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

Percentage Accurate: 85.4% → 91.9%

Time: 20.1s

Alternatives: 19

Speedup: 0.5×

• 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

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

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
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (-
    (+ (* b c) (* t (- (* z (* 18.0 (* x y))) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (* x (- (* 18.0 (* t (* y z))) (* 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 tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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 tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= Double.POSITIVE_INFINITY) {
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (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):
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= math.inf:
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (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)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(z * Float64(18.0 * Float64(x * y))) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - 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)
	tmp = 0.0;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= Inf)
		tmp = ((b * c) + (t * ((z * (18.0 * (x * y))) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (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_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(z * N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $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 #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 97.9%

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

   3. Simplified 95.9%

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

      1. pow1 95.9%

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

      2. associate-*r* 97.6%

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

      3. *-commutative 97.6%

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

      4. *-commutative 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. unpow1 97.6%

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

      2. *-commutative 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*r* 97.5%

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

   8. Simplified 97.5%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) 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 20.0%

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

   5. Taylor expanded in x around inf 70.0%

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

4. Final simplification 95.4%

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

Alternative 2: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-146}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-13}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} + j \cdot -27\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (+ (* j (* k -27.0)) (* a (* t -4.0))))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (* b c) (* x (* 4.0 i)))))
   (if (<= t_2 -4e+188)
     t_1
     (if (<= t_2 2e-146)
       t_3
       (if (<= t_2 1e-95)
         t_1
         (if (<= t_2 1e-13) t_3 (* k (+ (* 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 t_1 = (j * (k * -27.0)) + (a * (t * -4.0));
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (t_2 <= -4e+188) {
		tmp = t_1;
	} else if (t_2 <= 2e-146) {
		tmp = t_3;
	} else if (t_2 <= 1e-95) {
		tmp = t_1;
	} else if (t_2 <= 1e-13) {
		tmp = t_3;
	} else {
		tmp = k * ((b * (c / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    t_2 = (j * 27.0d0) * k
    t_3 = (b * c) - (x * (4.0d0 * i))
    if (t_2 <= (-4d+188)) then
        tmp = t_1
    else if (t_2 <= 2d-146) then
        tmp = t_3
    else if (t_2 <= 1d-95) then
        tmp = t_1
    else if (t_2 <= 1d-13) then
        tmp = t_3
    else
        tmp = k * ((b * (c / 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 t_1 = (j * (k * -27.0)) + (a * (t * -4.0));
	double t_2 = (j * 27.0) * k;
	double t_3 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (t_2 <= -4e+188) {
		tmp = t_1;
	} else if (t_2 <= 2e-146) {
		tmp = t_3;
	} else if (t_2 <= 1e-95) {
		tmp = t_1;
	} else if (t_2 <= 1e-13) {
		tmp = t_3;
	} else {
		tmp = k * ((b * (c / 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):
	t_1 = (j * (k * -27.0)) + (a * (t * -4.0))
	t_2 = (j * 27.0) * k
	t_3 = (b * c) - (x * (4.0 * i))
	tmp = 0
	if t_2 <= -4e+188:
		tmp = t_1
	elif t_2 <= 2e-146:
		tmp = t_3
	elif t_2 <= 1e-95:
		tmp = t_1
	elif t_2 <= 1e-13:
		tmp = t_3
	else:
		tmp = k * ((b * (c / 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)
	t_1 = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)))
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (t_2 <= -4e+188)
		tmp = t_1;
	elseif (t_2 <= 2e-146)
		tmp = t_3;
	elseif (t_2 <= 1e-95)
		tmp = t_1;
	elseif (t_2 <= 1e-13)
		tmp = t_3;
	else
		tmp = Float64(k * Float64(Float64(b * Float64(c / 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)
	t_1 = (j * (k * -27.0)) + (a * (t * -4.0));
	t_2 = (j * 27.0) * k;
	t_3 = (b * c) - (x * (4.0 * i));
	tmp = 0.0;
	if (t_2 <= -4e+188)
		tmp = t_1;
	elseif (t_2 <= 2e-146)
		tmp = t_3;
	elseif (t_2 <= 1e-95)
		tmp = t_1;
	elseif (t_2 <= 1e-13)
		tmp = t_3;
	else
		tmp = k * ((b * (c / 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_] := Block[{t$95$1 = N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+188], t$95$1, If[LessEqual[t$95$2, 2e-146], t$95$3, If[LessEqual[t$95$2, 1e-95], t$95$1, If[LessEqual[t$95$2, 1e-13], t$95$3, N[(k * N[(N[(b * N[(c / k), $MachinePrecision]), $MachinePrecision] + N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000001e188 or 2.00000000000000005e-146 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999989e-96

   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 87.5%

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

   5. Taylor expanded in a around inf 79.7%

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

      1. metadata-eval 79.7%

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

      2. distribute-lft-neg-in 79.7%

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

      3. *-commutative 79.7%

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

      4. associate-*l* 79.7%

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

      5. *-commutative 79.7%

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

      6. distribute-rgt-neg-in 79.7%

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

      7. distribute-lft-neg-in 79.7%

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

      8. metadata-eval 79.7%

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

   7. Simplified 79.7%

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

   if -4.0000000000000001e188 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.00000000000000005e-146 or 9.99999999999999989e-96 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e-13

   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 93.6%

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

   5. Taylor expanded in t around 0 62.5%

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

   6. Taylor expanded in i around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   8. Simplified 59.4%

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

   if 1e-13 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 87.0%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in t around 0 66.0%

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

   6. Taylor expanded in i around 0 59.7%

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

      1. associate-*r* 61.4%

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

      2. *-commutative 61.4%

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

      3. associate-*r* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in k around inf 61.3%

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

       1. cancel-sign-sub-inv 61.3%

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

       2. metadata-eval 61.3%

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

       3. associate-/l* 61.3%

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

       4. *-commutative 61.3%

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

   11. Simplified 61.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+188}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-146}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-95}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{-13}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} + j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+188}:\\ \;\;\;\;t\_1 + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-174}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

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 (* (* j 27.0) k)))
   (if (<= t_2 -4e+188)
     (+ t_1 (* a (* t -4.0)))
     (if (<= t_2 2e-174)
       (- (* b c) (* x (* 4.0 i)))
       (if (<= t_2 5e+101)
         (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
         (+ t_1 (* 18.0 (* z (* y (* x t))))))))))

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 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+188) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (t_2 <= 2e-174) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t_2 <= 5e+101) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = t_1 + (18.0 * (z * (y * (x * t))));
	}
	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 = (j * 27.0d0) * k
    if (t_2 <= (-4d+188)) then
        tmp = t_1 + (a * (t * (-4.0d0)))
    else if (t_2 <= 2d-174) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t_2 <= 5d+101) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else
        tmp = t_1 + (18.0d0 * (z * (y * (x * t))))
    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 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -4e+188) {
		tmp = t_1 + (a * (t * -4.0));
	} else if (t_2 <= 2e-174) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t_2 <= 5e+101) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = t_1 + (18.0 * (z * (y * (x * t))));
	}
	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 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -4e+188:
		tmp = t_1 + (a * (t * -4.0))
	elif t_2 <= 2e-174:
		tmp = (b * c) - (x * (4.0 * i))
	elif t_2 <= 5e+101:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	else:
		tmp = t_1 + (18.0 * (z * (y * (x * t))))
	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(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -4e+188)
		tmp = Float64(t_1 + Float64(a * Float64(t * -4.0)));
	elseif (t_2 <= 2e-174)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t_2 <= 5e+101)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(z * Float64(y * Float64(x * t)))));
	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 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -4e+188)
		tmp = t_1 + (a * (t * -4.0));
	elseif (t_2 <= 2e-174)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t_2 <= 5e+101)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	else
		tmp = t_1 + (18.0 * (z * (y * (x * t))));
	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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+188], N[(t$95$1 + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-174], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+101], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000001e188

   1. Initial program 87.9%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 78.8%

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

      1. metadata-eval 78.8%

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

      2. distribute-lft-neg-in 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-*l* 78.8%

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

      5. *-commutative 78.8%

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

      6. distribute-rgt-neg-in 78.8%

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

      7. distribute-lft-neg-in 78.8%

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

      8. metadata-eval 78.8%

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

   7. Simplified 78.8%

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

   if -4.0000000000000001e188 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-174

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 62.4%

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

   6. Taylor expanded in i around inf 58.8%

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

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   8. Simplified 58.8%

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

   if 2e-174 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999989e101

   1. Initial program 90.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 90.1%

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

      2. associate-*r* 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*r* 90.1%

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

      5. *-commutative 90.1%

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

      6. *-commutative 90.1%

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

   4. Applied egg-rr 90.1%

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

      1. unpow1 90.1%

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

      2. associate-*r* 92.6%

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

      3. *-commutative 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*r* 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in x around inf 54.7%

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

      1. cancel-sign-sub-inv 54.7%

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

      2. associate-*r* 59.6%

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

      3. metadata-eval 59.6%

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

   9. Simplified 59.6%

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

   if 4.99999999999999989e101 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 83.4%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in y around inf 64.9%

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

      1. pow1 64.9%

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

      2. *-commutative 64.9%

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

   7. Applied egg-rr 64.9%

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

      1. unpow1 64.9%

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

      2. associate-*r* 66.8%

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

      3. *-commutative 66.8%

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

      4. associate-*r* 75.1%

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

   9. Simplified 75.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+188}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-174}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ t_3 := t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+158}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \left(t\_1 - a \cdot 4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* 18.0 (* x (* y z))))
        (t_2
         (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k)))
        (t_3 (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))))
   (if (<= t -4.1e+158)
     t_3
     (if (<= t -1.3e+74)
       t_2
       (if (<= t -1.45e-31)
         (- (* t (- t_1 (* a 4.0))) (* 27.0 (* j k)))
         (if (<= t 5.2e+163) 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 = 18.0 * (x * (y * z));
	double t_2 = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double t_3 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (t <= -4.1e+158) {
		tmp = t_3;
	} else if (t <= -1.3e+74) {
		tmp = t_2;
	} else if (t <= -1.45e-31) {
		tmp = (t * (t_1 - (a * 4.0))) - (27.0 * (j * k));
	} else if (t <= 5.2e+163) {
		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 = 18.0d0 * (x * (y * z))
    t_2 = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    t_3 = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    if (t <= (-4.1d+158)) then
        tmp = t_3
    else if (t <= (-1.3d+74)) then
        tmp = t_2
    else if (t <= (-1.45d-31)) then
        tmp = (t * (t_1 - (a * 4.0d0))) - (27.0d0 * (j * k))
    else if (t <= 5.2d+163) 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 = 18.0 * (x * (y * z));
	double t_2 = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double t_3 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (t <= -4.1e+158) {
		tmp = t_3;
	} else if (t <= -1.3e+74) {
		tmp = t_2;
	} else if (t <= -1.45e-31) {
		tmp = (t * (t_1 - (a * 4.0))) - (27.0 * (j * k));
	} else if (t <= 5.2e+163) {
		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 = 18.0 * (x * (y * z))
	t_2 = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	t_3 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	tmp = 0
	if t <= -4.1e+158:
		tmp = t_3
	elif t <= -1.3e+74:
		tmp = t_2
	elif t <= -1.45e-31:
		tmp = (t * (t_1 - (a * 4.0))) - (27.0 * (j * k))
	elif t <= 5.2e+163:
		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(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	t_3 = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (t <= -4.1e+158)
		tmp = t_3;
	elseif (t <= -1.3e+74)
		tmp = t_2;
	elseif (t <= -1.45e-31)
		tmp = Float64(Float64(t * Float64(t_1 - Float64(a * 4.0))) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 5.2e+163)
		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 = 18.0 * (x * (y * z));
	t_2 = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	t_3 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	tmp = 0.0;
	if (t <= -4.1e+158)
		tmp = t_3;
	elseif (t <= -1.3e+74)
		tmp = t_2;
	elseif (t <= -1.45e-31)
		tmp = (t * (t_1 - (a * 4.0))) - (27.0 * (j * k));
	elseif (t <= 5.2e+163)
		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[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+158], t$95$3, If[LessEqual[t, -1.3e+74], t$95$2, If[LessEqual[t, -1.45e-31], N[(N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+163], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.10000000000000004e158 or 5.2000000000000003e163 < t

   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 87.4%

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

   5. Taylor expanded in t around inf 91.3%

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

   if -4.10000000000000004e158 < t < -1.3e74 or -1.45e-31 < t < 5.2000000000000003e163

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 91.4%

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

   if -1.3e74 < t < -1.45e-31

   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 89.9%

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

   5. Taylor expanded in i around 0 87.9%

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

   6. Taylor expanded in b around 0 84.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+74}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+163}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 30.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -6.6 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-221}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-197}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-99}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= c -6.6e-127)
     (* b c)
     (if (<= c -7.8e-221)
       (* 18.0 (* z (* y (* x t))))
       (if (<= c -7.2e-282)
         t_1
         (if (<= c 6.2e-197)
           (* k (* j -27.0))
           (if (<= c 2.2e-99)
             (* (* 18.0 t) (* z (* x y)))
             (if (<= c 1.3e+15)
               t_1
               (if (<= c 7.5e+136) (* 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 t_1 = -4.0 * (x * i);
	double tmp;
	if (c <= -6.6e-127) {
		tmp = b * c;
	} else if (c <= -7.8e-221) {
		tmp = 18.0 * (z * (y * (x * t)));
	} else if (c <= -7.2e-282) {
		tmp = t_1;
	} else if (c <= 6.2e-197) {
		tmp = k * (j * -27.0);
	} else if (c <= 2.2e-99) {
		tmp = (18.0 * t) * (z * (x * y));
	} else if (c <= 1.3e+15) {
		tmp = t_1;
	} else if (c <= 7.5e+136) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (c <= (-6.6d-127)) then
        tmp = b * c
    else if (c <= (-7.8d-221)) then
        tmp = 18.0d0 * (z * (y * (x * t)))
    else if (c <= (-7.2d-282)) then
        tmp = t_1
    else if (c <= 6.2d-197) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 2.2d-99) then
        tmp = (18.0d0 * t) * (z * (x * y))
    else if (c <= 1.3d+15) then
        tmp = t_1
    else if (c <= 7.5d+136) 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 t_1 = -4.0 * (x * i);
	double tmp;
	if (c <= -6.6e-127) {
		tmp = b * c;
	} else if (c <= -7.8e-221) {
		tmp = 18.0 * (z * (y * (x * t)));
	} else if (c <= -7.2e-282) {
		tmp = t_1;
	} else if (c <= 6.2e-197) {
		tmp = k * (j * -27.0);
	} else if (c <= 2.2e-99) {
		tmp = (18.0 * t) * (z * (x * y));
	} else if (c <= 1.3e+15) {
		tmp = t_1;
	} else if (c <= 7.5e+136) {
		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):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if c <= -6.6e-127:
		tmp = b * c
	elif c <= -7.8e-221:
		tmp = 18.0 * (z * (y * (x * t)))
	elif c <= -7.2e-282:
		tmp = t_1
	elif c <= 6.2e-197:
		tmp = k * (j * -27.0)
	elif c <= 2.2e-99:
		tmp = (18.0 * t) * (z * (x * y))
	elif c <= 1.3e+15:
		tmp = t_1
	elif c <= 7.5e+136:
		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)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (c <= -6.6e-127)
		tmp = Float64(b * c);
	elseif (c <= -7.8e-221)
		tmp = Float64(18.0 * Float64(z * Float64(y * Float64(x * t))));
	elseif (c <= -7.2e-282)
		tmp = t_1;
	elseif (c <= 6.2e-197)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 2.2e-99)
		tmp = Float64(Float64(18.0 * t) * Float64(z * Float64(x * y)));
	elseif (c <= 1.3e+15)
		tmp = t_1;
	elseif (c <= 7.5e+136)
		tmp = Float64(j * Float64(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)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (c <= -6.6e-127)
		tmp = b * c;
	elseif (c <= -7.8e-221)
		tmp = 18.0 * (z * (y * (x * t)));
	elseif (c <= -7.2e-282)
		tmp = t_1;
	elseif (c <= 6.2e-197)
		tmp = k * (j * -27.0);
	elseif (c <= 2.2e-99)
		tmp = (18.0 * t) * (z * (x * y));
	elseif (c <= 1.3e+15)
		tmp = t_1;
	elseif (c <= 7.5e+136)
		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_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.6e-127], N[(b * c), $MachinePrecision], If[LessEqual[c, -7.8e-221], N[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.2e-282], t$95$1, If[LessEqual[c, 6.2e-197], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-99], N[(N[(18.0 * t), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e+15], t$95$1, If[LessEqual[c, 7.5e+136], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.59999999999999961e-127 or 7.5000000000000002e136 < c

   1. Initial program 92.6%

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

   3. Simplified 89.3%

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

      1. pow1 89.3%

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

      2. associate-*r* 91.8%

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

      3. *-commutative 91.8%

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

      4. *-commutative 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. unpow1 91.8%

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

      2. *-commutative 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*r* 91.8%

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

   8. Simplified 91.8%

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

   9. Taylor expanded in b around inf 37.1%

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

   if -6.59999999999999961e-127 < c < -7.7999999999999997e-221

   1. Initial program 82.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 82.7%

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

      2. associate-*r* 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. *-commutative 82.7%

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

   4. Applied egg-rr 82.7%

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

      1. unpow1 82.7%

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

      2. associate-*r* 79.0%

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

      3. *-commutative 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-*r* 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in x around inf 45.8%

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

      1. cancel-sign-sub-inv 45.8%

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

      2. associate-*r* 50.0%

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

      3. metadata-eval 50.0%

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

   9. Simplified 50.0%

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

   10. Taylor expanded in t around inf 36.3%

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

       1. associate-*r* 36.5%

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

       2. associate-*r* 40.3%

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

   12. Simplified 40.3%

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

   if -7.7999999999999997e-221 < c < -7.1999999999999995e-282 or 2.20000000000000004e-99 < c < 1.3e15

   1. Initial program 89.1%

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

   3. Simplified 94.7%

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

      1. pow1 94.7%

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

      2. associate-*r* 92.0%

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

      3. *-commutative 92.0%

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

      4. *-commutative 92.0%

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

   6. Applied egg-rr 92.0%

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

      1. unpow1 92.0%

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

      2. *-commutative 92.0%

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

      3. *-commutative 92.0%

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

      4. associate-*r* 92.0%

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

   8. Simplified 92.0%

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

   9. Taylor expanded in i around inf 31.9%

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

       1. *-commutative 31.9%

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

   11. Simplified 31.9%

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

   if -7.1999999999999995e-282 < c < 6.20000000000000057e-197

   1. Initial program 96.1%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in j around inf 37.2%

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

      1. associate-*r* 37.2%

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

   7. Simplified 37.2%

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

   if 6.20000000000000057e-197 < c < 2.20000000000000004e-99

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 86.9%

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

      2. associate-*r* 86.9%

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

      3. *-commutative 86.9%

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

      4. associate-*r* 86.9%

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

      5. *-commutative 86.9%

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

      6. *-commutative 86.9%

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

   4. Applied egg-rr 86.9%

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

      1. unpow1 86.9%

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

      2. associate-*r* 86.9%

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

      3. *-commutative 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-*r* 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 58.2%

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

      1. cancel-sign-sub-inv 58.2%

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

      2. associate-*r* 58.2%

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

      3. metadata-eval 58.2%

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

   9. Simplified 58.2%

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

   10. Taylor expanded in t around inf 48.6%

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

       1. associate-*r* 48.6%

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

       2. associate-*r* 48.6%

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

   12. Simplified 48.6%

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

   if 1.3e15 < c < 7.5000000000000002e136

   1. Initial program 85.3%

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

   3. Simplified 85.4%

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

      1. pow1 85.4%

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

      2. associate-*r* 89.0%

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

      3. *-commutative 89.0%

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

      4. *-commutative 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. unpow1 89.0%

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

      2. *-commutative 89.0%

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

      3. *-commutative 89.0%

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

      4. associate-*r* 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in j around inf 27.5%

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

       1. *-commutative 27.5%

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

       2. associate-*r* 27.5%

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

   11. Simplified 27.5%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-221}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-282}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-197}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-99}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+15}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-197}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* z (* y (* x t))))) (t_2 (* -4.0 (* x i))))
   (if (<= c -8.2e-127)
     (* b c)
     (if (<= c -6.2e-221)
       t_1
       (if (<= c -4.5e-283)
         t_2
         (if (<= c 3.6e-197)
           (* k (* j -27.0))
           (if (<= c 2.7e-99)
             t_1
             (if (<= c 2.25e+15)
               t_2
               (if (<= c 8e+136) (* 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 t_1 = 18.0 * (z * (y * (x * t)));
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (c <= -8.2e-127) {
		tmp = b * c;
	} else if (c <= -6.2e-221) {
		tmp = t_1;
	} else if (c <= -4.5e-283) {
		tmp = t_2;
	} else if (c <= 3.6e-197) {
		tmp = k * (j * -27.0);
	} else if (c <= 2.7e-99) {
		tmp = t_1;
	} else if (c <= 2.25e+15) {
		tmp = t_2;
	} else if (c <= 8e+136) {
		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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (z * (y * (x * t)))
    t_2 = (-4.0d0) * (x * i)
    if (c <= (-8.2d-127)) then
        tmp = b * c
    else if (c <= (-6.2d-221)) then
        tmp = t_1
    else if (c <= (-4.5d-283)) then
        tmp = t_2
    else if (c <= 3.6d-197) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 2.7d-99) then
        tmp = t_1
    else if (c <= 2.25d+15) then
        tmp = t_2
    else if (c <= 8d+136) 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 t_1 = 18.0 * (z * (y * (x * t)));
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (c <= -8.2e-127) {
		tmp = b * c;
	} else if (c <= -6.2e-221) {
		tmp = t_1;
	} else if (c <= -4.5e-283) {
		tmp = t_2;
	} else if (c <= 3.6e-197) {
		tmp = k * (j * -27.0);
	} else if (c <= 2.7e-99) {
		tmp = t_1;
	} else if (c <= 2.25e+15) {
		tmp = t_2;
	} else if (c <= 8e+136) {
		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):
	t_1 = 18.0 * (z * (y * (x * t)))
	t_2 = -4.0 * (x * i)
	tmp = 0
	if c <= -8.2e-127:
		tmp = b * c
	elif c <= -6.2e-221:
		tmp = t_1
	elif c <= -4.5e-283:
		tmp = t_2
	elif c <= 3.6e-197:
		tmp = k * (j * -27.0)
	elif c <= 2.7e-99:
		tmp = t_1
	elif c <= 2.25e+15:
		tmp = t_2
	elif c <= 8e+136:
		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)
	t_1 = Float64(18.0 * Float64(z * Float64(y * Float64(x * t))))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (c <= -8.2e-127)
		tmp = Float64(b * c);
	elseif (c <= -6.2e-221)
		tmp = t_1;
	elseif (c <= -4.5e-283)
		tmp = t_2;
	elseif (c <= 3.6e-197)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 2.7e-99)
		tmp = t_1;
	elseif (c <= 2.25e+15)
		tmp = t_2;
	elseif (c <= 8e+136)
		tmp = Float64(j * Float64(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)
	t_1 = 18.0 * (z * (y * (x * t)));
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if (c <= -8.2e-127)
		tmp = b * c;
	elseif (c <= -6.2e-221)
		tmp = t_1;
	elseif (c <= -4.5e-283)
		tmp = t_2;
	elseif (c <= 3.6e-197)
		tmp = k * (j * -27.0);
	elseif (c <= 2.7e-99)
		tmp = t_1;
	elseif (c <= 2.25e+15)
		tmp = t_2;
	elseif (c <= 8e+136)
		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_] := Block[{t$95$1 = N[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e-127], N[(b * c), $MachinePrecision], If[LessEqual[c, -6.2e-221], t$95$1, If[LessEqual[c, -4.5e-283], t$95$2, If[LessEqual[c, 3.6e-197], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e-99], t$95$1, If[LessEqual[c, 2.25e+15], t$95$2, If[LessEqual[c, 8e+136], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -8.199999999999999e-127 or 8.00000000000000047e136 < c

   1. Initial program 92.6%

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

   3. Simplified 89.3%

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

      1. pow1 89.3%

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

      2. associate-*r* 91.8%

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

      3. *-commutative 91.8%

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

      4. *-commutative 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. unpow1 91.8%

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

      2. *-commutative 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*r* 91.8%

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

   8. Simplified 91.8%

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

   9. Taylor expanded in b around inf 37.1%

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

   if -8.199999999999999e-127 < c < -6.1999999999999998e-221 or 3.5999999999999998e-197 < c < 2.7e-99

   1. Initial program 84.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 84.8%

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

      2. associate-*r* 82.8%

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

      3. *-commutative 82.8%

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

      4. associate-*r* 84.8%

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

      5. *-commutative 84.8%

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

      6. *-commutative 84.8%

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

   4. Applied egg-rr 84.8%

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

      1. unpow1 84.8%

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

      2. associate-*r* 82.9%

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

      3. *-commutative 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-*r* 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in x around inf 52.0%

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

      1. cancel-sign-sub-inv 52.0%

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

      2. associate-*r* 54.1%

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

      3. metadata-eval 54.1%

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

   9. Simplified 54.1%

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

   10. Taylor expanded in t around inf 42.5%

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

       1. associate-*r* 42.5%

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

       2. associate-*r* 44.5%

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

   12. Simplified 44.5%

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

   if -6.1999999999999998e-221 < c < -4.4999999999999997e-283 or 2.7e-99 < c < 2.25e15

   1. Initial program 89.1%

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

   3. Simplified 94.7%

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

      1. pow1 94.7%

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

      2. associate-*r* 92.0%

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

      3. *-commutative 92.0%

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

      4. *-commutative 92.0%

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

   6. Applied egg-rr 92.0%

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

      1. unpow1 92.0%

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

      2. *-commutative 92.0%

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

      3. *-commutative 92.0%

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

      4. associate-*r* 92.0%

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

   8. Simplified 92.0%

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

   9. Taylor expanded in i around inf 31.9%

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

       1. *-commutative 31.9%

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

   11. Simplified 31.9%

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

   if -4.4999999999999997e-283 < c < 3.5999999999999998e-197

   1. Initial program 96.1%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in j around inf 37.2%

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

      1. associate-*r* 37.2%

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

   7. Simplified 37.2%

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

   if 2.25e15 < c < 8.00000000000000047e136

   1. Initial program 85.3%

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

   3. Simplified 85.4%

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

      1. pow1 85.4%

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

      2. associate-*r* 89.0%

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

      3. *-commutative 89.0%

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

      4. *-commutative 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. unpow1 89.0%

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

      2. *-commutative 89.0%

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

      3. *-commutative 89.0%

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

      4. associate-*r* 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in j around inf 27.5%

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

       1. *-commutative 27.5%

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

       2. associate-*r* 27.5%

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

   11. Simplified 27.5%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{-127}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-283}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-197}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-99}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{+15}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+188}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-174}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} + j \cdot -27\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -4e+188)
     (+ (* j (* k -27.0)) (* a (* t -4.0)))
     (if (<= t_1 2e-174)
       (- (* b c) (* x (* 4.0 i)))
       (if (<= t_1 2e+156)
         (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
         (* k (+ (* 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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -4e+188) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if (t_1 <= 2e-174) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t_1 <= 2e+156) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = k * ((b * (c / 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) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-4d+188)) then
        tmp = (j * (k * (-27.0d0))) + (a * (t * (-4.0d0)))
    else if (t_1 <= 2d-174) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t_1 <= 2d+156) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else
        tmp = k * ((b * (c / 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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -4e+188) {
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	} else if (t_1 <= 2e-174) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t_1 <= 2e+156) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = k * ((b * (c / 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):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -4e+188:
		tmp = (j * (k * -27.0)) + (a * (t * -4.0))
	elif t_1 <= 2e-174:
		tmp = (b * c) - (x * (4.0 * i))
	elif t_1 <= 2e+156:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	else:
		tmp = k * ((b * (c / 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)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -4e+188)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(a * Float64(t * -4.0)));
	elseif (t_1 <= 2e-174)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t_1 <= 2e+156)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	else
		tmp = Float64(k * Float64(Float64(b * Float64(c / 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)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -4e+188)
		tmp = (j * (k * -27.0)) + (a * (t * -4.0));
	elseif (t_1 <= 2e-174)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t_1 <= 2e+156)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	else
		tmp = k * ((b * (c / 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_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+188], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-174], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+156], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(N[(b * N[(c / k), $MachinePrecision]), $MachinePrecision] + N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000001e188

   1. Initial program 87.9%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 78.8%

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

      1. metadata-eval 78.8%

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

      2. distribute-lft-neg-in 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-*l* 78.8%

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

      5. *-commutative 78.8%

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

      6. distribute-rgt-neg-in 78.8%

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

      7. distribute-lft-neg-in 78.8%

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

      8. metadata-eval 78.8%

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

   7. Simplified 78.8%

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

   if -4.0000000000000001e188 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e-174

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 62.4%

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

   6. Taylor expanded in i around inf 58.8%

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

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   8. Simplified 58.8%

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

   if 2e-174 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e156

   1. Initial program 89.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 89.4%

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

      2. associate-*r* 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*r* 89.4%

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

      5. *-commutative 89.4%

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

      6. *-commutative 89.4%

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

   4. Applied egg-rr 89.4%

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

      1. unpow1 89.4%

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

      2. associate-*r* 91.6%

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

      3. *-commutative 91.6%

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

      4. *-commutative 91.6%

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

      5. associate-*r* 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in x around inf 55.2%

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

      1. cancel-sign-sub-inv 55.2%

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

      2. associate-*r* 59.4%

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

      3. metadata-eval 59.4%

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

   9. Simplified 59.4%

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

   if 2e156 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 82.9%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in t around 0 73.4%

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

   6. Taylor expanded in i around 0 71.1%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in k around inf 71.1%

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

       1. cancel-sign-sub-inv 71.1%

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

       2. metadata-eval 71.1%

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

       3. associate-/l* 71.1%

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

       4. *-commutative 71.1%

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

   11. Simplified 71.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+188}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{-174}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(b \cdot \frac{c}{k} + j \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+155} \lor \neg \left(t \leq -3.8 \cdot 10^{+74} \lor \neg \left(t \leq -7 \cdot 10^{-32}\right) \land t \leq 2 \cdot 10^{+162}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

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 (or (<= t -1.95e+155)
         (not (or (<= t -3.8e+74) (and (not (<= t -7e-32)) (<= t 2e+162)))))
   (+ (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))) (* j (* k -27.0)))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x 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 tmp;
	if ((t <= -1.95e+155) || !((t <= -3.8e+74) || (!(t <= -7e-32) && (t <= 2e+162)))) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	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 <= (-1.95d+155)) .or. (.not. (t <= (-3.8d+74)) .or. (.not. (t <= (-7d-32))) .and. (t <= 2d+162))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    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 <= -1.95e+155) || !((t <= -3.8e+74) || (!(t <= -7e-32) && (t <= 2e+162)))) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * 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):
	tmp = 0
	if (t <= -1.95e+155) or not ((t <= -3.8e+74) or (not (t <= -7e-32) and (t <= 2e+162))):
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * 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)
	tmp = 0.0
	if ((t <= -1.95e+155) || !((t <= -3.8e+74) || (!(t <= -7e-32) && (t <= 2e+162))))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * 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)
	tmp = 0.0;
	if ((t <= -1.95e+155) || ~(((t <= -3.8e+74) || (~((t <= -7e-32)) && (t <= 2e+162)))))
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * 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_] := If[Or[LessEqual[t, -1.95e+155], N[Not[Or[LessEqual[t, -3.8e+74], And[N[Not[LessEqual[t, -7e-32]], $MachinePrecision], LessEqual[t, 2e+162]]]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9499999999999999e155 or -3.7999999999999998e74 < t < -6.9999999999999997e-32 or 1.9999999999999999e162 < t

   1. Initial program 84.6%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t around inf 89.0%

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

   if -1.9499999999999999e155 < t < -3.7999999999999998e74 or -6.9999999999999997e-32 < t < 1.9999999999999999e162

   1. Initial program 93.1%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in t around 0 82.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+155} \lor \neg \left(t \leq -3.8 \cdot 10^{+74} \lor \neg \left(t \leq -7 \cdot 10^{-32}\right) \land t \leq 2 \cdot 10^{+162}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c - \left(t\_2 + 4 \cdot \left(x \cdot i\right)\right)\\ t_4 := t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+155}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(t\_1 - a \cdot 4\right) - t\_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+162}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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 (* x (* y z))))
        (t_2 (* 27.0 (* j k)))
        (t_3 (- (* b c) (+ t_2 (* 4.0 (* x i)))))
        (t_4 (+ (* t (+ t_1 (* a -4.0))) (* j (* k -27.0)))))
   (if (<= t -2.3e+155)
     t_4
     (if (<= t -1.7e+74)
       t_3
       (if (<= t -4.4e-32)
         (- (* t (- t_1 (* a 4.0))) t_2)
         (if (<= t 2e+162) t_3 t_4))))))

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 * (x * (y * z));
	double t_2 = 27.0 * (j * k);
	double t_3 = (b * c) - (t_2 + (4.0 * (x * i)));
	double t_4 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (t <= -2.3e+155) {
		tmp = t_4;
	} else if (t <= -1.7e+74) {
		tmp = t_3;
	} else if (t <= -4.4e-32) {
		tmp = (t * (t_1 - (a * 4.0))) - t_2;
	} else if (t <= 2e+162) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 = 18.0d0 * (x * (y * z))
    t_2 = 27.0d0 * (j * k)
    t_3 = (b * c) - (t_2 + (4.0d0 * (x * i)))
    t_4 = (t * (t_1 + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    if (t <= (-2.3d+155)) then
        tmp = t_4
    else if (t <= (-1.7d+74)) then
        tmp = t_3
    else if (t <= (-4.4d-32)) then
        tmp = (t * (t_1 - (a * 4.0d0))) - t_2
    else if (t <= 2d+162) then
        tmp = t_3
    else
        tmp = t_4
    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 * (x * (y * z));
	double t_2 = 27.0 * (j * k);
	double t_3 = (b * c) - (t_2 + (4.0 * (x * i)));
	double t_4 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	double tmp;
	if (t <= -2.3e+155) {
		tmp = t_4;
	} else if (t <= -1.7e+74) {
		tmp = t_3;
	} else if (t <= -4.4e-32) {
		tmp = (t * (t_1 - (a * 4.0))) - t_2;
	} else if (t <= 2e+162) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 * (x * (y * z))
	t_2 = 27.0 * (j * k)
	t_3 = (b * c) - (t_2 + (4.0 * (x * i)))
	t_4 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0))
	tmp = 0
	if t <= -2.3e+155:
		tmp = t_4
	elif t <= -1.7e+74:
		tmp = t_3
	elif t <= -4.4e-32:
		tmp = (t * (t_1 - (a * 4.0))) - t_2
	elif t <= 2e+162:
		tmp = t_3
	else:
		tmp = t_4
	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(x * Float64(y * z)))
	t_2 = Float64(27.0 * Float64(j * k))
	t_3 = Float64(Float64(b * c) - Float64(t_2 + Float64(4.0 * Float64(x * i))))
	t_4 = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (t <= -2.3e+155)
		tmp = t_4;
	elseif (t <= -1.7e+74)
		tmp = t_3;
	elseif (t <= -4.4e-32)
		tmp = Float64(Float64(t * Float64(t_1 - Float64(a * 4.0))) - t_2);
	elseif (t <= 2e+162)
		tmp = t_3;
	else
		tmp = t_4;
	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 * (x * (y * z));
	t_2 = 27.0 * (j * k);
	t_3 = (b * c) - (t_2 + (4.0 * (x * i)));
	t_4 = (t * (t_1 + (a * -4.0))) + (j * (k * -27.0));
	tmp = 0.0;
	if (t <= -2.3e+155)
		tmp = t_4;
	elseif (t <= -1.7e+74)
		tmp = t_3;
	elseif (t <= -4.4e-32)
		tmp = (t * (t_1 - (a * 4.0))) - t_2;
	elseif (t <= 2e+162)
		tmp = t_3;
	else
		tmp = t_4;
	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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(t$95$2 + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+155], t$95$4, If[LessEqual[t, -1.7e+74], t$95$3, If[LessEqual[t, -4.4e-32], N[(N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 2e+162], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.29999999999999998e155 or 1.9999999999999999e162 < t

   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 87.4%

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

   5. Taylor expanded in t around inf 91.3%

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

   if -2.29999999999999998e155 < t < -1.7e74 or -4.4e-32 < t < 1.9999999999999999e162

   1. Initial program 93.1%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in t around 0 82.3%

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

   if -1.7e74 < t < -4.4e-32

   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 89.9%

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

   5. Taylor expanded in i around 0 87.9%

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

   6. Taylor expanded in b around 0 84.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+162}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+210}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+66}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{+278}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -2e+210)
   (- (+ (* b c) (* (* t a) -4.0)) (* 27.0 (* j k)))
   (if (<= (* b c) 2e+66)
     (- (* -4.0 (+ (* t a) (* x i))) (* (* j 27.0) k))
     (if (<= (* b c) 1e+278)
       (+ (* j (* k -27.0)) (* 18.0 (* z (* y (* x t)))))
       (- (* b c) (* x (* 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 tmp;
	if ((b * c) <= -2e+210) {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	} else if ((b * c) <= 2e+66) {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	} else if ((b * c) <= 1e+278) {
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	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 ((b * c) <= (-2d+210)) then
        tmp = ((b * c) + ((t * a) * (-4.0d0))) - (27.0d0 * (j * k))
    else if ((b * c) <= 2d+66) then
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - ((j * 27.0d0) * k)
    else if ((b * c) <= 1d+278) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (z * (y * (x * t))))
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    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 ((b * c) <= -2e+210) {
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	} else if ((b * c) <= 2e+66) {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	} else if ((b * c) <= 1e+278) {
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))));
	} else {
		tmp = (b * c) - (x * (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):
	tmp = 0
	if (b * c) <= -2e+210:
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k))
	elif (b * c) <= 2e+66:
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k)
	elif (b * c) <= 1e+278:
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))))
	else:
		tmp = (b * c) - (x * (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)
	tmp = 0.0
	if (Float64(b * c) <= -2e+210)
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(t * a) * -4.0)) - Float64(27.0 * Float64(j * k)));
	elseif (Float64(b * c) <= 2e+66)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= 1e+278)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(z * Float64(y * Float64(x * t)))));
	else
		tmp = Float64(Float64(b * c) - Float64(x * 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)
	tmp = 0.0;
	if ((b * c) <= -2e+210)
		tmp = ((b * c) + ((t * a) * -4.0)) - (27.0 * (j * k));
	elseif ((b * c) <= 2e+66)
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	elseif ((b * c) <= 1e+278)
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))));
	else
		tmp = (b * c) - (x * (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_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+210], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+66], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+278], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999985e210

   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 79.3%

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

   5. Taylor expanded in x around 0 79.6%

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

   if -1.99999999999999985e210 < (*.f64 b c) < 1.99999999999999989e66

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 82.5%

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

   4. Taylor expanded in b around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-lft-out 77.3%

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

      3. distribute-lft-neg-in 77.3%

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

      4. metadata-eval 77.3%

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

   6. Simplified 77.3%

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

   if 1.99999999999999989e66 < (*.f64 b c) < 9.99999999999999964e277

   1. Initial program 86.7%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around inf 60.2%

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

      1. pow1 60.2%

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

      2. *-commutative 60.2%

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

   7. Applied egg-rr 60.2%

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

      1. unpow1 60.2%

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

      2. associate-*r* 60.3%

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

      3. *-commutative 60.3%

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

      4. associate-*r* 66.5%

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

   9. Simplified 66.5%

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

   if 9.99999999999999964e277 < (*.f64 b c)

   1. Initial program 90.5%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+210}:\\ \;\;\;\;\left(b \cdot c + \left(t \cdot a\right) \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+66}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{+278}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+199}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+66}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{+278}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (<= (* b c) -5e+199)
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))
   (if (<= (* b c) 2e+66)
     (- (* -4.0 (+ (* t a) (* x i))) (* (* j 27.0) k))
     (if (<= (* b c) 1e+278)
       (+ (* j (* k -27.0)) (* 18.0 (* z (* y (* x t)))))
       (- (* b c) (* x (* 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 tmp;
	if ((b * c) <= -5e+199) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else if ((b * c) <= 2e+66) {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	} else if ((b * c) <= 1e+278) {
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	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 ((b * c) <= (-5d+199)) then
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    else if ((b * c) <= 2d+66) then
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - ((j * 27.0d0) * k)
    else if ((b * c) <= 1d+278) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (z * (y * (x * t))))
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    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 ((b * c) <= -5e+199) {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	} else if ((b * c) <= 2e+66) {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	} else if ((b * c) <= 1e+278) {
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))));
	} else {
		tmp = (b * c) - (x * (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):
	tmp = 0
	if (b * c) <= -5e+199:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	elif (b * c) <= 2e+66:
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k)
	elif (b * c) <= 1e+278:
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))))
	else:
		tmp = (b * c) - (x * (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)
	tmp = 0.0
	if (Float64(b * c) <= -5e+199)
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	elseif (Float64(b * c) <= 2e+66)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= 1e+278)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(z * Float64(y * Float64(x * t)))));
	else
		tmp = Float64(Float64(b * c) - Float64(x * 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)
	tmp = 0.0;
	if ((b * c) <= -5e+199)
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	elseif ((b * c) <= 2e+66)
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	elseif ((b * c) <= 1e+278)
		tmp = (j * (k * -27.0)) + (18.0 * (z * (y * (x * t))));
	else
		tmp = (b * c) - (x * (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_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+199], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+66], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+278], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.9999999999999998e199

   1. Initial program 83.3%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in t around 0 76.8%

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

   if -4.9999999999999998e199 < (*.f64 b c) < 1.99999999999999989e66

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 82.4%

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

   4. Taylor expanded in b around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-lft-out 77.2%

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

      3. distribute-lft-neg-in 77.2%

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

      4. metadata-eval 77.2%

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

   6. Simplified 77.2%

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

   if 1.99999999999999989e66 < (*.f64 b c) < 9.99999999999999964e277

   1. Initial program 86.7%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around inf 60.2%

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

      1. pow1 60.2%

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

      2. *-commutative 60.2%

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

   7. Applied egg-rr 60.2%

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

      1. unpow1 60.2%

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

      2. associate-*r* 60.3%

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

      3. *-commutative 60.3%

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

      4. associate-*r* 66.5%

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

   9. Simplified 66.5%

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

   if 9.99999999999999964e277 < (*.f64 b c)

   1. Initial program 90.5%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+199}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+66}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{+278}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+210}:\\ \;\;\;\;b \cdot c + t\_1\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+66}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{+278}:\\ \;\;\;\;t\_1 + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

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 (* j (* k -27.0))))
   (if (<= (* b c) -2e+210)
     (+ (* b c) t_1)
     (if (<= (* b c) 2e+66)
       (- (* -4.0 (+ (* t a) (* x i))) (* (* j 27.0) k))
       (if (<= (* b c) 1e+278)
         (+ t_1 (* 18.0 (* z (* y (* x t)))))
         (- (* b c) (* x (* 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 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -2e+210) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 2e+66) {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	} else if ((b * c) <= 1e+278) {
		tmp = t_1 + (18.0 * (z * (y * (x * t))));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	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 ((b * c) <= (-2d+210)) then
        tmp = (b * c) + t_1
    else if ((b * c) <= 2d+66) then
        tmp = ((-4.0d0) * ((t * a) + (x * i))) - ((j * 27.0d0) * k)
    else if ((b * c) <= 1d+278) then
        tmp = t_1 + (18.0d0 * (z * (y * (x * t))))
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    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 ((b * c) <= -2e+210) {
		tmp = (b * c) + t_1;
	} else if ((b * c) <= 2e+66) {
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	} else if ((b * c) <= 1e+278) {
		tmp = t_1 + (18.0 * (z * (y * (x * t))));
	} else {
		tmp = (b * c) - (x * (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 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -2e+210:
		tmp = (b * c) + t_1
	elif (b * c) <= 2e+66:
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k)
	elif (b * c) <= 1e+278:
		tmp = t_1 + (18.0 * (z * (y * (x * t))))
	else:
		tmp = (b * c) - (x * (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(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -2e+210)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (Float64(b * c) <= 2e+66)
		tmp = Float64(Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= 1e+278)
		tmp = Float64(t_1 + Float64(18.0 * Float64(z * Float64(y * Float64(x * t)))));
	else
		tmp = Float64(Float64(b * c) - Float64(x * 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 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -2e+210)
		tmp = (b * c) + t_1;
	elseif ((b * c) <= 2e+66)
		tmp = (-4.0 * ((t * a) + (x * i))) - ((j * 27.0) * k);
	elseif ((b * c) <= 1e+278)
		tmp = t_1 + (18.0 * (z * (y * (x * t))));
	else
		tmp = (b * c) - (x * (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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -2e+210], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+66], N[(N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+278], N[(t$95$1 + N[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.99999999999999985e210

   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 79.3%

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

   5. Taylor expanded in b around inf 72.9%

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

   if -1.99999999999999985e210 < (*.f64 b c) < 1.99999999999999989e66

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 82.5%

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

   4. Taylor expanded in b around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-lft-out 77.3%

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

      3. distribute-lft-neg-in 77.3%

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

      4. metadata-eval 77.3%

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

   6. Simplified 77.3%

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

   if 1.99999999999999989e66 < (*.f64 b c) < 9.99999999999999964e277

   1. Initial program 86.7%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around inf 60.2%

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

      1. pow1 60.2%

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

      2. *-commutative 60.2%

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

   7. Applied egg-rr 60.2%

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

      1. unpow1 60.2%

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

      2. associate-*r* 60.3%

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

      3. *-commutative 60.3%

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

      4. associate-*r* 66.5%

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

   9. Simplified 66.5%

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

   if 9.99999999999999964e277 < (*.f64 b c)

   1. Initial program 90.5%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around 0 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+210}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+66}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 10^{+278}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-34}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t\_1 - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+162}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 18.0 (* x (* y z)))))
   (if (<= t -6.2e-34)
     (- (+ (* b c) (* t (- t_1 (* a 4.0)))) (* 27.0 (* j k)))
     (if (<= t 3.4e+162)
       (- (- (- (* b c) (* 4.0 (* t a))) (* (* x 4.0) i)) (* (* j 27.0) k))
       (+ (* t (+ t_1 (* a -4.0))) (* 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 t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -6.2e-34) {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 3.4e+162) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = (t * (t_1 + (a * -4.0))) + (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) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (y * z))
    if (t <= (-6.2d-34)) then
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else if (t <= 3.4d+162) then
        tmp = (((b * c) - (4.0d0 * (t * a))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = (t * (t_1 + (a * (-4.0d0)))) + (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 t_1 = 18.0 * (x * (y * z));
	double tmp;
	if (t <= -6.2e-34) {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	} else if (t <= 3.4e+162) {
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = (t * (t_1 + (a * -4.0))) + (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):
	t_1 = 18.0 * (x * (y * z))
	tmp = 0
	if t <= -6.2e-34:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k))
	elif t <= 3.4e+162:
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = (t * (t_1 + (a * -4.0))) + (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)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	tmp = 0.0
	if (t <= -6.2e-34)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 3.4e+162)
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + 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)
	t_1 = 18.0 * (x * (y * z));
	tmp = 0.0;
	if (t <= -6.2e-34)
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - (27.0 * (j * k));
	elseif (t <= 3.4e+162)
		tmp = (((b * c) - (4.0 * (t * a))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = (t * (t_1 + (a * -4.0))) + (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_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e-34], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+162], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.1999999999999996e-34

   1. Initial program 88.6%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in i around 0 86.6%

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

   if -6.1999999999999996e-34 < t < 3.40000000000000003e162

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 91.1%

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

   if 3.40000000000000003e162 < t

   1. Initial program 83.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around inf 90.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-34}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+162}:\\ \;\;\;\;\left(\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -1.1 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-146}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

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 (* -4.0 (* x i))))
   (if (<= j -1.1e+81)
     (* j (* k -27.0))
     (if (<= j -1.7e-25)
       t_1
       (if (<= j -6.8e-146)
         (* b c)
         (if (<= j 5e-80) t_1 (* (* 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 t_1 = -4.0 * (x * i);
	double tmp;
	if (j <= -1.1e+81) {
		tmp = j * (k * -27.0);
	} else if (j <= -1.7e-25) {
		tmp = t_1;
	} else if (j <= -6.8e-146) {
		tmp = b * c;
	} else if (j <= 5e-80) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (j <= (-1.1d+81)) then
        tmp = j * (k * (-27.0d0))
    else if (j <= (-1.7d-25)) then
        tmp = t_1
    else if (j <= (-6.8d-146)) then
        tmp = b * c
    else if (j <= 5d-80) then
        tmp = t_1
    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 t_1 = -4.0 * (x * i);
	double tmp;
	if (j <= -1.1e+81) {
		tmp = j * (k * -27.0);
	} else if (j <= -1.7e-25) {
		tmp = t_1;
	} else if (j <= -6.8e-146) {
		tmp = b * c;
	} else if (j <= 5e-80) {
		tmp = t_1;
	} 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):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if j <= -1.1e+81:
		tmp = j * (k * -27.0)
	elif j <= -1.7e-25:
		tmp = t_1
	elif j <= -6.8e-146:
		tmp = b * c
	elif j <= 5e-80:
		tmp = t_1
	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)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (j <= -1.1e+81)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (j <= -1.7e-25)
		tmp = t_1;
	elseif (j <= -6.8e-146)
		tmp = Float64(b * c);
	elseif (j <= 5e-80)
		tmp = t_1;
	else
		tmp = Float64(Float64(j * 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)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (j <= -1.1e+81)
		tmp = j * (k * -27.0);
	elseif (j <= -1.7e-25)
		tmp = t_1;
	elseif (j <= -6.8e-146)
		tmp = b * c;
	elseif (j <= 5e-80)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.1e+81], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.7e-25], t$95$1, If[LessEqual[j, -6.8e-146], N[(b * c), $MachinePrecision], If[LessEqual[j, 5e-80], t$95$1, N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.09999999999999993e81

   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 94.2%

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

      1. pow1 94.2%

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

      2. associate-*r* 92.4%

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

      3. *-commutative 92.4%

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

      4. *-commutative 92.4%

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

   6. Applied egg-rr 92.4%

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

      1. unpow1 92.4%

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

      2. *-commutative 92.4%

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

      3. *-commutative 92.4%

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

      4. associate-*r* 92.4%

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

   8. Simplified 92.4%

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

   9. Taylor expanded in j around inf 46.5%

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

       1. *-commutative 46.5%

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

       2. associate-*r* 46.6%

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

   11. Simplified 46.6%

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

   if -1.09999999999999993e81 < j < -1.70000000000000001e-25 or -6.8000000000000001e-146 < j < 5e-80

   1. Initial program 88.9%

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

   3. Simplified 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. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 87.1%

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

      2. associate-*r* 91.0%

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

      3. *-commutative 91.0%

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

      4. *-commutative 91.0%

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

   6. Applied egg-rr 91.0%

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

      1. unpow1 91.0%

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

      2. *-commutative 91.0%

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

      3. *-commutative 91.0%

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

      4. associate-*r* 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in i around inf 32.1%

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

       1. *-commutative 32.1%

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

   11. Simplified 32.1%

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

   if -1.70000000000000001e-25 < j < -6.8000000000000001e-146

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

      1. pow1 93.3%

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

      2. associate-*r* 93.3%

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

      3. *-commutative 93.3%

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

      4. *-commutative 93.3%

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

   6. Applied egg-rr 93.3%

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

      1. unpow1 93.3%

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

      2. *-commutative 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*r* 93.3%

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

   8. Simplified 93.3%

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

   9. Taylor expanded in b around inf 33.6%

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

   if 5e-80 < j

   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 89.7%

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

   5. Taylor expanded in j around inf 31.7%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-25}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-146}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot k\right) \cdot -27\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-156}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* -4.0 (* x i))) (t_2 (* (* j k) -27.0)))
   (if (<= j -1.7e+81)
     t_2
     (if (<= j -1.42e-24)
       t_1
       (if (<= j -1.85e-156) (* b c) (if (<= j 2.35e-80) t_1 t_2))))))

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 = -4.0 * (x * i);
	double t_2 = (j * k) * -27.0;
	double tmp;
	if (j <= -1.7e+81) {
		tmp = t_2;
	} else if (j <= -1.42e-24) {
		tmp = t_1;
	} else if (j <= -1.85e-156) {
		tmp = b * c;
	} else if (j <= 2.35e-80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (-4.0d0) * (x * i)
    t_2 = (j * k) * (-27.0d0)
    if (j <= (-1.7d+81)) then
        tmp = t_2
    else if (j <= (-1.42d-24)) then
        tmp = t_1
    else if (j <= (-1.85d-156)) then
        tmp = b * c
    else if (j <= 2.35d-80) then
        tmp = t_1
    else
        tmp = t_2
    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 = -4.0 * (x * i);
	double t_2 = (j * k) * -27.0;
	double tmp;
	if (j <= -1.7e+81) {
		tmp = t_2;
	} else if (j <= -1.42e-24) {
		tmp = t_1;
	} else if (j <= -1.85e-156) {
		tmp = b * c;
	} else if (j <= 2.35e-80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = -4.0 * (x * i)
	t_2 = (j * k) * -27.0
	tmp = 0
	if j <= -1.7e+81:
		tmp = t_2
	elif j <= -1.42e-24:
		tmp = t_1
	elif j <= -1.85e-156:
		tmp = b * c
	elif j <= 2.35e-80:
		tmp = t_1
	else:
		tmp = t_2
	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(-4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * k) * -27.0)
	tmp = 0.0
	if (j <= -1.7e+81)
		tmp = t_2;
	elseif (j <= -1.42e-24)
		tmp = t_1;
	elseif (j <= -1.85e-156)
		tmp = Float64(b * c);
	elseif (j <= 2.35e-80)
		tmp = t_1;
	else
		tmp = t_2;
	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 = -4.0 * (x * i);
	t_2 = (j * k) * -27.0;
	tmp = 0.0;
	if (j <= -1.7e+81)
		tmp = t_2;
	elseif (j <= -1.42e-24)
		tmp = t_1;
	elseif (j <= -1.85e-156)
		tmp = b * c;
	elseif (j <= 2.35e-80)
		tmp = t_1;
	else
		tmp = t_2;
	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[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]}, If[LessEqual[j, -1.7e+81], t$95$2, If[LessEqual[j, -1.42e-24], t$95$1, If[LessEqual[j, -1.85e-156], N[(b * c), $MachinePrecision], If[LessEqual[j, 2.35e-80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.70000000000000001e81 or 2.34999999999999986e-80 < j

   1. Initial program 90.6%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in j around inf 37.7%

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

   if -1.70000000000000001e81 < j < -1.42e-24 or -1.85e-156 < j < 2.34999999999999986e-80

   1. Initial program 88.8%

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

   3. Simplified 87.9%

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

      1. pow1 87.9%

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

      2. associate-*r* 90.9%

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

      3. *-commutative 90.9%

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

      4. *-commutative 90.9%

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

   6. Applied egg-rr 90.9%

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

      1. unpow1 90.9%

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

      2. *-commutative 90.9%

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

      3. *-commutative 90.9%

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

      4. associate-*r* 90.9%

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

   8. Simplified 90.9%

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

   9. Taylor expanded in i around inf 32.4%

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

       1. *-commutative 32.4%

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

   11. Simplified 32.4%

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

   if -1.42e-24 < j < -1.85e-156

   1. Initial program 93.5%

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

   3. Simplified 90.1%

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

      1. pow1 90.1%

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

      2. associate-*r* 93.5%

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

      3. *-commutative 93.5%

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

      4. *-commutative 93.5%

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

   6. Applied egg-rr 93.5%

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

      1. unpow1 93.5%

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

      2. *-commutative 93.5%

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

      3. *-commutative 93.5%

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

      4. associate-*r* 93.5%

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

   8. Simplified 93.5%

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

   9. Taylor expanded in b around inf 35.9%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+81}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-24}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-156}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* 18.0 (* z (* y (* x t))))))
   (if (<= x -1.6e+104)
     t_1
     (if (<= x -1.42e+45)
       (* -4.0 (* x i))
       (if (<= x 6.9e+46) (+ (* b c) (* j (* k -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 = 18.0 * (z * (y * (x * t)));
	double tmp;
	if (x <= -1.6e+104) {
		tmp = t_1;
	} else if (x <= -1.42e+45) {
		tmp = -4.0 * (x * i);
	} else if (x <= 6.9e+46) {
		tmp = (b * c) + (j * (k * -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 = 18.0d0 * (z * (y * (x * t)))
    if (x <= (-1.6d+104)) then
        tmp = t_1
    else if (x <= (-1.42d+45)) then
        tmp = (-4.0d0) * (x * i)
    else if (x <= 6.9d+46) then
        tmp = (b * c) + (j * (k * (-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 = 18.0 * (z * (y * (x * t)));
	double tmp;
	if (x <= -1.6e+104) {
		tmp = t_1;
	} else if (x <= -1.42e+45) {
		tmp = -4.0 * (x * i);
	} else if (x <= 6.9e+46) {
		tmp = (b * c) + (j * (k * -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 = 18.0 * (z * (y * (x * t)))
	tmp = 0
	if x <= -1.6e+104:
		tmp = t_1
	elif x <= -1.42e+45:
		tmp = -4.0 * (x * i)
	elif x <= 6.9e+46:
		tmp = (b * c) + (j * (k * -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(18.0 * Float64(z * Float64(y * Float64(x * t))))
	tmp = 0.0
	if (x <= -1.6e+104)
		tmp = t_1;
	elseif (x <= -1.42e+45)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (x <= 6.9e+46)
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -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 = 18.0 * (z * (y * (x * t)));
	tmp = 0.0;
	if (x <= -1.6e+104)
		tmp = t_1;
	elseif (x <= -1.42e+45)
		tmp = -4.0 * (x * i);
	elseif (x <= 6.9e+46)
		tmp = (b * c) + (j * (k * -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[(18.0 * N[(z * N[(y * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+104], t$95$1, If[LessEqual[x, -1.42e+45], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.9e+46], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e104 or 6.90000000000000018e46 < x

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. pow1 84.1%

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

      2. associate-*r* 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-*r* 84.1%

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

      5. *-commutative 84.1%

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

      6. *-commutative 84.1%

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

   4. Applied egg-rr 84.1%

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

      1. unpow1 84.1%

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

      2. associate-*r* 83.0%

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

      3. *-commutative 83.0%

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

      4. *-commutative 83.0%

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

      5. associate-*r* 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in x around inf 68.5%

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

      1. cancel-sign-sub-inv 68.5%

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

      2. associate-*r* 67.4%

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

      3. metadata-eval 67.4%

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

   9. Simplified 67.4%

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

   10. Taylor expanded in t around inf 44.9%

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

       1. associate-*r* 45.8%

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

       2. associate-*r* 49.3%

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

   12. Simplified 49.3%

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

   if -1.6e104 < x < -1.42e45

   1. Initial program 93.9%

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

   3. Simplified 99.9%

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

      1. pow1 99.9%

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

      2. associate-*r* 93.9%

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

      3. *-commutative 93.9%

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

      4. *-commutative 93.9%

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

   6. Applied egg-rr 93.9%

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

      1. unpow1 93.9%

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

      2. *-commutative 93.9%

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

      3. *-commutative 93.9%

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

      4. associate-*r* 93.9%

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

   8. Simplified 93.9%

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

   9. Taylor expanded in i around inf 58.8%

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

       1. *-commutative 58.8%

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

   11. Simplified 58.8%

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

   if -1.42e45 < x < 6.90000000000000018e46

   1. Initial program 93.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in b around inf 54.6%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{+45}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{+46}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(y \cdot \left(x \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+57} \lor \neg \left(j \leq 1.55 \cdot 10^{-79}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (or (<= j -3.6e+57) (not (<= j 1.55e-79)))
   (+ (* b c) (* j (* k -27.0)))
   (- (* b c) (* x (* 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 tmp;
	if ((j <= -3.6e+57) || !(j <= 1.55e-79)) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - (x * (4.0 * i));
	}
	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 ((j <= (-3.6d+57)) .or. (.not. (j <= 1.55d-79))) then
        tmp = (b * c) + (j * (k * (-27.0d0)))
    else
        tmp = (b * c) - (x * (4.0d0 * i))
    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 ((j <= -3.6e+57) || !(j <= 1.55e-79)) {
		tmp = (b * c) + (j * (k * -27.0));
	} else {
		tmp = (b * c) - (x * (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):
	tmp = 0
	if (j <= -3.6e+57) or not (j <= 1.55e-79):
		tmp = (b * c) + (j * (k * -27.0))
	else:
		tmp = (b * c) - (x * (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)
	tmp = 0.0
	if ((j <= -3.6e+57) || !(j <= 1.55e-79))
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(x * 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)
	tmp = 0.0;
	if ((j <= -3.6e+57) || ~((j <= 1.55e-79)))
		tmp = (b * c) + (j * (k * -27.0));
	else
		tmp = (b * c) - (x * (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_] := If[Or[LessEqual[j, -3.6e+57], N[Not[LessEqual[j, 1.55e-79]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.6000000000000002e57 or 1.55e-79 < j

   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 90.6%

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

   5. Taylor expanded in b around inf 56.9%

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

   if -3.6000000000000002e57 < j < 1.55e-79

   1. Initial program 90.8%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in t around 0 55.5%

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

   6. Taylor expanded in i around inf 48.9%

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

      1. associate-*r* 48.9%

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

      2. *-commutative 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+57} \lor \neg \left(j \leq 1.55 \cdot 10^{-79}\right):\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.8 \cdot 10^{+199} \lor \neg \left(b \cdot c \leq 1.06 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \end{array} \]

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 (<= (* b c) -5.8e+199) (not (<= (* b c) 1.06e+37)))
   (* 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 (((b * c) <= -5.8e+199) || !((b * c) <= 1.06e+37)) {
		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 (((b * c) <= (-5.8d+199)) .or. (.not. ((b * c) <= 1.06d+37))) 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 (((b * c) <= -5.8e+199) || !((b * c) <= 1.06e+37)) {
		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 ((b * c) <= -5.8e+199) or not ((b * c) <= 1.06e+37):
		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 ((Float64(b * c) <= -5.8e+199) || !(Float64(b * c) <= 1.06e+37))
		tmp = Float64(b * c);
	else
		tmp = Float64(Float64(j * 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 (((b * c) <= -5.8e+199) || ~(((b * c) <= 1.06e+37)))
		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[Or[LessEqual[N[(b * c), $MachinePrecision], -5.8e+199], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.06e+37]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.7999999999999998e199 or 1.06e37 < (*.f64 b c)

   1. Initial program 86.9%

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

   3. Simplified 85.7%

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

      1. pow1 85.7%

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

      2. associate-*r* 88.1%

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

      3. *-commutative 88.1%

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

      4. *-commutative 88.1%

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

   6. Applied egg-rr 88.1%

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

      1. unpow1 88.1%

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

      2. *-commutative 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*r* 88.1%

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

   8. Simplified 88.1%

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

   9. Taylor expanded in b around inf 55.8%

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

   if -5.7999999999999998e199 < (*.f64 b c) < 1.06e37

   1. Initial program 91.9%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in j around inf 30.4%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.8 \cdot 10^{+199} \lor \neg \left(b \cdot c \leq 1.06 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 23.3% 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 90.3%

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

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. Add Preprocessing
5. Step-by-step derivation

   1. pow1 90.0%

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

   2. associate-*r* 91.5%

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

   3. *-commutative 91.5%

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

   4. *-commutative 91.5%

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

6. Applied egg-rr 91.5%

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

   1. unpow1 91.5%

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

   2. *-commutative 91.5%

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

   3. *-commutative 91.5%

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

   4. associate-*r* 91.5%

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

8. Simplified 91.5%

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

9. Taylor expanded in b around inf 22.3%

   \[\leadsto \color{blue}{b \cdot c} \]
10. Add Preprocessing

Developer target: 89.4% accurate, 0.8× 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 2024090 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (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)))