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

Percentage Accurate: 95.8% → 98.7%

Time: 12.3s

Alternatives: 12

Speedup: 0.9×

• 27.0% 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: 95.8% 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: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.8 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(z, y \cdot \left(t \cdot -9\right), b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.8e-48)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* t (* z -9.0)))))
   (fma x 2.0 (fma z (* y (* t -9.0)) (* b (* a 27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.8e-48) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (t * (z * -9.0)))));
	} else {
		tmp = fma(x, 2.0, fma(z, (y * (t * -9.0)), (b * (a * 27.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 4.8e-48)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(z * -9.0)))));
	else
		tmp = fma(x, 2.0, fma(z, Float64(y * Float64(t * -9.0)), Float64(b * Float64(a * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 4.8e-48], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.8e-48

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-+r- 97.7%

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

      3. cancel-sign-sub-inv 97.7%

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

      4. *-commutative 97.7%

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

      5. distribute-rgt-neg-out 97.7%

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

      6. associate-*r* 92.0%

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

      7. *-commutative 92.0%

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

      8. distribute-rgt-neg-in 92.0%

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

      9. associate-+r+ 92.0%

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

      10. sub-neg 92.0%

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

      11. associate-*l* 92.1%

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

      12. fma-def 92.0%

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

      13. fma-neg 92.0%

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

      14. associate-*l* 92.1%

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

      15. *-commutative 92.1%

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

      16. associate-*r* 96.2%

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

      17. distribute-rgt-neg-in 96.2%

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

   3. Simplified 96.7%

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

   if 4.8e-48 < z

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-+r- 93.5%

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

      3. cancel-sign-sub-inv 93.5%

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

      4. *-commutative 93.5%

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

      5. distribute-rgt-neg-out 93.5%

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

      6. associate-*r* 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-neg-in 99.8%

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

      9. associate-+r+ 99.8%

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

      10. sub-neg 99.8%

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

      11. +-commutative 99.8%

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

      12. associate-+l- 99.8%

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

      13. fma-neg 99.8%

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

      14. associate-*l* 97.3%

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

      15. fma-neg 97.3%

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

      16. *-commutative 97.3%

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

      17. fma-neg 97.3%

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

   3. Simplified 99.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.8 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(z, y \cdot \left(t \cdot -9\right), b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;x \cdot 2 - \left(z \cdot y\right) \cdot \left(t \cdot 9\right)\\ \mathbf{elif}\;x \cdot 2 \leq 5 \cdot 10^{+70}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x 2.0) -5e+62)
   (- (* x 2.0) (* (* z y) (* t 9.0)))
   (if (<= (* x 2.0) 5e+70)
     (- (* 27.0 (* a b)) (* 9.0 (* t (* z y))))
     (+ (* a (* 27.0 b)) (* x 2.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * 2.0) <= -5e+62) {
		tmp = (x * 2.0) - ((z * y) * (t * 9.0));
	} else if ((x * 2.0) <= 5e+70) {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	} else {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 ((x * 2.0d0) <= (-5d+62)) then
        tmp = (x * 2.0d0) - ((z * y) * (t * 9.0d0))
    else if ((x * 2.0d0) <= 5d+70) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (t * (z * y)))
    else
        tmp = (a * (27.0d0 * b)) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * 2.0) <= -5e+62) {
		tmp = (x * 2.0) - ((z * y) * (t * 9.0));
	} else if ((x * 2.0) <= 5e+70) {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	} else {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x * 2.0) <= -5e+62:
		tmp = (x * 2.0) - ((z * y) * (t * 9.0))
	elif (x * 2.0) <= 5e+70:
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)))
	else:
		tmp = (a * (27.0 * b)) + (x * 2.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * 2.0) <= -5e+62)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(z * y) * Float64(t * 9.0)));
	elseif (Float64(x * 2.0) <= 5e+70)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(t * Float64(z * y))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * 2.0) <= -5e+62)
		tmp = (x * 2.0) - ((z * y) * (t * 9.0));
	elseif ((x * 2.0) <= 5e+70)
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	else
		tmp = (a * (27.0 * b)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -5e+62], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 5e+70], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 2) < -5.00000000000000029e62

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-lft-neg-in 98.1%

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

      3. associate-*l* 98.0%

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

      4. *-commutative 98.0%

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

      5. *-commutative 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. *-commutative 98.0%

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

      8. *-commutative 98.0%

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

      9. associate-*l* 98.1%

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

      10. associate-*l* 96.4%

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

      11. 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. Taylor expanded in y around 0 98.2%

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

      1. associate-*r* 98.1%

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

      2. *-commutative 98.1%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in a around 0 88.6%

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

      1. associate-*r* 88.5%

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

   9. Simplified 88.5%

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

   if -5.00000000000000029e62 < (*.f64 x 2) < 5.0000000000000002e70

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. distribute-lft-neg-in 96.7%

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

      3. associate-*l* 96.7%

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

      4. *-commutative 96.7%

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

      5. *-commutative 96.7%

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

      6. cancel-sign-sub-inv 96.7%

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

      7. *-commutative 96.7%

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

      8. *-commutative 96.7%

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

      9. associate-*l* 96.7%

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

      10. associate-*l* 97.9%

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

      11. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around 0 85.7%

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

   if 5.0000000000000002e70 < (*.f64 x 2)

   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. distribute-lft-neg-in 94.3%

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

      3. associate-*l* 94.3%

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

      4. *-commutative 94.3%

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

      5. *-commutative 94.3%

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

      6. cancel-sign-sub-inv 94.3%

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

      7. *-commutative 94.3%

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

      8. *-commutative 94.3%

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

      9. associate-*l* 94.3%

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

      10. associate-*l* 94.5%

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

      11. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around 0 82.8%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 82.8%

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

      2. *-commutative 82.8%

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

      3. fma-def 82.8%

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

      4. *-commutative 82.8%

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

   6. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-*r* 82.8%

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

      4. *-commutative 82.8%

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

      5. *-commutative 82.8%

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

   8. Applied egg-rr 82.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;x \cdot 2 - \left(z \cdot y\right) \cdot \left(t \cdot 9\right)\\ \mathbf{elif}\;x \cdot 2 \leq 5 \cdot 10^{+70}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \end{array} \]

Alternative 3: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.8e+54)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* y 9.0) (* z t))))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.8e+54) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= 1.8d+54) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.8e+54) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.8e+54:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.8e+54)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.8e+54)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.8e+54], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $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 z < 1.8000000000000001e54

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

      5. *-commutative 97.8%

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

      6. cancel-sign-sub-inv 97.8%

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

      7. *-commutative 97.8%

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

      8. *-commutative 97.8%

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

      9. associate-*l* 97.9%

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

      10. associate-*l* 97.0%

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

      11. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   if 1.8000000000000001e54 < z

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. distribute-lft-neg-in 91.2%

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

      3. associate-*l* 91.2%

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

      4. *-commutative 91.2%

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

      5. *-commutative 91.2%

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

      6. cancel-sign-sub-inv 91.2%

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

      7. *-commutative 91.2%

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

      8. *-commutative 91.2%

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

      9. associate-*l* 91.2%

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

      10. associate-*l* 96.4%

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

      11. 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. Taylor expanded in a around 0 67.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-lft-neg-in 96.5%

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

   3. associate-*l* 96.5%

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

   4. *-commutative 96.5%

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

   5. *-commutative 96.5%

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

   6. cancel-sign-sub-inv 96.5%

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

   7. *-commutative 96.5%

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

   8. *-commutative 96.5%

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

   9. associate-*l* 96.5%

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

   10. associate-*l* 96.9%

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

   11. 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. Taylor expanded in y around 0 96.5%

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

   1. associate-*r* 96.2%

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

   2. *-commutative 96.2%

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

6. Simplified 96.2%

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

7. Final simplification 96.2%

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

Alternative 5: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -5.6e+112)
     (* x 2.0)
     (if (<= x 4.2e-272)
       t_1
       (if (<= x 4.2e-41)
         (* 27.0 (* a b))
         (if (<= x 2.3e+57) t_1 (* x 2.0)))))))

C

assert(y < z && z < t);
assert(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 (x <= -5.6e+112) {
		tmp = x * 2.0;
	} else if (x <= 4.2e-272) {
		tmp = t_1;
	} else if (x <= 4.2e-41) {
		tmp = 27.0 * (a * b);
	} else if (x <= 2.3e+57) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-5.6d+112)) then
        tmp = x * 2.0d0
    else if (x <= 4.2d-272) then
        tmp = t_1
    else if (x <= 4.2d-41) then
        tmp = 27.0d0 * (a * b)
    else if (x <= 2.3d+57) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert 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 (x <= -5.6e+112) {
		tmp = x * 2.0;
	} else if (x <= 4.2e-272) {
		tmp = t_1;
	} else if (x <= 4.2e-41) {
		tmp = 27.0 * (a * b);
	} else if (x <= 2.3e+57) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	tmp = 0
	if x <= -5.6e+112:
		tmp = x * 2.0
	elif x <= 4.2e-272:
		tmp = t_1
	elif x <= 4.2e-41:
		tmp = 27.0 * (a * b)
	elif x <= 2.3e+57:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (x <= -5.6e+112)
		tmp = Float64(x * 2.0);
	elseif (x <= 4.2e-272)
		tmp = t_1;
	elseif (x <= 4.2e-41)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (x <= 2.3e+57)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (x <= -5.6e+112)
		tmp = x * 2.0;
	elseif (x <= 4.2e-272)
		tmp = t_1;
	elseif (x <= 4.2e-41)
		tmp = 27.0 * (a * b);
	elseif (x <= 2.3e+57)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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[x, -5.6e+112], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 4.2e-272], t$95$1, If[LessEqual[x, 4.2e-41], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+57], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.6000000000000003e112 or 2.2999999999999999e57 < x

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. distribute-lft-neg-in 95.8%

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

      3. associate-*l* 95.8%

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

      4. *-commutative 95.8%

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

      5. *-commutative 95.8%

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

      6. cancel-sign-sub-inv 95.8%

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

      7. *-commutative 95.8%

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

      8. *-commutative 95.8%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.9%

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

      11. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 63.0%

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

   if -5.6000000000000003e112 < x < 4.19999999999999974e-272 or 4.20000000000000025e-41 < x < 2.2999999999999999e57

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. distribute-lft-neg-in 97.2%

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

      3. associate-*l* 97.2%

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

      4. *-commutative 97.2%

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

      5. *-commutative 97.2%

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

      6. cancel-sign-sub-inv 97.2%

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

      7. *-commutative 97.2%

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

      8. *-commutative 97.2%

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

      9. associate-*l* 97.2%

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

      10. associate-*l* 97.2%

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

      11. 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. Taylor expanded in y around inf 56.4%

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

   if 4.19999999999999974e-272 < x < 4.20000000000000025e-41

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. distribute-lft-neg-in 96.2%

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

      3. associate-*l* 96.2%

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

      4. *-commutative 96.2%

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

      5. *-commutative 96.2%

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

      6. cancel-sign-sub-inv 96.2%

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

      7. *-commutative 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 97.9%

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

      11. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around inf 60.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+57}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 6: 48.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-37}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.82e+112)
   (* x 2.0)
   (if (<= x 2.2e-273)
     (* t (* -9.0 (* z y)))
     (if (<= x 1.56e-37)
       (* 27.0 (* a b))
       (if (<= x 5.2e+59) (* -9.0 (* t (* z y))) (* x 2.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.82e+112) {
		tmp = x * 2.0;
	} else if (x <= 2.2e-273) {
		tmp = t * (-9.0 * (z * y));
	} else if (x <= 1.56e-37) {
		tmp = 27.0 * (a * b);
	} else if (x <= 5.2e+59) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-1.82d+112)) then
        tmp = x * 2.0d0
    else if (x <= 2.2d-273) then
        tmp = t * ((-9.0d0) * (z * y))
    else if (x <= 1.56d-37) then
        tmp = 27.0d0 * (a * b)
    else if (x <= 5.2d+59) then
        tmp = (-9.0d0) * (t * (z * y))
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.82e+112) {
		tmp = x * 2.0;
	} else if (x <= 2.2e-273) {
		tmp = t * (-9.0 * (z * y));
	} else if (x <= 1.56e-37) {
		tmp = 27.0 * (a * b);
	} else if (x <= 5.2e+59) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.82e+112:
		tmp = x * 2.0
	elif x <= 2.2e-273:
		tmp = t * (-9.0 * (z * y))
	elif x <= 1.56e-37:
		tmp = 27.0 * (a * b)
	elif x <= 5.2e+59:
		tmp = -9.0 * (t * (z * y))
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.82e+112)
		tmp = Float64(x * 2.0);
	elseif (x <= 2.2e-273)
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	elseif (x <= 1.56e-37)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (x <= 5.2e+59)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.82e+112)
		tmp = x * 2.0;
	elseif (x <= 2.2e-273)
		tmp = t * (-9.0 * (z * y));
	elseif (x <= 1.56e-37)
		tmp = 27.0 * (a * b);
	elseif (x <= 5.2e+59)
		tmp = -9.0 * (t * (z * y));
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.82e+112], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 2.2e-273], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.56e-37], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+59], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.82000000000000001e112 or 5.19999999999999999e59 < x

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. distribute-lft-neg-in 95.8%

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

      3. associate-*l* 95.8%

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

      4. *-commutative 95.8%

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

      5. *-commutative 95.8%

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

      6. cancel-sign-sub-inv 95.8%

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

      7. *-commutative 95.8%

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

      8. *-commutative 95.8%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.9%

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

      11. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around inf 63.0%

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

   if -1.82000000000000001e112 < x < 2.1999999999999998e-273

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. distribute-lft-neg-in 96.9%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. *-commutative 96.8%

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

      6. cancel-sign-sub-inv 96.8%

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

      7. *-commutative 96.8%

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

      8. *-commutative 96.8%

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

      9. associate-*l* 96.9%

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

      10. associate-*l* 96.8%

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

      11. 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. Taylor expanded in y around 0 96.9%

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

      1. associate-*r* 95.9%

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

      2. *-commutative 95.9%

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

   6. Simplified 95.9%

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

      1. associate-*r* 95.9%

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

      2. add-cube-cbrt 95.6%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot z\right) \cdot \left(9 \cdot t\right)\right) + \color{blue}{\left(\sqrt[3]{\left(a \cdot 27\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot 27\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot 27\right) \cdot b}} \]

      3. pow3 95.6%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot z\right) \cdot \left(9 \cdot t\right)\right) + \color{blue}{{\left(\sqrt[3]{\left(a \cdot 27\right) \cdot b}\right)}^{3}} \]

      4. associate-*r* 95.6%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot z\right) \cdot \left(9 \cdot t\right)\right) + {\left(\sqrt[3]{\color{blue}{a \cdot \left(27 \cdot b\right)}}\right)}^{3} \]

   8. Applied egg-rr 95.6%

      \[\leadsto \left(x \cdot 2 - \left(y \cdot z\right) \cdot \left(9 \cdot t\right)\right) + \color{blue}{{\left(\sqrt[3]{a \cdot \left(27 \cdot b\right)}\right)}^{3}} \]

   9. Taylor expanded in y around inf 54.7%

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

       1. associate-*r* 53.7%

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

       2. *-commutative 53.7%

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

       3. associate-*l* 54.7%

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

   11. Simplified 54.7%

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

   if 2.1999999999999998e-273 < x < 1.56e-37

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. distribute-lft-neg-in 96.2%

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

      3. associate-*l* 96.2%

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

      4. *-commutative 96.2%

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

      5. *-commutative 96.2%

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

      6. cancel-sign-sub-inv 96.2%

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

      7. *-commutative 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*l* 96.2%

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

      10. associate-*l* 97.9%

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

      11. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around inf 60.7%

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

   if 1.56e-37 < x < 5.19999999999999999e59

   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. distribute-lft-neg-in 99.4%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. cancel-sign-sub-inv 99.2%

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

      7. *-commutative 99.2%

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

      8. *-commutative 99.2%

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

      9. associate-*l* 99.4%

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

      10. associate-*l* 99.3%

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

      11. 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. Taylor expanded in y around inf 67.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.56 \cdot 10^{-37}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 7: 78.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-20} \lor \neg \left(z \leq 5 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-20) (not (<= z 5e-58)))
   (- (* x 2.0) (* 9.0 (* t (* z y))))
   (+ (* a (* 27.0 b)) (* x 2.0))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-20) || !(z <= 5e-58)) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= (-1.05d-20)) .or. (.not. (z <= 5d-58))) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else
        tmp = (a * (27.0d0 * b)) + (x * 2.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-20) || !(z <= 5e-58)) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-20) or not (z <= 5e-58):
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	else:
		tmp = (a * (27.0 * b)) + (x * 2.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-20) || !(z <= 5e-58))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-20) || ~((z <= 5e-58)))
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	else
		tmp = (a * (27.0 * b)) + (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-20], N[Not[LessEqual[z, 5e-58]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e-20 or 4.99999999999999977e-58 < z

   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. distribute-lft-neg-in 93.8%

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

      3. associate-*l* 93.8%

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

      4. *-commutative 93.8%

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

      5. *-commutative 93.8%

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

      6. cancel-sign-sub-inv 93.8%

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

      7. *-commutative 93.8%

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

      8. *-commutative 93.8%

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

      9. associate-*l* 93.8%

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

      10. associate-*l* 94.6%

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

      11. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in a around 0 68.5%

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

   if -1.0499999999999999e-20 < z < 4.99999999999999977e-58

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 76.6%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

      3. fma-def 76.6%

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

      4. *-commutative 76.6%

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

   6. Simplified 76.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

      5. *-commutative 76.6%

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

   8. Applied egg-rr 76.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-20} \lor \neg \left(z \leq 5 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \end{array} \]

Alternative 8: 78.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 2 - \left(z \cdot y\right) \cdot \left(t \cdot 9\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e-20)
   (- (* x 2.0) (* (* z y) (* t 9.0)))
   (if (<= z 2.2e-58)
     (+ (* a (* 27.0 b)) (* x 2.0))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e-20) {
		tmp = (x * 2.0) - ((z * y) * (t * 9.0));
	} else if (z <= 2.2e-58) {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= (-1.15d-20)) then
        tmp = (x * 2.0d0) - ((z * y) * (t * 9.0d0))
    else if (z <= 2.2d-58) then
        tmp = (a * (27.0d0 * b)) + (x * 2.0d0)
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e-20) {
		tmp = (x * 2.0) - ((z * y) * (t * 9.0));
	} else if (z <= 2.2e-58) {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e-20:
		tmp = (x * 2.0) - ((z * y) * (t * 9.0))
	elif z <= 2.2e-58:
		tmp = (a * (27.0 * b)) + (x * 2.0)
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e-20)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(z * y) * Float64(t * 9.0)));
	elseif (z <= 2.2e-58)
		tmp = Float64(Float64(a * Float64(27.0 * 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

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e-20)
		tmp = (x * 2.0) - ((z * y) * (t * 9.0));
	elseif (z <= 2.2e-58)
		tmp = (a * (27.0 * b)) + (x * 2.0);
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e-20], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-58], N[(N[(a * N[(27.0 * 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 3 regimes

2. if z < -1.15e-20

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-lft-neg-in 94.0%

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

      3. associate-*l* 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

      6. cancel-sign-sub-inv 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 91.5%

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

      11. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around 0 94.1%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in a around 0 71.6%

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

      1. associate-*r* 71.6%

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

   9. Simplified 71.6%

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

   if -1.15e-20 < z < 2.20000000000000006e-58

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 76.6%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 76.6%

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

      2. *-commutative 76.6%

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

      3. fma-def 76.6%

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

      4. *-commutative 76.6%

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

   6. Simplified 76.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.6%

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

      4. *-commutative 76.6%

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

      5. *-commutative 76.6%

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

   8. Applied egg-rr 76.6%

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

   if 2.20000000000000006e-58 < z

   1. Initial program 93.7%

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

      1. sub-neg 93.7%

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

      2. distribute-lft-neg-in 93.7%

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

      3. associate-*l* 93.6%

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

      4. *-commutative 93.6%

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

      5. *-commutative 93.6%

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

      6. cancel-sign-sub-inv 93.6%

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

      7. *-commutative 93.6%

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

      8. *-commutative 93.6%

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

      9. associate-*l* 93.7%

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

      10. associate-*l* 97.4%

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

      11. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around 0 65.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 2 - \left(z \cdot y\right) \cdot \left(t \cdot 9\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 9: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 59000000000000:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.55e-20)
   (* y (* t (* z -9.0)))
   (if (<= z 59000000000000.0)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (* t (* y (* z -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e-20) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 59000000000000.0) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= (-2.55d-20)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 59000000000000.0d0) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e-20) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 59000000000000.0) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.55e-20:
		tmp = y * (t * (z * -9.0))
	elif z <= 59000000000000.0:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.55e-20)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 59000000000000.0)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.55e-20)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 59000000000000.0)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = t * (y * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.55e-20], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 59000000000000.0], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55000000000000009e-20

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-lft-neg-in 94.0%

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

      3. associate-*l* 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

      6. cancel-sign-sub-inv 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 91.5%

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

      11. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-*r* 50.1%

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

      3. *-commutative 50.1%

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

      4. associate-*r* 50.1%

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

      5. associate-*l* 44.5%

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

   6. Simplified 44.5%

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

   if -2.55000000000000009e-20 < z < 5.9e13

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.7%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 75.9%

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

   if 5.9e13 < z

   1. Initial program 92.8%

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

      1. sub-neg 92.8%

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

      2. distribute-lft-neg-in 92.8%

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

      3. associate-*l* 92.8%

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

      4. *-commutative 92.8%

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

      5. *-commutative 92.8%

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

      6. cancel-sign-sub-inv 92.8%

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

      7. *-commutative 92.8%

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

      8. *-commutative 92.8%

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

      9. associate-*l* 92.8%

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

      10. associate-*l* 97.0%

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

      11. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*r* 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-*r* 52.2%

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

      5. *-commutative 52.2%

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

      6. associate-*l* 46.5%

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

   6. Simplified 46.5%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 59000000000000:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e-20)
   (* y (* t (* z -9.0)))
   (if (<= z 6.3e+16) (+ (* a (* 27.0 b)) (* x 2.0)) (* t (* y (* z -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e-20) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 6.3e+16) {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 <= (-2.05d-20)) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (z <= 6.3d+16) then
        tmp = (a * (27.0d0 * b)) + (x * 2.0d0)
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e-20) {
		tmp = y * (t * (z * -9.0));
	} else if (z <= 6.3e+16) {
		tmp = (a * (27.0 * b)) + (x * 2.0);
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.05e-20:
		tmp = y * (t * (z * -9.0))
	elif z <= 6.3e+16:
		tmp = (a * (27.0 * b)) + (x * 2.0)
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.05e-20)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (z <= 6.3e+16)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0));
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.05e-20)
		tmp = y * (t * (z * -9.0));
	elseif (z <= 6.3e+16)
		tmp = (a * (27.0 * b)) + (x * 2.0);
	else
		tmp = t * (y * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.05e-20], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3e+16], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e-20

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-lft-neg-in 94.0%

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

      3. associate-*l* 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

      6. cancel-sign-sub-inv 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 91.5%

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

      11. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-*r* 50.1%

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

      3. *-commutative 50.1%

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

      4. associate-*r* 50.1%

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

      5. associate-*l* 44.5%

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

   6. Simplified 44.5%

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

   if -2.05e-20 < z < 6.3e16

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.7%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 76.1%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 76.1%

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

      2. *-commutative 76.1%

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

      3. fma-def 76.1%

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

      4. *-commutative 76.1%

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

   6. Simplified 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r* 76.1%

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

      4. *-commutative 76.1%

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

      5. *-commutative 76.1%

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

   8. Applied egg-rr 76.1%

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

   if 6.3e16 < z

   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. distribute-lft-neg-in 92.7%

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

      3. associate-*l* 92.6%

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

      4. *-commutative 92.6%

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

      5. *-commutative 92.6%

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

      6. cancel-sign-sub-inv 92.6%

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

      7. *-commutative 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-*l* 92.7%

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

      10. associate-*l* 97.0%

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

      11. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*r* 53.0%

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

      3. *-commutative 53.0%

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

      4. associate-*r* 53.0%

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

      5. *-commutative 53.0%

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

      6. associate-*l* 47.2%

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

   6. Simplified 47.2%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]

Alternative 11: 47.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -12000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+80}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -12000.0)
   (* x 2.0)
   (if (<= x 2.45e+80) (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -12000.0) {
		tmp = x * 2.0;
	} else if (x <= 2.45e+80) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 (x <= (-12000.0d0)) then
        tmp = x * 2.0d0
    else if (x <= 2.45d+80) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -12000.0) {
		tmp = x * 2.0;
	} else if (x <= 2.45e+80) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -12000.0:
		tmp = x * 2.0
	elif x <= 2.45e+80:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -12000.0)
		tmp = Float64(x * 2.0);
	elseif (x <= 2.45e+80)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -12000.0)
		tmp = x * 2.0;
	elseif (x <= 2.45e+80)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -12000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 2.45e+80], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -12000 or 2.4499999999999998e80 < x

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. distribute-lft-neg-in 96.4%

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

      3. associate-*l* 96.3%

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

      4. *-commutative 96.3%

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

      5. *-commutative 96.3%

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

      6. cancel-sign-sub-inv 96.3%

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

      7. *-commutative 96.3%

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

      8. *-commutative 96.3%

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

      9. associate-*l* 96.4%

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

      10. associate-*l* 95.7%

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

      11. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around inf 57.8%

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

   if -12000 < x < 2.4499999999999998e80

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. distribute-lft-neg-in 96.6%

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

      3. associate-*l* 96.6%

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

      4. *-commutative 96.6%

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

      5. *-commutative 96.6%

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

      6. cancel-sign-sub-inv 96.6%

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

      7. *-commutative 96.6%

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

      8. *-commutative 96.6%

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

      9. associate-*l* 96.6%

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

      10. associate-*l* 97.8%

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

      11. 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. Taylor expanded in a around inf 43.5%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+80}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 12: 31.1% accurate, 5.7× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: 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 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-lft-neg-in 96.5%

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

   3. associate-*l* 96.5%

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

   4. *-commutative 96.5%

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

   5. *-commutative 96.5%

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

   6. cancel-sign-sub-inv 96.5%

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

   7. *-commutative 96.5%

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

   8. *-commutative 96.5%

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

   9. associate-*l* 96.5%

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

   10. associate-*l* 96.9%

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

   11. 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. Taylor expanded in x around inf 31.4%

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

5. Final simplification 31.4%

   \[\leadsto x \cdot 2 \]

Developer target: 95.4% accurate, 0.9× 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 2023285 
(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)))