadata-eval 68.9%

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

       21. *-commutative 68.9%

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

       22. associate-*l* 74.6%

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

   11. Simplified 74.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 6500000000:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 13: 65.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-47} \lor \neg \left(t \leq 6.5 \cdot 10^{-91}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -3.3e-47) (not (<= t 6.5e-91)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.3e-47) || !(t <= 6.5e-91)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-3.3d-47)) .or. (.not. (t <= 6.5d-91))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -3.3e-47) || !(t <= 6.5e-91)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -3.3e-47) or not (t <= 6.5e-91):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -3.3e-47) || !(t <= 6.5e-91))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -3.3e-47) || ~((t <= 6.5e-91)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -3.3e-47], N[Not[LessEqual[t, 6.5e-91]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.30000000000000004e-47 or 6.5000000000000001e-91 < t

   1. Initial program 85.0%

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

   3. Simplified 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 i around 0 85.5%

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

   5. Taylor expanded in j around 0 78.2%

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

   if -3.30000000000000004e-47 < t < 6.5000000000000001e-91

   1. Initial program 85.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in b around inf 67.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-47} \lor \neg \left(t \leq 6.5 \cdot 10^{-91}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 14: 32.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -0.125:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-260}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= t -0.125)
     t_1
     (if (<= t -5.2e-187)
       (* b c)
       (if (<= t -1e-260)
         (* (* j k) -27.0)
         (if (<= t 2.1e-290)
           (* b c)
           (if (<= t 1.8e+30) (* k (* j -27.0)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (t <= -0.125) {
		tmp = t_1;
	} else if (t <= -5.2e-187) {
		tmp = b * c;
	} else if (t <= -1e-260) {
		tmp = (j * k) * -27.0;
	} else if (t <= 2.1e-290) {
		tmp = b * c;
	} else if (t <= 1.8e+30) {
		tmp = k * (j * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (t <= (-0.125d0)) then
        tmp = t_1
    else if (t <= (-5.2d-187)) then
        tmp = b * c
    else if (t <= (-1d-260)) then
        tmp = (j * k) * (-27.0d0)
    else if (t <= 2.1d-290) then
        tmp = b * c
    else if (t <= 1.8d+30) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (t <= -0.125) {
		tmp = t_1;
	} else if (t <= -5.2e-187) {
		tmp = b * c;
	} else if (t <= -1e-260) {
		tmp = (j * k) * -27.0;
	} else if (t <= 2.1e-290) {
		tmp = b * c;
	} else if (t <= 1.8e+30) {
		tmp = k * (j * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if t <= -0.125:
		tmp = t_1
	elif t <= -5.2e-187:
		tmp = b * c
	elif t <= -1e-260:
		tmp = (j * k) * -27.0
	elif t <= 2.1e-290:
		tmp = b * c
	elif t <= 1.8e+30:
		tmp = k * (j * -27.0)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (t <= -0.125)
		tmp = t_1;
	elseif (t <= -5.2e-187)
		tmp = Float64(b * c);
	elseif (t <= -1e-260)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (t <= 2.1e-290)
		tmp = Float64(b * c);
	elseif (t <= 1.8e+30)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (t <= -0.125)
		tmp = t_1;
	elseif (t <= -5.2e-187)
		tmp = b * c;
	elseif (t <= -1e-260)
		tmp = (j * k) * -27.0;
	elseif (t <= 2.1e-290)
		tmp = b * c;
	elseif (t <= 1.8e+30)
		tmp = k * (j * -27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.125], t$95$1, If[LessEqual[t, -5.2e-187], N[(b * c), $MachinePrecision], If[LessEqual[t, -1e-260], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[t, 2.1e-290], N[(b * c), $MachinePrecision], If[LessEqual[t, 1.8e+30], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.125 or 1.8000000000000001e30 < t

   1. Initial program 83.7%

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

   3. Simplified 86.2%

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

      1. associate-*r* 88.5%

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

      2. distribute-rgt-out-- 83.7%

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

      3. associate-*l* 77.4%

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

      4. *-commutative 77.4%

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

      5. *-commutative 77.4%

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

   5. Applied egg-rr 77.4%

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

   6. Taylor expanded in a around inf 40.8%

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

      1. *-commutative 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*r* 40.8%

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

   8. Simplified 40.8%

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

   if -0.125 < t < -5.1999999999999999e-187 or -9.99999999999999961e-261 < t < 2.1000000000000001e-290

   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 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. Step-by-step derivation

      1. associate-*r* 91.6%

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

      2. distribute-rgt-out-- 91.6%

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

      3. associate-*l* 93.4%

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

      4. *-commutative 93.4%

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

      5. *-commutative 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in b around inf 40.2%

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

   if -5.1999999999999999e-187 < t < -9.99999999999999961e-261

   1. Initial program 74.8%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in j around inf 63.4%

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

   if 2.1000000000000001e-290 < t < 1.8000000000000001e30

   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 0 71.2%

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

   5. Taylor expanded in j around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 38.5%

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

   7. Simplified 38.5%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.125:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-260}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-290}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 15: 47.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* z (* (* x y) (* 18.0 t)))))
   (if (<= t -5.7e-42)
     t_1
     (if (<= t 3.2e+39)
       (+ (* b c) (* j (* k -27.0)))
       (if (<= t 1.7e+173) t_1 (* t (* a -4.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * ((x * y) * (18.0 * t));
	double tmp;
	if (t <= -5.7e-42) {
		tmp = t_1;
	} else if (t <= 3.2e+39) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 1.7e+173) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) * (18.0d0 * t))
    if (t <= (-5.7d-42)) then
        tmp = t_1
    else if (t <= 3.2d+39) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else if (t <= 1.7d+173) then
        tmp = t_1
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * ((x * y) * (18.0 * t));
	double tmp;
	if (t <= -5.7e-42) {
		tmp = t_1;
	} else if (t <= 3.2e+39) {
		tmp = (b * c) + (j * (k * -27.0));
	} else if (t <= 1.7e+173) {
		tmp = t_1;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = z * ((x * y) * (18.0 * t))
	tmp = 0
	if t <= -5.7e-42:
		tmp = t_1
	elif t <= 3.2e+39:
		tmp = (b * c) + (j * (k * -27.0))
	elif t <= 1.7e+173:
		tmp = t_1
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(z * Float64(Float64(x * y) * Float64(18.0 * t)))
	tmp = 0.0
	if (t <= -5.7e-42)
		tmp = t_1;
	elseif (t <= 3.2e+39)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	elseif (t <= 1.7e+173)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = z * ((x * y) * (18.0 * t));
	tmp = 0.0;
	if (t <= -5.7e-42)
		tmp = t_1;
	elseif (t <= 3.2e+39)
		tmp = (b * c) + (j * (k * -27.0));
	elseif (t <= 1.7e+173)
		tmp = t_1;
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e-42], t$95$1, If[LessEqual[t, 3.2e+39], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+173], t$95$1, N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6999999999999999e-42 or 3.19999999999999993e39 < t < 1.70000000000000011e173

   1. Initial program 86.4%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in x around inf 59.4%

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

      1. expm1-log1p-u 28.2%

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

      2. expm1-udef 28.1%

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

   6. Applied egg-rr 28.1%

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

      1. expm1-def 28.2%

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

      2. expm1-log1p 59.4%

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

      3. associate-*r* 57.9%

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

   8. Simplified 57.9%

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

   9. Taylor expanded in t around inf 49.7%

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

       1. associate-*r* 49.7%

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

       2. associate-*r* 50.7%

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

       3. associate-*r* 51.5%

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

       4. *-commutative 51.5%

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

       5. *-commutative 51.5%

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

   11. Simplified 51.5%

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

   if -5.6999999999999999e-42 < t < 3.19999999999999993e39

   1. Initial program 86.1%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in b around inf 62.3%

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

   if 1.70000000000000011e173 < t

   1. Initial program 75.0%

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

   3. Simplified 79.2%

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

      1. associate-*r* 87.5%

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

      2. distribute-rgt-out-- 75.0%

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

      3. associate-*l* 62.7%

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

      4. *-commutative 62.7%

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

      5. *-commutative 62.7%

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

   5. Applied egg-rr 62.7%

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

   6. Taylor expanded in a around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

      3. associate-*r* 51.5%

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

   8. Simplified 51.5%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 16: 52.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+91} \lor \neg \left(a \leq 1.8 \cdot 10^{+55}\right):\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))))
   (if (or (<= a -5.4e+91) (not (<= a 1.8e+55)))
     (+ t_1 (* -4.0 (* t a)))
     (+ (* b c) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((a <= -5.4e+91) || !(a <= 1.8e+55)) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    if ((a <= (-5.4d+91)) .or. (.not. (a <= 1.8d+55))) then
        tmp = t_1 + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * -27.0);
	double tmp;
	if ((a <= -5.4e+91) || !(a <= 1.8e+55)) {
		tmp = t_1 + (-4.0 * (t * a));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	tmp = 0
	if (a <= -5.4e+91) or not (a <= 1.8e+55):
		tmp = t_1 + (-4.0 * (t * a))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if ((a <= -5.4e+91) || !(a <= 1.8e+55))
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	tmp = 0.0;
	if ((a <= -5.4e+91) || ~((a <= 1.8e+55)))
		tmp = t_1 + (-4.0 * (t * a));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -5.4e+91], N[Not[LessEqual[a, 1.8e+55]], $MachinePrecision]], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4e91 or 1.79999999999999994e55 < a

   1. Initial program 80.9%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in a around inf 67.7%

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

      1. *-commutative 67.7%

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

   6. Simplified 67.7%

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

   if -5.4e91 < a < 1.79999999999999994e55

   1. Initial program 87.7%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in b around inf 51.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+91} \lor \neg \left(a \leq 1.8 \cdot 10^{+55}\right):\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 17: 34.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -4.6 \cdot 10^{-91} \lor \neg \left(k \leq 2.3 \cdot 10^{+135}\right):\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -4.6e-91) (not (<= k 2.3e+135))) (* (* j k) -27.0) (* b c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -4.6e-91) || !(k <= 2.3e+135)) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-4.6d-91)) .or. (.not. (k <= 2.3d+135))) then
        tmp = (j * k) * (-27.0d0)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -4.6e-91) || !(k <= 2.3e+135)) {
		tmp = (j * k) * -27.0;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -4.6e-91) or not (k <= 2.3e+135):
		tmp = (j * k) * -27.0
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -4.6e-91) || !(k <= 2.3e+135))
		tmp = Float64(Float64(j * k) * -27.0);
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -4.6e-91) || ~((k <= 2.3e+135)))
		tmp = (j * k) * -27.0;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -4.6e-91], N[Not[LessEqual[k, 2.3e+135]], $MachinePrecision]], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -4.59999999999999991e-91 or 2.3000000000000001e135 < k

   1. Initial program 82.6%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in j around inf 40.4%

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

   if -4.59999999999999991e-91 < k < 2.3000000000000001e135

   1. Initial program 87.5%

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

   3. Simplified 89.0%

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

      1. associate-*r* 89.7%

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

      2. distribute-rgt-out-- 87.5%

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

      3. associate-*l* 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

   5. Applied egg-rr 85.4%

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

   6. Taylor expanded in b around inf 26.1%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.6 \cdot 10^{-91} \lor \neg \left(k \leq 2.3 \cdot 10^{+135}\right):\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18: 34.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -5.2e-91)
   (* (* j k) -27.0)
   (if (<= k 2e+135) (* b c) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -5.2e-91) {
		tmp = (j * k) * -27.0;
	} else if (k <= 2e+135) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-5.2d-91)) then
        tmp = (j * k) * (-27.0d0)
    else if (k <= 2d+135) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -5.2e-91) {
		tmp = (j * k) * -27.0;
	} else if (k <= 2e+135) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -5.2e-91:
		tmp = (j * k) * -27.0
	elif k <= 2e+135:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -5.2e-91)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (k <= 2e+135)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -5.2e-91)
		tmp = (j * k) * -27.0;
	elseif (k <= 2e+135)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -5.2e-91], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[k, 2e+135], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -5.20000000000000028e-91

   1. Initial program 82.7%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in j around inf 34.7%

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

   if -5.20000000000000028e-91 < k < 1.99999999999999992e135

   1. Initial program 87.5%

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

   3. Simplified 89.0%

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

      1. associate-*r* 89.7%

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

      2. distribute-rgt-out-- 87.5%

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

      3. associate-*l* 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

   5. Applied egg-rr 85.4%

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

   6. Taylor expanded in b around inf 26.1%

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

   if 1.99999999999999992e135 < k

   1. Initial program 82.4%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in j around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-*r* 52.3%

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

      3. *-commutative 52.3%

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

   6. Simplified 52.3%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 2 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 19: 34.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -5.2e-91)
   (* (* j k) -27.0)
   (if (<= k 2.1e+135) (* b c) (* k (* j -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -5.2e-91) {
		tmp = (j * k) * -27.0;
	} else if (k <= 2.1e+135) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-5.2d-91)) then
        tmp = (j * k) * (-27.0d0)
    else if (k <= 2.1d+135) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -5.2e-91) {
		tmp = (j * k) * -27.0;
	} else if (k <= 2.1e+135) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -5.2e-91:
		tmp = (j * k) * -27.0
	elif k <= 2.1e+135:
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -5.2e-91)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (k <= 2.1e+135)
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -5.2e-91)
		tmp = (j * k) * -27.0;
	elseif (k <= 2.1e+135)
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -5.2e-91], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[k, 2.1e+135], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -5.20000000000000028e-91

   1. Initial program 82.7%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in j around inf 34.7%

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

   if -5.20000000000000028e-91 < k < 2.1000000000000001e135

   1. Initial program 87.5%

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

   3. Simplified 89.0%

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

      1. associate-*r* 89.7%

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

      2. distribute-rgt-out-- 87.5%

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

      3. associate-*l* 85.4%

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

      4. *-commutative 85.4%

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

      5. *-commutative 85.4%

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

   5. Applied egg-rr 85.4%

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

   6. Taylor expanded in b around inf 26.1%

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

   if 2.1000000000000001e135 < k

   1. Initial program 82.4%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in i around 0 74.8%

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

   5. Taylor expanded in j around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-*l* 52.4%

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

   7. Simplified 52.4%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 20: 24.1% accurate, 10.3× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 85.3%

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

   1. associate-*r* 87.5%

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

   2. distribute-rgt-out-- 85.2%

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

   3. associate-*l* 82.9%

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

   4. *-commutative 82.9%

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

   5. *-commutative 82.9%

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

5. Applied egg-rr 82.9%

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

6. Taylor expanded in b around inf 22.2%

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

7. Final simplification 22.2%

   \[\leadsto b \cdot c \]

Developer target: 89.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023331 
(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)))