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

Percentage Accurate: 95.4% → 99.0%

Time: 16.1s

Alternatives: 15

Speedup: 0.7×

• 28.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5e-67)
   (fma a (* 27.0 b) (- (* x 2.0) (* y (* (* z 9.0) t))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* y (* z -9.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e-67) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (y * ((z * 9.0) * t))));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (y * (z * -9.0)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5e-67)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(y * Float64(Float64(z * 9.0) * t))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(y * Float64(z * -9.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5e-67], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e-67

   1. Initial program 92.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 92.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 92.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 92.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 98.2%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 98.2%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 98.2%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 98.2%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 98.2%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 98.2%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-def 98.2%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 98.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-def 98.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. distribute-lft-neg-in 98.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(\left(y \cdot 9\right) \cdot t\right) \cdot z}\right)\right) \]

      15. distribute-rgt-neg-in 98.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(y \cdot 9\right) \cdot t\right) \cdot \left(-z\right)}\right)\right) \]

      16. *-commutative 98.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right)} \cdot \left(-z\right)\right)\right) \]

      17. associate-*r* 92.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot \left(-z\right)\right)}\right)\right) \]

      18. associate-*l* 92.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(9 \cdot \left(-z\right)\right)\right)}\right)\right) \]

      19. neg-mul-1 92.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 92.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 92.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-9 \cdot z\right) \cdot y\right)}\right)\right) \]

      2. associate-*r* 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-9 \cdot z\right)\right) \cdot y}\right)\right) \]

      3. *-commutative 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(z \cdot -9\right)}\right) \cdot y\right)\right) \]

      4. associate-*l* 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(t \cdot z\right) \cdot -9\right)} \cdot y\right)\right) \]

      5. *-commutative 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(\color{blue}{\left(z \cdot t\right)} \cdot -9\right) \cdot y\right)\right) \]

      6. associate-*l* 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)}\right)\right) \]

      7. metadata-eval 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(\color{blue}{\left(-9\right)} \cdot y\right)\right)\right) \]

      8. distribute-lft-neg-in 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \color{blue}{\left(-9 \cdot y\right)}\right)\right) \]

      9. *-commutative 95.2%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(-\color{blue}{y \cdot 9}\right)\right)\right) \]

      10. distribute-rgt-neg-in 95.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) \]

      11. *-commutative 95.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, -\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) \]

      12. fma-neg 95.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      13. associate-*l* 95.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) \]

      14. associate-*r* 95.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   6. Applied egg-rr 95.2%

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   if -4.9999999999999999e-67 < z

   1. Initial program 95.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 95.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 95.0%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 95.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 95.0%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 92.9%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 92.9%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 92.9%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 92.9%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 92.9%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 92.9%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-def 93.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 93.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-def 93.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. distribute-lft-neg-in 93.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(\left(y \cdot 9\right) \cdot t\right) \cdot z}\right)\right) \]

      15. distribute-rgt-neg-in 93.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(y \cdot 9\right) \cdot t\right) \cdot \left(-z\right)}\right)\right) \]

      16. *-commutative 93.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right)} \cdot \left(-z\right)\right)\right) \]

      17. associate-*r* 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot \left(-z\right)\right)}\right)\right) \]

      18. associate-*l* 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(9 \cdot \left(-z\right)\right)\right)}\right)\right) \]

      19. neg-mul-1 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t_1 \leq 10^{+104}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot t_1\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* y 9.0))))
   (if (<= t_1 1e+104)
     (+ (- (* x 2.0) (* t t_1)) (* b (* a 27.0)))
     (fma a (* 27.0 b) (- (* x 2.0) (* y (* (* z 9.0) t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 1e+104) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (y * ((z * 9.0) * t))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= 1e+104)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * t_1)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(y * Float64(Float64(z * 9.0) * t))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+104], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1e104

   1. Initial program 96.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   if 1e104 < (*.f64 (*.f64 y 9) z)

   1. Initial program 87.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 87.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 87.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 87.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 87.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 94.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 94.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 94.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 94.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 94.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 94.1%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-def 98.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 98.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-def 98.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. distribute-lft-neg-in 98.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(\left(y \cdot 9\right) \cdot t\right) \cdot z}\right)\right) \]

      15. distribute-rgt-neg-in 98.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(y \cdot 9\right) \cdot t\right) \cdot \left(-z\right)}\right)\right) \]

      16. *-commutative 98.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right)} \cdot \left(-z\right)\right)\right) \]

      17. associate-*r* 91.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot \left(-z\right)\right)}\right)\right) \]

      18. associate-*l* 91.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(9 \cdot \left(-z\right)\right)\right)}\right)\right) \]

      19. neg-mul-1 91.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 91.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 91.0%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-9 \cdot z\right) \cdot y\right)}\right)\right) \]

      2. associate-*r* 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-9 \cdot z\right)\right) \cdot y}\right)\right) \]

      3. *-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(z \cdot -9\right)}\right) \cdot y\right)\right) \]

      4. associate-*l* 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(t \cdot z\right) \cdot -9\right)} \cdot y\right)\right) \]

      5. *-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(\color{blue}{\left(z \cdot t\right)} \cdot -9\right) \cdot y\right)\right) \]

      6. associate-*l* 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)}\right)\right) \]

      7. metadata-eval 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(\color{blue}{\left(-9\right)} \cdot y\right)\right)\right) \]

      8. distribute-lft-neg-in 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \color{blue}{\left(-9 \cdot y\right)}\right)\right) \]

      9. *-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(-\color{blue}{y \cdot 9}\right)\right)\right) \]

      10. distribute-rgt-neg-in 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) \]

      11. *-commutative 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, -\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) \]

      12. fma-neg 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      13. associate-*l* 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) \]

      14. associate-*r* 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   6. Applied egg-rr 97.9%

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+104}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))))
   (if (<= y -2.5e+165)
     t_1
     (if (<= y -8e+121)
       (* x 2.0)
       (if (<= y -1.16e+108)
         t_1
         (if (<= y -6e+40)
           (* x 2.0)
           (if (<= y -1.55e-106)
             (* b (* a 27.0))
             (if (<= y 4.8e-141) (* x 2.0) t_1))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (y <= -2.5e+165) {
		tmp = t_1;
	} else if (y <= -8e+121) {
		tmp = x * 2.0;
	} else if (y <= -1.16e+108) {
		tmp = t_1;
	} else if (y <= -6e+40) {
		tmp = x * 2.0;
	} else if (y <= -1.55e-106) {
		tmp = b * (a * 27.0);
	} else if (y <= 4.8e-141) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    if (y <= (-2.5d+165)) then
        tmp = t_1
    else if (y <= (-8d+121)) then
        tmp = x * 2.0d0
    else if (y <= (-1.16d+108)) then
        tmp = t_1
    else if (y <= (-6d+40)) then
        tmp = x * 2.0d0
    else if (y <= (-1.55d-106)) then
        tmp = b * (a * 27.0d0)
    else if (y <= 4.8d-141) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (y <= -2.5e+165) {
		tmp = t_1;
	} else if (y <= -8e+121) {
		tmp = x * 2.0;
	} else if (y <= -1.16e+108) {
		tmp = t_1;
	} else if (y <= -6e+40) {
		tmp = x * 2.0;
	} else if (y <= -1.55e-106) {
		tmp = b * (a * 27.0);
	} else if (y <= 4.8e-141) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	tmp = 0
	if y <= -2.5e+165:
		tmp = t_1
	elif y <= -8e+121:
		tmp = x * 2.0
	elif y <= -1.16e+108:
		tmp = t_1
	elif y <= -6e+40:
		tmp = x * 2.0
	elif y <= -1.55e-106:
		tmp = b * (a * 27.0)
	elif y <= 4.8e-141:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (y <= -2.5e+165)
		tmp = t_1;
	elseif (y <= -8e+121)
		tmp = Float64(x * 2.0);
	elseif (y <= -1.16e+108)
		tmp = t_1;
	elseif (y <= -6e+40)
		tmp = Float64(x * 2.0);
	elseif (y <= -1.55e-106)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (y <= 4.8e-141)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (y <= -2.5e+165)
		tmp = t_1;
	elseif (y <= -8e+121)
		tmp = x * 2.0;
	elseif (y <= -1.16e+108)
		tmp = t_1;
	elseif (y <= -6e+40)
		tmp = x * 2.0;
	elseif (y <= -1.55e-106)
		tmp = b * (a * 27.0);
	elseif (y <= 4.8e-141)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+165], t$95$1, If[LessEqual[y, -8e+121], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -1.16e+108], t$95$1, If[LessEqual[y, -6e+40], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -1.55e-106], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-141], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999985e165 or -8.0000000000000003e121 < y < -1.15999999999999995e108 or 4.8000000000000002e-141 < y

   1. Initial program 90.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 90.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 90.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 48.7%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if -2.49999999999999985e165 < y < -8.0000000000000003e121 or -1.15999999999999995e108 < y < -6.0000000000000004e40 or -1.54999999999999993e-106 < y < 4.8000000000000002e-141

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 98.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 98.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.6%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -6.0000000000000004e40 < y < -1.54999999999999993e-106

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 96.4%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 96.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 96.5%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 96.5%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 96.5%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 96.5%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 96.5%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in x around 0 51.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 51.7%

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(-9\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval 51.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. fma-def 51.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative 51.7%

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9}\right) \]

      5. associate-*l* 51.6%

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)}\right) \]

   9. Simplified 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right)} \]

   10. Taylor expanded in a around inf 32.1%

       \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.1%

          \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

       2. *-commutative 32.1%

          \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   12. Simplified 32.1%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+108}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))))
   (if (<= y -2.5e+165)
     t_1
     (if (<= y -8e+121)
       (* x 2.0)
       (if (<= y -1.25e+108)
         t_1
         (if (<= y -1.5e+40)
           (* x 2.0)
           (if (<= y -1.3e-106)
             (* b (* a 27.0))
             (if (<= y 4.8e-141) (* x 2.0) (* -9.0 (* t (* z y)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (y <= -2.5e+165) {
		tmp = t_1;
	} else if (y <= -8e+121) {
		tmp = x * 2.0;
	} else if (y <= -1.25e+108) {
		tmp = t_1;
	} else if (y <= -1.5e+40) {
		tmp = x * 2.0;
	} else if (y <= -1.3e-106) {
		tmp = b * (a * 27.0);
	} else if (y <= 4.8e-141) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    if (y <= (-2.5d+165)) then
        tmp = t_1
    else if (y <= (-8d+121)) then
        tmp = x * 2.0d0
    else if (y <= (-1.25d+108)) then
        tmp = t_1
    else if (y <= (-1.5d+40)) then
        tmp = x * 2.0d0
    else if (y <= (-1.3d-106)) then
        tmp = b * (a * 27.0d0)
    else if (y <= 4.8d-141) then
        tmp = x * 2.0d0
    else
        tmp = (-9.0d0) * (t * (z * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (y <= -2.5e+165) {
		tmp = t_1;
	} else if (y <= -8e+121) {
		tmp = x * 2.0;
	} else if (y <= -1.25e+108) {
		tmp = t_1;
	} else if (y <= -1.5e+40) {
		tmp = x * 2.0;
	} else if (y <= -1.3e-106) {
		tmp = b * (a * 27.0);
	} else if (y <= 4.8e-141) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	tmp = 0
	if y <= -2.5e+165:
		tmp = t_1
	elif y <= -8e+121:
		tmp = x * 2.0
	elif y <= -1.25e+108:
		tmp = t_1
	elif y <= -1.5e+40:
		tmp = x * 2.0
	elif y <= -1.3e-106:
		tmp = b * (a * 27.0)
	elif y <= 4.8e-141:
		tmp = x * 2.0
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (y <= -2.5e+165)
		tmp = t_1;
	elseif (y <= -8e+121)
		tmp = Float64(x * 2.0);
	elseif (y <= -1.25e+108)
		tmp = t_1;
	elseif (y <= -1.5e+40)
		tmp = Float64(x * 2.0);
	elseif (y <= -1.3e-106)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (y <= 4.8e-141)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (y <= -2.5e+165)
		tmp = t_1;
	elseif (y <= -8e+121)
		tmp = x * 2.0;
	elseif (y <= -1.25e+108)
		tmp = t_1;
	elseif (y <= -1.5e+40)
		tmp = x * 2.0;
	elseif (y <= -1.3e-106)
		tmp = b * (a * 27.0);
	elseif (y <= 4.8e-141)
		tmp = x * 2.0;
	else
		tmp = -9.0 * (t * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+165], t$95$1, If[LessEqual[y, -8e+121], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -1.25e+108], t$95$1, If[LessEqual[y, -1.5e+40], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -1.3e-106], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-141], N[(x * 2.0), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.49999999999999985e165 or -8.0000000000000003e121 < y < -1.24999999999999998e108

   1. Initial program 90.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 90.7%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 90.7%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 90.7%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 88.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 88.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 88.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 88.5%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 88.5%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 88.4%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-def 88.4%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-def 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. distribute-lft-neg-in 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(\left(y \cdot 9\right) \cdot t\right) \cdot z}\right)\right) \]

      15. distribute-rgt-neg-in 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(y \cdot 9\right) \cdot t\right) \cdot \left(-z\right)}\right)\right) \]

      16. *-commutative 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right)} \cdot \left(-z\right)\right)\right) \]

      17. associate-*r* 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot \left(-z\right)\right)}\right)\right) \]

      18. associate-*l* 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(9 \cdot \left(-z\right)\right)\right)}\right)\right) \]

      19. neg-mul-1 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 90.7%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-9 \cdot z\right) \cdot y\right)}\right)\right) \]

      2. associate-*r* 98.7%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-9 \cdot z\right)\right) \cdot y}\right)\right) \]

      3. *-commutative 98.7%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(z \cdot -9\right)}\right) \cdot y\right)\right) \]

      4. associate-*l* 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(t \cdot z\right) \cdot -9\right)} \cdot y\right)\right) \]

      5. *-commutative 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(\color{blue}{\left(z \cdot t\right)} \cdot -9\right) \cdot y\right)\right) \]

      6. associate-*l* 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)}\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(\color{blue}{\left(-9\right)} \cdot y\right)\right)\right) \]

      8. distribute-lft-neg-in 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \color{blue}{\left(-9 \cdot y\right)}\right)\right) \]

      9. *-commutative 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(-\color{blue}{y \cdot 9}\right)\right)\right) \]

      10. distribute-rgt-neg-in 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) \]

      11. *-commutative 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, -\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) \]

      12. fma-neg 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      13. associate-*l* 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) \]

      14. associate-*r* 98.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   6. Applied egg-rr 98.7%

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   7. Taylor expanded in y around inf 59.8%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 65.4%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      3. *-commutative 65.4%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   9. Simplified 65.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -2.49999999999999985e165 < y < -8.0000000000000003e121 or -1.24999999999999998e108 < y < -1.5000000000000001e40 or -1.3e-106 < y < 4.8000000000000002e-141

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 98.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 98.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.6%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -1.5000000000000001e40 < y < -1.3e-106

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 96.4%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 96.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 96.5%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 96.5%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 96.5%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 96.5%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 96.5%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in x around 0 51.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 51.7%

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(-9\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval 51.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. fma-def 51.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative 51.7%

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9}\right) \]

      5. associate-*l* 51.6%

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)}\right) \]

   9. Simplified 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right)} \]

   10. Taylor expanded in a around inf 32.1%

       \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.1%

          \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

       2. *-commutative 32.1%

          \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   12. Simplified 32.1%

       \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   if 4.8000000000000002e-141 < y

   1. Initial program 91.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 91.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 91.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 95.2%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 95.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 43.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+108}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))))
   (if (<= y -2.5e+165)
     t_1
     (if (<= y -8e+121)
       (* x 2.0)
       (if (<= y -2.05e+108)
         t_1
         (if (<= y -1.4e+40)
           (* x 2.0)
           (if (<= y -3.4e-106)
             (* b (* a 27.0))
             (if (<= y 4.8e-141) (* x 2.0) (* -9.0 (* z (* y t)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (y <= -2.5e+165) {
		tmp = t_1;
	} else if (y <= -8e+121) {
		tmp = x * 2.0;
	} else if (y <= -2.05e+108) {
		tmp = t_1;
	} else if (y <= -1.4e+40) {
		tmp = x * 2.0;
	} else if (y <= -3.4e-106) {
		tmp = b * (a * 27.0);
	} else if (y <= 4.8e-141) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (z * (y * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    if (y <= (-2.5d+165)) then
        tmp = t_1
    else if (y <= (-8d+121)) then
        tmp = x * 2.0d0
    else if (y <= (-2.05d+108)) then
        tmp = t_1
    else if (y <= (-1.4d+40)) then
        tmp = x * 2.0d0
    else if (y <= (-3.4d-106)) then
        tmp = b * (a * 27.0d0)
    else if (y <= 4.8d-141) then
        tmp = x * 2.0d0
    else
        tmp = (-9.0d0) * (z * (y * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (y <= -2.5e+165) {
		tmp = t_1;
	} else if (y <= -8e+121) {
		tmp = x * 2.0;
	} else if (y <= -2.05e+108) {
		tmp = t_1;
	} else if (y <= -1.4e+40) {
		tmp = x * 2.0;
	} else if (y <= -3.4e-106) {
		tmp = b * (a * 27.0);
	} else if (y <= 4.8e-141) {
		tmp = x * 2.0;
	} else {
		tmp = -9.0 * (z * (y * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	tmp = 0
	if y <= -2.5e+165:
		tmp = t_1
	elif y <= -8e+121:
		tmp = x * 2.0
	elif y <= -2.05e+108:
		tmp = t_1
	elif y <= -1.4e+40:
		tmp = x * 2.0
	elif y <= -3.4e-106:
		tmp = b * (a * 27.0)
	elif y <= 4.8e-141:
		tmp = x * 2.0
	else:
		tmp = -9.0 * (z * (y * t))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (y <= -2.5e+165)
		tmp = t_1;
	elseif (y <= -8e+121)
		tmp = Float64(x * 2.0);
	elseif (y <= -2.05e+108)
		tmp = t_1;
	elseif (y <= -1.4e+40)
		tmp = Float64(x * 2.0);
	elseif (y <= -3.4e-106)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (y <= 4.8e-141)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (y <= -2.5e+165)
		tmp = t_1;
	elseif (y <= -8e+121)
		tmp = x * 2.0;
	elseif (y <= -2.05e+108)
		tmp = t_1;
	elseif (y <= -1.4e+40)
		tmp = x * 2.0;
	elseif (y <= -3.4e-106)
		tmp = b * (a * 27.0);
	elseif (y <= 4.8e-141)
		tmp = x * 2.0;
	else
		tmp = -9.0 * (z * (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+165], t$95$1, If[LessEqual[y, -8e+121], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -2.05e+108], t$95$1, If[LessEqual[y, -1.4e+40], N[(x * 2.0), $MachinePrecision], If[LessEqual[y, -3.4e-106], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-141], N[(x * 2.0), $MachinePrecision], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.49999999999999985e165 or -8.0000000000000003e121 < y < -2.05e108

   1. Initial program 90.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 90.7%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 90.7%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 90.7%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 88.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 88.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 88.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 88.5%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 88.5%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 88.4%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-def 88.4%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-def 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. distribute-lft-neg-in 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(\left(y \cdot 9\right) \cdot t\right) \cdot z}\right)\right) \]

      15. distribute-rgt-neg-in 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(y \cdot 9\right) \cdot t\right) \cdot \left(-z\right)}\right)\right) \]

      16. *-commutative 88.4%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right)} \cdot \left(-z\right)\right)\right) \]

      17. associate-*r* 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot \left(-z\right)\right)}\right)\right) \]

      18. associate-*l* 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(9 \cdot \left(-z\right)\right)\right)}\right)\right) \]

      19. neg-mul-1 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(9 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right)\right)\right) \]

      20. associate-*r* 90.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \color{blue}{\left(\left(9 \cdot -1\right) \cdot z\right)}\right)\right)\right) \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 90.7%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-9 \cdot z\right) \cdot y\right)}\right)\right) \]

      2. associate-*r* 98.7%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-9 \cdot z\right)\right) \cdot y}\right)\right) \]

      3. *-commutative 98.7%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(z \cdot -9\right)}\right) \cdot y\right)\right) \]

      4. associate-*l* 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(t \cdot z\right) \cdot -9\right)} \cdot y\right)\right) \]

      5. *-commutative 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(\color{blue}{\left(z \cdot t\right)} \cdot -9\right) \cdot y\right)\right) \]

      6. associate-*l* 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)}\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(\color{blue}{\left(-9\right)} \cdot y\right)\right)\right) \]

      8. distribute-lft-neg-in 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \color{blue}{\left(-9 \cdot y\right)}\right)\right) \]

      9. *-commutative 98.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(z \cdot t\right) \cdot \left(-\color{blue}{y \cdot 9}\right)\right)\right) \]

      10. distribute-rgt-neg-in 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{-\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) \]

      11. *-commutative 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, -\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\right) \]

      12. fma-neg 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      13. associate-*l* 98.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) \]

      14. associate-*r* 98.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   6. Applied egg-rr 98.7%

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right) \]

   7. Taylor expanded in y around inf 59.8%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 65.4%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      3. *-commutative 65.4%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   9. Simplified 65.4%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -2.49999999999999985e165 < y < -8.0000000000000003e121 or -2.05e108 < y < -1.4000000000000001e40 or -3.39999999999999982e-106 < y < 4.8000000000000002e-141

   1. Initial program 98.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 98.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 98.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.6%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -1.4000000000000001e40 < y < -3.39999999999999982e-106

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 96.4%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 96.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 96.5%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 96.5%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 96.5%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 96.5%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 96.5%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in x around 0 51.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 51.7%

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(-9\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval 51.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. fma-def 51.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      4. *-commutative 51.7%

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9}\right) \]

      5. associate-*l* 51.6%

         \[\leadsto \mathsf{fma}\left(27, a \cdot b, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)}\right) \]

   9. Simplified 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\right)} \]

   10. Taylor expanded in a around inf 32.1%

       \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.1%

          \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

       2. *-commutative 32.1%

          \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   12. Simplified 32.1%

       \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]

   if 4.8000000000000002e-141 < y

   1. Initial program 91.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 91.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 91.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 95.2%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 95.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 95.2%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 95.2%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 95.2%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 95.2%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 95.2%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 95.2%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 95.2%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 95.2%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in y around inf 43.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \]

   9. Simplified 45.5%

      \[\leadsto \color{blue}{-9 \cdot \left(\left(t \cdot y\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+165}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+121}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+108}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+40}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-141}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := t_1 + x \cdot 2\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -240000000:\\ \;\;\;\;t_1 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (+ t_1 (* x 2.0))))
   (if (<= a -4.6e+160)
     t_2
     (if (<= a -240000000.0)
       (- t_1 (* 9.0 (* t (* z y))))
       (if (<= a 4.8e-144) (+ (* x 2.0) (* -9.0 (* z (* y t)))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = t_1 + (x * 2.0);
	double tmp;
	if (a <= -4.6e+160) {
		tmp = t_2;
	} else if (a <= -240000000.0) {
		tmp = t_1 - (9.0 * (t * (z * y)));
	} else if (a <= 4.8e-144) {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = t_1 + (x * 2.0d0)
    if (a <= (-4.6d+160)) then
        tmp = t_2
    else if (a <= (-240000000.0d0)) then
        tmp = t_1 - (9.0d0 * (t * (z * y)))
    else if (a <= 4.8d-144) then
        tmp = (x * 2.0d0) + ((-9.0d0) * (z * (y * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = t_1 + (x * 2.0);
	double tmp;
	if (a <= -4.6e+160) {
		tmp = t_2;
	} else if (a <= -240000000.0) {
		tmp = t_1 - (9.0 * (t * (z * y)));
	} else if (a <= 4.8e-144) {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = t_1 + (x * 2.0)
	tmp = 0
	if a <= -4.6e+160:
		tmp = t_2
	elif a <= -240000000.0:
		tmp = t_1 - (9.0 * (t * (z * y)))
	elif a <= 4.8e-144:
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(t_1 + Float64(x * 2.0))
	tmp = 0.0
	if (a <= -4.6e+160)
		tmp = t_2;
	elseif (a <= -240000000.0)
		tmp = Float64(t_1 - Float64(9.0 * Float64(t * Float64(z * y))));
	elseif (a <= 4.8e-144)
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(z * Float64(y * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = t_1 + (x * 2.0);
	tmp = 0.0;
	if (a <= -4.6e+160)
		tmp = t_2;
	elseif (a <= -240000000.0)
		tmp = t_1 - (9.0 * (t * (z * y)));
	elseif (a <= 4.8e-144)
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+160], t$95$2, If[LessEqual[a, -240000000.0], N[(t$95$1 - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-144], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.59999999999999975e160 or 4.79999999999999988e-144 < a

   1. Initial program 92.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 92.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 92.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.5%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.6%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if -4.59999999999999975e160 < a < -2.4e8

   1. Initial program 90.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 90.5%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 90.5%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 93.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 93.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if -2.4e8 < a < 4.79999999999999988e-144

   1. Initial program 97.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 97.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 97.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 98.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 98.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 98.4%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 98.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 98.3%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 98.3%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 98.4%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 98.4%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 98.4%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in a around 0 87.3%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 87.3%

         \[\leadsto \color{blue}{2 \cdot x + \left(-9\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval 87.3%

         \[\leadsto 2 \cdot x + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 86.3%

         \[\leadsto 2 \cdot x + -9 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \]

   9. Simplified 86.3%

      \[\leadsto \color{blue}{2 \cdot x + -9 \cdot \left(\left(t \cdot y\right) \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+160}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{elif}\;a \leq -240000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+190}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot t_1\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* y 9.0))))
   (if (<= t_1 2e+190)
     (+ (- (* x 2.0) (* t t_1)) (* b (* a 27.0)))
     (+ (+ (* y (* z (* t -9.0))) (* x 2.0)) (* a (* 27.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 2e+190) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = z * (y * 9.0d0)
    if (t_1 <= 2d+190) then
        tmp = ((x * 2.0d0) - (t * t_1)) + (b * (a * 27.0d0))
    else
        tmp = ((y * (z * (t * (-9.0d0)))) + (x * 2.0d0)) + (a * (27.0d0 * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 2e+190) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (y * 9.0)
	tmp = 0
	if t_1 <= 2e+190:
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0))
	else:
		tmp = ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= 2e+190)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * t_1)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0)) + Float64(a * Float64(27.0 * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y * 9.0);
	tmp = 0.0;
	if (t_1 <= 2e+190)
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	else
		tmp = ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+190], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 2.0000000000000001e190

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   if 2.0000000000000001e190 < (*.f64 (*.f64 y 9) z)

   1. Initial program 82.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 82.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 82.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. sub-neg 96.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

      2. *-commutative 96.8%

         \[\leadsto \left(x \cdot 2 + \left(-\color{blue}{\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      3. distribute-rgt-neg-in 96.8%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot t\right) \cdot \left(-y \cdot 9\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      4. *-commutative 96.8%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(-\color{blue}{9 \cdot y}\right)\right) + a \cdot \left(27 \cdot b\right) \]

      5. distribute-lft-neg-in 96.8%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \color{blue}{\left(\left(-9\right) \cdot y\right)}\right) + a \cdot \left(27 \cdot b\right) \]

      6. metadata-eval 96.8%

         \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(\color{blue}{-9} \cdot y\right)\right) + a \cdot \left(27 \cdot b\right) \]

      7. associate-*l* 96.7%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right) \cdot y}\right) + a \cdot \left(27 \cdot b\right) \]

      8. associate-*r* 96.7%

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y\right) + a \cdot \left(27 \cdot b\right) \]

      9. *-commutative 96.7%

         \[\leadsto \left(x \cdot 2 + \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right) + a \cdot \left(27 \cdot b\right) \]

   6. Applied egg-rr 96.7%

      \[\leadsto \color{blue}{\left(x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 2 \cdot 10^{+190}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right) + a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t_1 \leq 10^{+190}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot t_1\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* y 9.0))))
   (if (<= t_1 1e+190)
     (+ (- (* x 2.0) (* t t_1)) (* b (* a 27.0)))
     (- (+ (* 27.0 (* a b)) (* x 2.0)) (* y (* (* z 9.0) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 1e+190) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = z * (y * 9.0d0)
    if (t_1 <= 1d+190) then
        tmp = ((x * 2.0d0) - (t * t_1)) + (b * (a * 27.0d0))
    else
        tmp = ((27.0d0 * (a * b)) + (x * 2.0d0)) - (y * ((z * 9.0d0) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 1e+190) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (y * 9.0)
	tmp = 0
	if t_1 <= 1e+190:
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0))
	else:
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= 1e+190)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * t_1)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0)) - Float64(y * Float64(Float64(z * 9.0) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y * 9.0);
	tmp = 0.0;
	if (t_1 <= 1e+190)
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	else
		tmp = ((27.0 * (a * b)) + (x * 2.0)) - (y * ((z * 9.0) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+190], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1.0000000000000001e190

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing

   if 1.0000000000000001e190 < (*.f64 (*.f64 y 9) z)

   1. Initial program 82.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 82.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 82.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 96.8%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 96.8%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 96.7%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 96.7%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 96.8%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 96.8%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 96.8%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+190}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -210000000 \lor \neg \left(a \leq 4.8 \cdot 10^{-144}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -210000000.0) (not (<= a 4.8e-144)))
   (+ (* 27.0 (* a b)) (* x 2.0))
   (+ (* x 2.0) (* -9.0 (* z (* y t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -210000000.0) || !(a <= 4.8e-144)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((a <= (-210000000.0d0)) .or. (.not. (a <= 4.8d-144))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) + ((-9.0d0) * (z * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -210000000.0) || !(a <= 4.8e-144)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -210000000.0) or not (a <= 4.8e-144):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -210000000.0) || !(a <= 4.8e-144))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -210000000.0) || ~((a <= 4.8e-144)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -210000000.0], N[Not[LessEqual[a, 4.8e-144]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1e8 or 4.79999999999999988e-144 < a

   1. Initial program 92.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 92.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 92.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 95.9%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 95.9%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.1%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if -2.1e8 < a < 4.79999999999999988e-144

   1. Initial program 97.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 97.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 97.3%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 98.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 98.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 98.4%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 98.4%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 98.3%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 98.3%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 98.4%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 98.4%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 98.4%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in a around 0 87.3%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 87.3%

         \[\leadsto \color{blue}{2 \cdot x + \left(-9\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

      2. metadata-eval 87.3%

         \[\leadsto 2 \cdot x + \color{blue}{-9} \cdot \left(t \cdot \left(y \cdot z\right)\right) \]

      3. associate-*r* 86.3%

         \[\leadsto 2 \cdot x + -9 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \]

   9. Simplified 86.3%

      \[\leadsto \color{blue}{2 \cdot x + -9 \cdot \left(\left(t \cdot y\right) \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -210000000 \lor \neg \left(a \leq 4.8 \cdot 10^{-144}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+160} \lor \neg \left(a \leq 4.8 \cdot 10^{-144}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7e+160) (not (<= a 4.8e-144)))
   (+ (* 27.0 (* a b)) (* x 2.0))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e+160) || !(a <= 4.8e-144)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((a <= (-7d+160)) .or. (.not. (a <= 4.8d-144))) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e+160) || !(a <= 4.8e-144)) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7e+160) or not (a <= 4.8e-144):
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7e+160) || !(a <= 4.8e-144))
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7e+160) || ~((a <= 4.8e-144)))
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7e+160], N[Not[LessEqual[a, 4.8e-144]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.00000000000000051e160 or 4.79999999999999988e-144 < a

   1. Initial program 92.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 92.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 92.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.5%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.6%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if -7.00000000000000051e160 < a < 4.79999999999999988e-144

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 95.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 97.2%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 97.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 78.0%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+160} \lor \neg \left(a \leq 4.8 \cdot 10^{-144}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+27}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+21}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.95e+27)
   (* -9.0 (* z (* y t)))
   (if (<= z 3.5e+21) (+ (* 27.0 (* a b)) (* x 2.0)) (* (* t -9.0) (* z y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.95e+27) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 3.5e+21) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (t * -9.0) * (z * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-1.95d+27)) then
        tmp = (-9.0d0) * (z * (y * t))
    else if (z <= 3.5d+21) then
        tmp = (27.0d0 * (a * b)) + (x * 2.0d0)
    else
        tmp = (t * (-9.0d0)) * (z * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.95e+27) {
		tmp = -9.0 * (z * (y * t));
	} else if (z <= 3.5e+21) {
		tmp = (27.0 * (a * b)) + (x * 2.0);
	} else {
		tmp = (t * -9.0) * (z * y);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.95e+27:
		tmp = -9.0 * (z * (y * t))
	elif z <= 3.5e+21:
		tmp = (27.0 * (a * b)) + (x * 2.0)
	else:
		tmp = (t * -9.0) * (z * y)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.95e+27)
		tmp = Float64(-9.0 * Float64(z * Float64(y * t)));
	elseif (z <= 3.5e+21)
		tmp = Float64(Float64(27.0 * Float64(a * b)) + Float64(x * 2.0));
	else
		tmp = Float64(Float64(t * -9.0) * Float64(z * y));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.95e+27)
		tmp = -9.0 * (z * (y * t));
	elseif (z <= 3.5e+21)
		tmp = (27.0 * (a * b)) + (x * 2.0);
	else
		tmp = (t * -9.0) * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.95e+27], N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+21], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * -9.0), $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9499999999999999e27

   1. Initial program 88.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 88.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 88.7%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 93.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 93.1%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 93.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)} \]

      2. associate-+r- 93.1%

         \[\leadsto \color{blue}{\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \]

      3. associate-*r* 93.0%

         \[\leadsto \left(\color{blue}{\left(a \cdot 27\right) \cdot b} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      4. *-commutative 93.0%

         \[\leadsto \left(\color{blue}{\left(27 \cdot a\right)} \cdot b + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      5. associate-*l* 93.1%

         \[\leadsto \left(\color{blue}{27 \cdot \left(a \cdot b\right)} + x \cdot 2\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right) \]

      6. associate-*l* 93.2%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)} \]

      7. associate-*r* 93.3%

         \[\leadsto \left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \]

   6. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\left(27 \cdot \left(a \cdot b\right) + x \cdot 2\right) - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)} \]

   7. Taylor expanded in y around inf 46.9%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 53.7%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \]

   9. Simplified 53.7%

      \[\leadsto \color{blue}{-9 \cdot \left(\left(t \cdot y\right) \cdot z\right)} \]

   if -1.9499999999999999e27 < z < 3.5e21

   1. Initial program 99.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 99.4%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 99.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 99.4%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.8%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   if 3.5e21 < z

   1. Initial program 86.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 86.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 86.9%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 93.8%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 93.8%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 50.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.4%

         \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} \]

      2. *-commutative 50.4%

         \[\leadsto \color{blue}{\left(t \cdot -9\right)} \cdot \left(y \cdot z\right) \]

   7. Simplified 50.4%

      \[\leadsto \color{blue}{\left(t \cdot -9\right) \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+27}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+21}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -9\right) \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right) + a \cdot \left(27 \cdot b\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (* y (* z (* t -9.0))) (* x 2.0)) (* a (* 27.0 b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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
    code = ((y * (z * (t * (-9.0d0)))) + (x * 2.0d0)) + (a * (27.0d0 * b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(y * Float64(z * Float64(t * -9.0))) + Float64(x * 2.0)) + Float64(a * Float64(27.0 * b)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((y * (z * (t * -9.0))) + (x * 2.0)) + (a * (27.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.3%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg 94.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

   2. sub-neg 94.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

   3. associate-*l* 96.9%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   4. associate-*l* 96.9%

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

3. Simplified 96.9%

   \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. sub-neg 96.9%

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

   2. *-commutative 96.9%

      \[\leadsto \left(x \cdot 2 + \left(-\color{blue}{\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right)\right) + a \cdot \left(27 \cdot b\right) \]

   3. distribute-rgt-neg-in 96.9%

      \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot t\right) \cdot \left(-y \cdot 9\right)}\right) + a \cdot \left(27 \cdot b\right) \]

   4. *-commutative 96.9%

      \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(-\color{blue}{9 \cdot y}\right)\right) + a \cdot \left(27 \cdot b\right) \]

   5. distribute-lft-neg-in 96.9%

      \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \color{blue}{\left(\left(-9\right) \cdot y\right)}\right) + a \cdot \left(27 \cdot b\right) \]

   6. metadata-eval 96.9%

      \[\leadsto \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(\color{blue}{-9} \cdot y\right)\right) + a \cdot \left(27 \cdot b\right) \]

   7. associate-*l* 96.9%

      \[\leadsto \left(x \cdot 2 + \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right) \cdot y}\right) + a \cdot \left(27 \cdot b\right) \]

   8. associate-*r* 96.5%

      \[\leadsto \left(x \cdot 2 + \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \cdot y\right) + a \cdot \left(27 \cdot b\right) \]

   9. *-commutative 96.5%

      \[\leadsto \left(x \cdot 2 + \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)}\right) + a \cdot \left(27 \cdot b\right) \]

6. Applied egg-rr 96.5%

   \[\leadsto \color{blue}{\left(x \cdot 2 + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)} + a \cdot \left(27 \cdot b\right) \]

7. Final simplification 96.5%

   \[\leadsto \left(y \cdot \left(z \cdot \left(t \cdot -9\right)\right) + x \cdot 2\right) + a \cdot \left(27 \cdot b\right) \]
8. Add Preprocessing

Alternative 13: 45.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{+34} \lor \neg \left(a \leq 2.75 \cdot 10^{-120}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.56e+34) (not (<= a 2.75e-120))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.56e+34) || !(a <= 2.75e-120)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((a <= (-1.56d+34)) .or. (.not. (a <= 2.75d-120))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.56e+34) || !(a <= 2.75e-120)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.56e+34) or not (a <= 2.75e-120):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.56e+34) || !(a <= 2.75e-120))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.56e+34) || ~((a <= 2.75e-120)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.56e+34], N[Not[LessEqual[a, 2.75e-120]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5600000000000001e34 or 2.7500000000000001e-120 < a

   1. Initial program 92.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 92.2%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 92.2%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 95.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 95.5%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -1.5600000000000001e34 < a < 2.7500000000000001e-120

   1. Initial program 96.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 96.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 98.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 98.5%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 44.3%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{+34} \lor \neg \left(a \leq 2.75 \cdot 10^{-120}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+33}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.5e+33)
   (* 27.0 (* a b))
   (if (<= a 8e-85) (* x 2.0) (* a (* 27.0 b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.5e+33) {
		tmp = 27.0 * (a * b);
	} else if (a <= 8e-85) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= (-7.5d+33)) then
        tmp = 27.0d0 * (a * b)
    else if (a <= 8d-85) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.5e+33) {
		tmp = 27.0 * (a * b);
	} else if (a <= 8e-85) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.5e+33:
		tmp = 27.0 * (a * b)
	elif a <= 8e-85:
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.5e+33)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (a <= 8e-85)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.5e+33)
		tmp = 27.0 * (a * b);
	elseif (a <= 8e-85)
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.5e+33], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-85], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.50000000000000046e33

   1. Initial program 93.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 93.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 93.8%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 93.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 93.6%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 57.9%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -7.50000000000000046e33 < a < 7.9999999999999998e-85

   1. Initial program 97.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 97.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 97.0%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 98.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 98.6%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 46.3%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 7.9999999999999998e-85 < a

   1. Initial program 90.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 90.6%

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. sub-neg 90.6%

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 96.3%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*l* 96.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 44.4%

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

      1. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(27 \cdot a\right) \cdot b} \]

      2. *-commutative 44.5%

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      3. associate-*r* 44.5%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   7. Simplified 44.5%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+33}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.2% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 94.3%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg 94.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]

   2. sub-neg 94.3%

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b \]

   3. associate-*l* 96.9%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   4. associate-*l* 96.9%

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

3. Simplified 96.9%

   \[\leadsto \color{blue}{\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 34.4%

   \[\leadsto \color{blue}{2 \cdot x} \]

6. Final simplification 34.4%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer target: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))