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

Percentage Accurate: 95.3% → 98.2%

Time: 13.8s

Alternatives: 18

Speedup: 0.8×

• 27.7% 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: 95.3% 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: 98.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(2 \cdot \frac{x}{z} + 27 \cdot \frac{a \cdot b}{z}\right) - 9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.7e+55)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* z (* t -9.0)))))
   (* z (- (+ (* 2.0 (/ x z)) (* 27.0 (/ (* a b) z))) (* 9.0 (* y t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.7e+55) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (z * (t * -9.0)))));
	} else {
		tmp = z * (((2.0 * (x / z)) + (27.0 * ((a * b) / z))) - (9.0 * (y * t)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.7e+55)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(z * Float64(t * -9.0)))));
	else
		tmp = Float64(z * Float64(Float64(Float64(2.0 * Float64(x / z)) + Float64(27.0 * Float64(Float64(a * b) / z))) - Float64(9.0 * Float64(y * t))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3.7e+55], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(N[(2.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.7000000000000002e55

   1. Initial program 96.6%

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

   3. Simplified 96.3%

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

   if 3.7000000000000002e55 < z

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-*l* 88.3%

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

      5. associate-+l- 88.3%

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

      6. associate-*l* 88.3%

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

      7. *-commutative 88.3%

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

      8. *-commutative 88.3%

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

      9. associate-*l* 86.7%

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

      10. associate-*l* 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around inf 97.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(2 \cdot \frac{x}{z} + 27 \cdot \frac{a \cdot b}{z}\right) - 9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+241}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* z (* y 9.0)) 1e+241)
   (fma a (* 27.0 b) (fma x 2.0 (* t (* y (* z -9.0)))))
   (- (* x 2.0) (* z (* y (* t 9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 1e+241) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (y * (z * -9.0)))));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * Float64(y * 9.0)) <= 1e+241)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(y * Float64(z * -9.0)))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(z * Float64(y * Float64(t * 9.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision], 1e+241], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(y * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1.0000000000000001e241

   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. +-commutative 96.5%

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

      2. associate-+r- 96.5%

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

      3. *-commutative 96.5%

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

      4. cancel-sign-sub-inv 96.5%

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

      5. associate-*r* 95.4%

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

      6. distribute-lft-neg-in 95.4%

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

      7. *-commutative 95.4%

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

      8. cancel-sign-sub-inv 95.4%

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

      9. associate-+r- 95.4%

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

      10. associate-*l* 95.4%

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

      11. fma-define 96.2%

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

      12. cancel-sign-sub-inv 96.2%

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

      13. fma-define 96.2%

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

      14. *-commutative 96.2%

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

      15. distribute-rgt-neg-in 96.2%

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

      16. distribute-lft-neg-out 96.2%

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

      17. associate-*r* 97.3%

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

      18. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   if 1.0000000000000001e241 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. *-commutative 76.8%

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

      4. associate-*l* 76.8%

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

      5. associate-+l- 76.8%

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

      6. associate-*l* 76.8%

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

      7. *-commutative 76.8%

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

      8. *-commutative 76.8%

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

      9. associate-*l* 88.2%

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

      10. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in a around 0 76.9%

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

      1. pow1 76.9%

         \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

      2. *-commutative 76.9%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)}^{1} \]

      3. associate-*r* 82.3%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right)}^{1} \]

      4. *-commutative 82.3%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right)}^{1} \]

   7. Applied egg-rr 82.3%

      \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 82.3%

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

      2. associate-*r* 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*r* 82.3%

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

      5. *-commutative 82.3%

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

      6. *-commutative 82.3%

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

      7. *-commutative 82.3%

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

      8. associate-*l* 82.3%

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

   9. Simplified 82.3%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+241}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-279}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-74}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.9e-57)
   (* a (* 27.0 b))
   (if (<= b -7.2e-172)
     (* (* z t) (* y -9.0))
     (if (<= b 1.7e-279)
       (* x 2.0)
       (if (<= b 9e-74)
         (* -9.0 (* y (* z t)))
         (if (<= b 5.6e+37) (* x 2.0) (* b (* a 27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.9e-57) {
		tmp = a * (27.0 * b);
	} else if (b <= -7.2e-172) {
		tmp = (z * t) * (y * -9.0);
	} else if (b <= 1.7e-279) {
		tmp = x * 2.0;
	} else if (b <= 9e-74) {
		tmp = -9.0 * (y * (z * t));
	} else if (b <= 5.6e+37) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.9d-57)) then
        tmp = a * (27.0d0 * b)
    else if (b <= (-7.2d-172)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (b <= 1.7d-279) then
        tmp = x * 2.0d0
    else if (b <= 9d-74) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (b <= 5.6d+37) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.9e-57) {
		tmp = a * (27.0 * b);
	} else if (b <= -7.2e-172) {
		tmp = (z * t) * (y * -9.0);
	} else if (b <= 1.7e-279) {
		tmp = x * 2.0;
	} else if (b <= 9e-74) {
		tmp = -9.0 * (y * (z * t));
	} else if (b <= 5.6e+37) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.9e-57:
		tmp = a * (27.0 * b)
	elif b <= -7.2e-172:
		tmp = (z * t) * (y * -9.0)
	elif b <= 1.7e-279:
		tmp = x * 2.0
	elif b <= 9e-74:
		tmp = -9.0 * (y * (z * t))
	elif b <= 5.6e+37:
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.9e-57)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= -7.2e-172)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (b <= 1.7e-279)
		tmp = Float64(x * 2.0);
	elseif (b <= 9e-74)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (b <= 5.6e+37)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.9e-57)
		tmp = a * (27.0 * b);
	elseif (b <= -7.2e-172)
		tmp = (z * t) * (y * -9.0);
	elseif (b <= 1.7e-279)
		tmp = x * 2.0;
	elseif (b <= 9e-74)
		tmp = -9.0 * (y * (z * t));
	elseif (b <= 5.6e+37)
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.9e-57], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e-172], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-279], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 9e-74], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+37], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.90000000000000006e-57

   1. Initial program 93.6%

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

      1. +-commutative 93.6%

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

      2. associate-+r- 93.6%

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

      3. *-commutative 93.6%

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

      4. cancel-sign-sub-inv 93.6%

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

      5. associate-*r* 92.6%

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

      6. distribute-lft-neg-in 92.6%

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

      7. *-commutative 92.6%

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

      8. cancel-sign-sub-inv 92.6%

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

      9. associate-+r- 92.6%

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

      10. associate-*l* 92.7%

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

      11. fma-define 95.1%

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

      12. cancel-sign-sub-inv 95.1%

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

      13. fma-define 95.1%

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

      14. *-commutative 95.1%

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

      15. distribute-rgt-neg-in 95.1%

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

      16. distribute-lft-neg-out 95.1%

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

      17. associate-*r* 96.1%

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

      18. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 63.8%

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

   6. Taylor expanded in a around inf 53.4%

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

   7. Taylor expanded in x around 0 44.8%

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

   if -3.90000000000000006e-57 < b < -7.20000000000000029e-172

   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. +-commutative 96.6%

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

      2. associate-+r- 96.6%

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

      3. *-commutative 96.6%

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

      4. cancel-sign-sub-inv 96.6%

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

      5. associate-*r* 93.1%

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

      6. distribute-lft-neg-in 93.1%

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

      7. *-commutative 93.1%

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

      8. cancel-sign-sub-inv 93.1%

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

      9. associate-+r- 93.1%

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

      10. associate-*l* 93.1%

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

      11. fma-define 93.1%

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

      12. cancel-sign-sub-inv 93.1%

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

      13. fma-define 93.1%

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

      14. *-commutative 93.1%

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

      15. distribute-rgt-neg-in 93.1%

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

      16. distribute-lft-neg-out 93.1%

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

      17. associate-*r* 96.6%

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

      18. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. associate-*r* 49.7%

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

      3. associate-*l* 49.7%

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

   7. Simplified 49.7%

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

   8. Taylor expanded in t around 0 49.9%

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

      1. *-commutative 49.9%

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

      2. associate-*r* 49.8%

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

      3. *-commutative 49.8%

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

      4. associate-*l* 49.8%

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

      5. *-commutative 49.8%

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

      6. associate-*l* 49.8%

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

      7. *-commutative 49.8%

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

      8. *-commutative 49.8%

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

   10. Simplified 49.8%

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

   if -7.20000000000000029e-172 < b < 1.70000000000000007e-279 or 8.9999999999999998e-74 < b < 5.5999999999999996e37

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-+r- 95.9%

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

      3. *-commutative 95.9%

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

      4. cancel-sign-sub-inv 95.9%

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

      5. associate-*r* 96.1%

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

      6. distribute-lft-neg-in 96.1%

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

      7. *-commutative 96.1%

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

      8. cancel-sign-sub-inv 96.1%

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

      9. associate-+r- 96.1%

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

      10. associate-*l* 96.1%

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

      11. fma-define 96.1%

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

      12. cancel-sign-sub-inv 96.1%

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

      13. fma-define 96.1%

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

      14. *-commutative 96.1%

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

      15. distribute-rgt-neg-in 96.1%

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

      16. distribute-lft-neg-out 96.1%

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

      17. associate-*r* 95.9%

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

      18. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 72.6%

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

   6. Taylor expanded in x around inf 58.0%

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

   if 1.70000000000000007e-279 < b < 8.9999999999999998e-74

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-+r- 97.8%

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

      3. *-commutative 97.8%

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

      4. cancel-sign-sub-inv 97.8%

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

      5. associate-*r* 97.9%

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

      6. distribute-lft-neg-in 97.9%

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

      7. *-commutative 97.9%

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

      8. cancel-sign-sub-inv 97.9%

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

      9. associate-+r- 97.9%

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

      10. associate-*l* 97.9%

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

      11. fma-define 97.9%

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

      12. cancel-sign-sub-inv 97.9%

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

      13. fma-define 97.9%

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

      14. *-commutative 97.9%

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

      15. distribute-rgt-neg-in 97.9%

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

      16. distribute-lft-neg-out 97.9%

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

      17. associate-*r* 97.8%

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

      18. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

      1. fma-undefine 97.8%

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

      2. fma-undefine 97.8%

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

      3. associate-+r+ 97.8%

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

      4. *-commutative 97.8%

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

      5. associate-*l* 93.4%

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

      6. *-commutative 93.4%

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

      7. associate-*r* 93.5%

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

      8. *-commutative 93.5%

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

      9. *-commutative 93.5%

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

      10. associate-*r* 93.4%

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

      11. associate-*l* 93.5%

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

      12. metadata-eval 93.5%

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

      13. distribute-lft-neg-in 93.5%

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

      14. *-commutative 93.5%

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

      15. distribute-rgt-neg-in 93.5%

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

      16. *-commutative 93.5%

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

      17. associate-+r+ 93.5%

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

      18. sub-neg 93.5%

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

   6. Applied egg-rr 93.4%

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

   7. Taylor expanded in y around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-*r* 46.1%

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

      3. *-commutative 46.1%

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

   9. Simplified 46.1%

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

   if 5.5999999999999996e37 < b

   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. +-commutative 94.0%

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

      2. associate-+r- 94.0%

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

      3. *-commutative 94.0%

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

      4. cancel-sign-sub-inv 94.0%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 95.9%

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

      11. fma-define 97.8%

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

      12. cancel-sign-sub-inv 97.8%

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

      13. fma-define 97.8%

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

      14. *-commutative 97.8%

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

      15. distribute-rgt-neg-in 97.8%

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

      16. distribute-lft-neg-out 97.8%

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

      17. associate-*r* 95.9%

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

      18. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 57.9%

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

      1. *-commutative 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-*r* 58.0%

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

      4. *-commutative 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-172}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-279}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-74}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-280}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))))
   (if (<= b -4.5e-58)
     (* a (* 27.0 b))
     (if (<= b -3.4e-173)
       t_1
       (if (<= b 6.5e-280)
         (* x 2.0)
         (if (<= b 1e-73)
           t_1
           (if (<= b 6.5e+33) (* x 2.0) (* b (* a 27.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (b <= -4.5e-58) {
		tmp = a * (27.0 * b);
	} else if (b <= -3.4e-173) {
		tmp = t_1;
	} else if (b <= 6.5e-280) {
		tmp = x * 2.0;
	} else if (b <= 1e-73) {
		tmp = t_1;
	} else if (b <= 6.5e+33) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    if (b <= (-4.5d-58)) then
        tmp = a * (27.0d0 * b)
    else if (b <= (-3.4d-173)) then
        tmp = t_1
    else if (b <= 6.5d-280) then
        tmp = x * 2.0d0
    else if (b <= 1d-73) then
        tmp = t_1
    else if (b <= 6.5d+33) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (b <= -4.5e-58) {
		tmp = a * (27.0 * b);
	} else if (b <= -3.4e-173) {
		tmp = t_1;
	} else if (b <= 6.5e-280) {
		tmp = x * 2.0;
	} else if (b <= 1e-73) {
		tmp = t_1;
	} else if (b <= 6.5e+33) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	tmp = 0
	if b <= -4.5e-58:
		tmp = a * (27.0 * b)
	elif b <= -3.4e-173:
		tmp = t_1
	elif b <= 6.5e-280:
		tmp = x * 2.0
	elif b <= 1e-73:
		tmp = t_1
	elif b <= 6.5e+33:
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (b <= -4.5e-58)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= -3.4e-173)
		tmp = t_1;
	elseif (b <= 6.5e-280)
		tmp = Float64(x * 2.0);
	elseif (b <= 1e-73)
		tmp = t_1;
	elseif (b <= 6.5e+33)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (b <= -4.5e-58)
		tmp = a * (27.0 * b);
	elseif (b <= -3.4e-173)
		tmp = t_1;
	elseif (b <= 6.5e-280)
		tmp = x * 2.0;
	elseif (b <= 1e-73)
		tmp = t_1;
	elseif (b <= 6.5e+33)
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e-58], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-173], t$95$1, If[LessEqual[b, 6.5e-280], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1e-73], t$95$1, If[LessEqual[b, 6.5e+33], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.5000000000000003e-58

   1. Initial program 93.6%

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

      1. +-commutative 93.6%

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

      2. associate-+r- 93.6%

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

      3. *-commutative 93.6%

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

      4. cancel-sign-sub-inv 93.6%

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

      5. associate-*r* 92.6%

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

      6. distribute-lft-neg-in 92.6%

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

      7. *-commutative 92.6%

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

      8. cancel-sign-sub-inv 92.6%

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

      9. associate-+r- 92.6%

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

      10. associate-*l* 92.7%

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

      11. fma-define 95.1%

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

      12. cancel-sign-sub-inv 95.1%

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

      13. fma-define 95.1%

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

      14. *-commutative 95.1%

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

      15. distribute-rgt-neg-in 95.1%

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

      16. distribute-lft-neg-out 95.1%

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

      17. associate-*r* 96.1%

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

      18. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 63.8%

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

   6. Taylor expanded in a around inf 53.4%

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

   7. Taylor expanded in x around 0 44.8%

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

   if -4.5000000000000003e-58 < b < -3.3999999999999999e-173 or 6.5000000000000005e-280 < b < 9.99999999999999997e-74

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-+r- 97.3%

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

      3. *-commutative 97.3%

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

      4. cancel-sign-sub-inv 97.3%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 96.0%

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

      11. fma-define 96.0%

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

      12. cancel-sign-sub-inv 96.0%

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

      13. fma-define 96.0%

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

      14. *-commutative 96.0%

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

      15. distribute-rgt-neg-in 96.0%

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

      16. distribute-lft-neg-out 96.0%

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

      17. associate-*r* 97.3%

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

      18. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

      1. fma-undefine 97.3%

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

      2. fma-undefine 97.3%

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

      3. associate-+r+ 97.3%

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

      4. *-commutative 97.3%

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

      5. associate-*l* 93.3%

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

      6. *-commutative 93.3%

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

      7. associate-*r* 93.4%

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

      8. *-commutative 93.4%

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

      9. *-commutative 93.4%

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

      10. associate-*r* 93.3%

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

      11. associate-*l* 93.4%

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

      12. metadata-eval 93.4%

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

      13. distribute-lft-neg-in 93.4%

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

      14. *-commutative 93.4%

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

      15. distribute-rgt-neg-in 93.4%

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

      16. *-commutative 93.4%

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

      17. associate-+r+ 93.4%

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

      18. sub-neg 93.4%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in y around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*r* 47.6%

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

      3. *-commutative 47.6%

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

   9. Simplified 47.6%

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

   if -3.3999999999999999e-173 < b < 6.5000000000000005e-280 or 9.99999999999999997e-74 < b < 6.49999999999999993e33

   1. Initial program 95.7%

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

      1. +-commutative 95.7%

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

      2. associate-+r- 95.7%

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

      3. *-commutative 95.7%

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

      4. cancel-sign-sub-inv 95.7%

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

      5. associate-*r* 95.9%

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

      6. distribute-lft-neg-in 95.9%

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

      7. *-commutative 95.9%

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

      8. cancel-sign-sub-inv 95.9%

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

      9. associate-+r- 95.9%

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

      10. associate-*l* 95.9%

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

      11. fma-define 95.9%

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

      12. cancel-sign-sub-inv 95.9%

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

      13. fma-define 95.9%

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

      14. *-commutative 95.9%

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

      15. distribute-rgt-neg-in 95.9%

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

      16. distribute-lft-neg-out 95.9%

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

      17. associate-*r* 95.7%

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

      18. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around 0 73.5%

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

   6. Taylor expanded in x around inf 60.4%

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

   if 6.49999999999999993e33 < b

   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. +-commutative 94.3%

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

      2. associate-+r- 94.3%

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

      3. *-commutative 94.3%

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

      4. cancel-sign-sub-inv 94.3%

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

      5. associate-*r* 96.1%

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

      6. distribute-lft-neg-in 96.1%

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

      7. *-commutative 96.1%

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

      8. cancel-sign-sub-inv 96.1%

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

      9. associate-+r- 96.1%

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

      10. associate-*l* 96.0%

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

      11. fma-define 97.9%

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

      12. cancel-sign-sub-inv 97.9%

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

      13. fma-define 97.9%

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

      14. *-commutative 97.9%

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

      15. distribute-rgt-neg-in 97.9%

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

      16. distribute-lft-neg-out 97.9%

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

      17. associate-*r* 96.1%

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

      18. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in a around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. associate-*r* 57.7%

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

      4. *-commutative 57.7%

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

   7. Simplified 57.7%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-173}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-280}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 10^{-73}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-280}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))))
   (if (<= b -4.3e-58)
     (* a (* 27.0 b))
     (if (<= b -5.8e-173)
       t_1
       (if (<= b 5.8e-280)
         (* x 2.0)
         (if (<= b 9.5e-74)
           t_1
           (if (<= b 4e+35) (* x 2.0) (* b (* a 27.0)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (b <= -4.3e-58) {
		tmp = a * (27.0 * b);
	} else if (b <= -5.8e-173) {
		tmp = t_1;
	} else if (b <= 5.8e-280) {
		tmp = x * 2.0;
	} else if (b <= 9.5e-74) {
		tmp = t_1;
	} else if (b <= 4e+35) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    if (b <= (-4.3d-58)) then
        tmp = a * (27.0d0 * b)
    else if (b <= (-5.8d-173)) then
        tmp = t_1
    else if (b <= 5.8d-280) then
        tmp = x * 2.0d0
    else if (b <= 9.5d-74) then
        tmp = t_1
    else if (b <= 4d+35) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (b <= -4.3e-58) {
		tmp = a * (27.0 * b);
	} else if (b <= -5.8e-173) {
		tmp = t_1;
	} else if (b <= 5.8e-280) {
		tmp = x * 2.0;
	} else if (b <= 9.5e-74) {
		tmp = t_1;
	} else if (b <= 4e+35) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	tmp = 0
	if b <= -4.3e-58:
		tmp = a * (27.0 * b)
	elif b <= -5.8e-173:
		tmp = t_1
	elif b <= 5.8e-280:
		tmp = x * 2.0
	elif b <= 9.5e-74:
		tmp = t_1
	elif b <= 4e+35:
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (b <= -4.3e-58)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= -5.8e-173)
		tmp = t_1;
	elseif (b <= 5.8e-280)
		tmp = Float64(x * 2.0);
	elseif (b <= 9.5e-74)
		tmp = t_1;
	elseif (b <= 4e+35)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (b <= -4.3e-58)
		tmp = a * (27.0 * b);
	elseif (b <= -5.8e-173)
		tmp = t_1;
	elseif (b <= 5.8e-280)
		tmp = x * 2.0;
	elseif (b <= 9.5e-74)
		tmp = t_1;
	elseif (b <= 4e+35)
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.3e-58], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-173], t$95$1, If[LessEqual[b, 5.8e-280], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 9.5e-74], t$95$1, If[LessEqual[b, 4e+35], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.2999999999999999e-58

   1. Initial program 93.6%

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

      1. +-commutative 93.6%

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

      2. associate-+r- 93.6%

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

      3. *-commutative 93.6%

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

      4. cancel-sign-sub-inv 93.6%

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

      5. associate-*r* 92.6%

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

      6. distribute-lft-neg-in 92.6%

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

      7. *-commutative 92.6%

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

      8. cancel-sign-sub-inv 92.6%

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

      9. associate-+r- 92.6%

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

      10. associate-*l* 92.7%

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

      11. fma-define 95.1%

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

      12. cancel-sign-sub-inv 95.1%

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

      13. fma-define 95.1%

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

      14. *-commutative 95.1%

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

      15. distribute-rgt-neg-in 95.1%

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

      16. distribute-lft-neg-out 95.1%

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

      17. associate-*r* 96.1%

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

      18. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 63.8%

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

   6. Taylor expanded in a around inf 53.4%

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

   7. Taylor expanded in x around 0 44.8%

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

   if -4.2999999999999999e-58 < b < -5.7999999999999997e-173 or 5.8e-280 < b < 9.5000000000000007e-74

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-+r- 97.3%

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

      3. *-commutative 97.3%

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

      4. cancel-sign-sub-inv 97.3%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 96.0%

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

      11. fma-define 96.0%

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

      12. cancel-sign-sub-inv 96.0%

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

      13. fma-define 96.0%

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

      14. *-commutative 96.0%

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

      15. distribute-rgt-neg-in 96.0%

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

      16. distribute-lft-neg-out 96.0%

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

      17. associate-*r* 97.3%

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

      18. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 48.8%

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

   if -5.7999999999999997e-173 < b < 5.8e-280 or 9.5000000000000007e-74 < b < 3.9999999999999999e35

   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. +-commutative 95.8%

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

      2. associate-+r- 95.8%

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

      3. *-commutative 95.8%

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

      4. cancel-sign-sub-inv 95.8%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 96.0%

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

      11. fma-define 96.0%

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

      12. cancel-sign-sub-inv 96.0%

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

      13. fma-define 96.0%

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

      14. *-commutative 96.0%

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

      15. distribute-rgt-neg-in 96.0%

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

      16. distribute-lft-neg-out 96.0%

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

      17. associate-*r* 95.8%

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

      18. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around 0 72.0%

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

   6. Taylor expanded in x around inf 59.2%

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

   if 3.9999999999999999e35 < b

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-+r- 94.1%

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

      3. *-commutative 94.1%

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

      4. cancel-sign-sub-inv 94.1%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 95.9%

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

      11. fma-define 97.9%

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

      12. cancel-sign-sub-inv 97.9%

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

      13. fma-define 97.9%

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

      14. *-commutative 97.9%

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

      15. distribute-rgt-neg-in 97.9%

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

      16. distribute-lft-neg-out 97.9%

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

      17. associate-*r* 96.0%

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

      18. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. *-commutative 58.7%

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

      3. associate-*r* 58.8%

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

      4. *-commutative 58.8%

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

   7. Simplified 58.8%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-280}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+35}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(2 \cdot \frac{x}{z} + 27 \cdot \frac{a \cdot b}{z}\right) - 9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 8e+41)
   (+ (- (* x 2.0) (* (* y 9.0) (* z t))) (* a (* 27.0 b)))
   (* z (- (+ (* 2.0 (/ x z)) (* 27.0 (/ (* a b) z))) (* 9.0 (* y t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8e+41) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = z * (((2.0 * (x / z)) + (27.0 * ((a * b) / z))) - (9.0 * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 8d+41) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (z * t))) + (a * (27.0d0 * b))
    else
        tmp = z * (((2.0d0 * (x / z)) + (27.0d0 * ((a * b) / z))) - (9.0d0 * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8e+41) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = z * (((2.0 * (x / z)) + (27.0 * ((a * b) / z))) - (9.0 * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 8e+41:
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b))
	else:
		tmp = z * (((2.0 * (x / z)) + (27.0 * ((a * b) / z))) - (9.0 * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 8e+41)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(z * Float64(Float64(Float64(2.0 * Float64(x / z)) + Float64(27.0 * Float64(Float64(a * b) / z))) - Float64(9.0 * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 8e+41)
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	else
		tmp = z * (((2.0 * (x / z)) + (27.0 * ((a * b) / z))) - (9.0 * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 8e+41], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(N[(2.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.00000000000000005e41

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. *-commutative 97.0%

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

      3. *-commutative 97.0%

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

      4. associate-*l* 97.0%

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

      5. associate-+l- 97.0%

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

      6. associate-*l* 97.0%

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

      7. *-commutative 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   if 8.00000000000000005e41 < z

   1. Initial program 87.7%

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

      1. associate-+l- 87.7%

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

      2. *-commutative 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-*l* 87.7%

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

      5. associate-+l- 87.7%

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

      6. associate-*l* 87.7%

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

      7. *-commutative 87.7%

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

      8. *-commutative 87.7%

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

      9. associate-*l* 84.6%

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

      10. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 95.8%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(2 \cdot \frac{x}{z} + 27 \cdot \frac{a \cdot b}{z}\right) - 9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq 10^{+241}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot t\_1\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* y 9.0))))
   (if (<= t_1 1e+241)
     (+ (- (* x 2.0) (* t t_1)) (* b (* a 27.0)))
     (- (* x 2.0) (* z (* y (* t 9.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 1e+241) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y * 9.0d0)
    if (t_1 <= 1d+241) then
        tmp = ((x * 2.0d0) - (t * t_1)) + (b * (a * 27.0d0))
    else
        tmp = (x * 2.0d0) - (z * (y * (t * 9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 1e+241) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (y * 9.0)
	tmp = 0
	if t_1 <= 1e+241:
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0))
	else:
		tmp = (x * 2.0) - (z * (y * (t * 9.0)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= 1e+241)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * t_1)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(z * Float64(y * Float64(t * 9.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y * 9.0);
	tmp = 0.0;
	if (t_1 <= 1e+241)
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	else
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+241], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(y * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1.0000000000000001e241

   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. Add Preprocessing

   if 1.0000000000000001e241 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. *-commutative 76.8%

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

      4. associate-*l* 76.8%

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

      5. associate-+l- 76.8%

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

      6. associate-*l* 76.8%

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

      7. *-commutative 76.8%

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

      8. *-commutative 76.8%

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

      9. associate-*l* 88.2%

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

      10. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in a around 0 76.9%

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

      1. pow1 76.9%

         \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

      2. *-commutative 76.9%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)}^{1} \]

      3. associate-*r* 82.3%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right)}^{1} \]

      4. *-commutative 82.3%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right)}^{1} \]

   7. Applied egg-rr 82.3%

      \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 82.3%

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

      2. associate-*r* 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*r* 82.3%

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

      5. *-commutative 82.3%

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

      6. *-commutative 82.3%

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

      7. *-commutative 82.3%

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

      8. associate-*l* 82.3%

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

   9. Simplified 82.3%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 10^{+241}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot y\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{-59}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot t\_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-9 \cdot \frac{t\_1}{b} + a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* z y))))
   (if (<= b -1.05e-59)
     (- (* 27.0 (* a b)) (* 9.0 t_1))
     (if (<= b 5.8e+34)
       (- (* x 2.0) (* z (* y (* t 9.0))))
       (* b (+ (* -9.0 (/ t_1 b)) (* a 27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * y);
	double tmp;
	if (b <= -1.05e-59) {
		tmp = (27.0 * (a * b)) - (9.0 * t_1);
	} else if (b <= 5.8e+34) {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	} else {
		tmp = b * ((-9.0 * (t_1 / b)) + (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (z * y)
    if (b <= (-1.05d-59)) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * t_1)
    else if (b <= 5.8d+34) then
        tmp = (x * 2.0d0) - (z * (y * (t * 9.0d0)))
    else
        tmp = b * (((-9.0d0) * (t_1 / b)) + (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z * y);
	double tmp;
	if (b <= -1.05e-59) {
		tmp = (27.0 * (a * b)) - (9.0 * t_1);
	} else if (b <= 5.8e+34) {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	} else {
		tmp = b * ((-9.0 * (t_1 / b)) + (a * 27.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z * y)
	tmp = 0
	if b <= -1.05e-59:
		tmp = (27.0 * (a * b)) - (9.0 * t_1)
	elif b <= 5.8e+34:
		tmp = (x * 2.0) - (z * (y * (t * 9.0)))
	else:
		tmp = b * ((-9.0 * (t_1 / b)) + (a * 27.0))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z * y))
	tmp = 0.0
	if (b <= -1.05e-59)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * t_1));
	elseif (b <= 5.8e+34)
		tmp = Float64(Float64(x * 2.0) - Float64(z * Float64(y * Float64(t * 9.0))));
	else
		tmp = Float64(b * Float64(Float64(-9.0 * Float64(t_1 / b)) + Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z * y);
	tmp = 0.0;
	if (b <= -1.05e-59)
		tmp = (27.0 * (a * b)) - (9.0 * t_1);
	elseif (b <= 5.8e+34)
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	else
		tmp = b * ((-9.0 * (t_1 / b)) + (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e-59], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+34], N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(y * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(-9.0 * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] + N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.04999999999999998e-59

   1. Initial program 92.6%

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

      1. associate-+l- 92.6%

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

      2. *-commutative 92.6%

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

      3. *-commutative 92.6%

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

      4. associate-*l* 92.7%

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

      5. associate-+l- 92.7%

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

      6. associate-*l* 92.6%

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

      7. *-commutative 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around 0 74.2%

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

   if -1.04999999999999998e-59 < b < 5.8000000000000003e34

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. *-commutative 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*l* 97.5%

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

      5. associate-+l- 97.5%

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

      6. associate-*l* 97.5%

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

      7. *-commutative 97.5%

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

      8. *-commutative 97.5%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around 0 87.3%

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

      1. pow1 87.3%

         \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

      2. *-commutative 87.3%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)}^{1} \]

      3. associate-*r* 84.9%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right)}^{1} \]

      4. *-commutative 84.9%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right)}^{1} \]

   7. Applied egg-rr 84.9%

      \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 84.9%

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

      2. associate-*r* 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*r* 84.9%

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

      5. *-commutative 84.9%

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

      6. *-commutative 84.9%

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

      7. *-commutative 84.9%

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

      8. associate-*l* 84.9%

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

   9. Simplified 84.9%

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

   if 5.8000000000000003e34 < b

   1. Initial program 94.1%

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

      1. associate-+l- 94.1%

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

      2. *-commutative 94.1%

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

      3. *-commutative 94.1%

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

      4. associate-*l* 94.2%

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

      5. associate-+l- 94.2%

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

      6. associate-*l* 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 90.7%

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

      10. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around 0 76.8%

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

   6. Taylor expanded in b around inf 78.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-59}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-9 \cdot \frac{t \cdot \left(z \cdot y\right)}{b} + a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-59} \lor \neg \left(b \leq 3.45 \cdot 10^{+34}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.3e-59) (not (<= b 3.45e+34)))
   (- (* 27.0 (* a b)) (* 9.0 (* t (* z y))))
   (- (* x 2.0) (* z (* y (* t 9.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e-59) || !(b <= 3.45e+34)) {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.3d-59)) .or. (.not. (b <= 3.45d+34))) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (t * (z * y)))
    else
        tmp = (x * 2.0d0) - (z * (y * (t * 9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e-59) || !(b <= 3.45e+34)) {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.3e-59) or not (b <= 3.45e+34):
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)))
	else:
		tmp = (x * 2.0) - (z * (y * (t * 9.0)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.3e-59) || !(b <= 3.45e+34))
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(t * Float64(z * y))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(z * Float64(y * Float64(t * 9.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.3e-59) || ~((b <= 3.45e+34)))
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	else
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.3e-59], N[Not[LessEqual[b, 3.45e+34]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(y * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.29999999999999979e-59 or 3.45000000000000019e34 < b

   1. Initial program 93.2%

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

      1. associate-+l- 93.2%

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

      2. *-commutative 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*l* 93.2%

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

      5. associate-+l- 93.2%

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

      6. associate-*l* 93.2%

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

      7. *-commutative 93.2%

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

      8. *-commutative 93.2%

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

      9. associate-*l* 91.5%

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

      10. 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. Add Preprocessing

   5. Taylor expanded in x around 0 75.2%

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

   if -2.29999999999999979e-59 < b < 3.45000000000000019e34

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. *-commutative 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*l* 97.5%

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

      5. associate-+l- 97.5%

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

      6. associate-*l* 97.5%

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

      7. *-commutative 97.5%

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

      8. *-commutative 97.5%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around 0 87.3%

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

      1. pow1 87.3%

         \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

      2. *-commutative 87.3%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)}^{1} \]

      3. associate-*r* 84.9%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right)}^{1} \]

      4. *-commutative 84.9%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right)}^{1} \]

   7. Applied egg-rr 84.9%

      \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 84.9%

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

      2. associate-*r* 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*r* 84.9%

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

      5. *-commutative 84.9%

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

      6. *-commutative 84.9%

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

      7. *-commutative 84.9%

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

      8. associate-*l* 84.9%

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

   9. Simplified 84.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-59} \lor \neg \left(b \leq 3.45 \cdot 10^{+34}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-43}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.4e-43)
   (- (* x 2.0) (* 9.0 (* t (* z y))))
   (if (<= x 3.7e+30)
     (+ (* a (* 27.0 b)) (* y (* -9.0 (* z t))))
     (+ (* x 2.0) (* 27.0 (* a b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.4e-43) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (x <= 3.7e+30) {
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5.4d-43)) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else if (x <= 3.7d+30) then
        tmp = (a * (27.0d0 * b)) + (y * ((-9.0d0) * (z * t)))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.4e-43) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (x <= 3.7e+30) {
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.4e-43:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	elif x <= 3.7e+30:
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.4e-43)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	elseif (x <= 3.7e+30)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(y * Float64(-9.0 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.4e-43)
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	elseif (x <= 3.7e+30)
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.4e-43], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+30], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.39999999999999982e-43

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. *-commutative 97.0%

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

      3. *-commutative 97.0%

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

      4. associate-*l* 97.0%

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

      5. associate-+l- 97.0%

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

      6. associate-*l* 97.0%

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

      7. *-commutative 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*l* 92.9%

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

      10. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in a around 0 82.3%

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

   if -5.39999999999999982e-43 < x < 3.70000000000000016e30

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. *-commutative 93.1%

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

      3. *-commutative 93.1%

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

      4. associate-*l* 93.1%

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

      5. associate-+l- 93.1%

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

      6. associate-*l* 93.1%

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

      7. *-commutative 93.1%

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

      8. *-commutative 93.1%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. pow1 83.5%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{{\left(t \cdot \left(y \cdot z\right)\right)}^{1}} \]

      2. *-commutative 83.5%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot {\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}}^{1} \]

      3. associate-*l* 82.3%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot {\color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}}^{1} \]

   7. Applied egg-rr 82.3%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{{\left(y \cdot \left(z \cdot t\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 82.3%

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

      2. *-commutative 82.3%

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

   9. Simplified 82.3%

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

       1. cancel-sign-sub-inv 82.3%

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

       2. metadata-eval 82.3%

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

       3. rem-cube-cbrt 81.8%

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

       4. +-commutative 81.8%

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

       5. *-commutative 81.8%

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

       6. rem-cube-cbrt 82.3%

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

       7. associate-*l* 82.3%

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

       8. *-commutative 82.3%

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

       9. *-commutative 82.3%

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

       10. associate-*l* 82.3%

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

   11. Applied egg-rr 82.3%

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

   if 3.70000000000000016e30 < x

   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. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. *-commutative 98.1%

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

      4. cancel-sign-sub-inv 98.1%

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

      5. associate-*r* 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. cancel-sign-sub-inv 99.9%

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

      9. associate-+r- 99.9%

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

      10. associate-*l* 99.9%

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

      11. fma-define 99.9%

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

      12. cancel-sign-sub-inv 99.9%

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

      13. fma-define 99.9%

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

      14. *-commutative 99.9%

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

      15. distribute-rgt-neg-in 99.9%

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

      16. distribute-lft-neg-out 99.9%

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

      17. associate-*r* 98.1%

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

      18. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 87.3%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-43}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(27 \cdot \frac{a \cdot b}{z} - 9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.5e+67)
   (+ (- (* x 2.0) (* (* y 9.0) (* z t))) (* a (* 27.0 b)))
   (* z (- (* 27.0 (/ (* a b) z)) (* 9.0 (* y t))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.5e+67) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = z * ((27.0 * ((a * b) / z)) - (9.0 * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 2.5d+67) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (z * t))) + (a * (27.0d0 * b))
    else
        tmp = z * ((27.0d0 * ((a * b) / z)) - (9.0d0 * (y * t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.5e+67) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = z * ((27.0 * ((a * b) / z)) - (9.0 * (y * t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2.5e+67:
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b))
	else:
		tmp = z * ((27.0 * ((a * b) / z)) - (9.0 * (y * t)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.5e+67)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(z * Float64(Float64(27.0 * Float64(Float64(a * b) / z)) - Float64(9.0 * Float64(y * t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2.5e+67)
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	else
		tmp = z * ((27.0 * ((a * b) / z)) - (9.0 * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2.5e+67], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(27.0 * N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.49999999999999988e67

   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. associate-+l- 96.6%

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

      2. *-commutative 96.6%

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

      3. *-commutative 96.6%

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

      4. associate-*l* 96.7%

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

      5. associate-+l- 96.7%

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

      6. associate-*l* 96.6%

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

      7. *-commutative 96.6%

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

      8. *-commutative 96.6%

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

      9. associate-*l* 94.9%

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

      10. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   if 2.49999999999999988e67 < z

   1. Initial program 87.4%

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

      1. associate-+l- 87.4%

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

      2. *-commutative 87.4%

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

      3. *-commutative 87.4%

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

      4. associate-*l* 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate-*l* 87.4%

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

      7. *-commutative 87.4%

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

      8. *-commutative 87.4%

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

      9. associate-*l* 85.8%

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

      10. associate-*l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around 0 70.3%

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

   6. Taylor expanded in z around inf 82.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+67}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(27 \cdot \frac{a \cdot b}{z} - 9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+73} \lor \neg \left(y \leq 2.6 \cdot 10^{-160}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.65e+73) (not (<= y 2.6e-160)))
   (- (* x 2.0) (* 9.0 (* t (* z y))))
   (+ (* x 2.0) (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.65e+73) || !(y <= 2.6e-160)) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.65d+73)) .or. (.not. (y <= 2.6d-160))) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.65e+73) || !(y <= 2.6e-160)) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.65e+73) or not (y <= 2.6e-160):
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.65e+73) || !(y <= 2.6e-160))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.65e+73) || ~((y <= 2.6e-160)))
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.65e+73], N[Not[LessEqual[y, 2.6e-160]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.65000000000000012e73 or 2.60000000000000003e-160 < y

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. *-commutative 91.1%

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

      3. *-commutative 91.1%

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

      4. associate-*l* 91.1%

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

      5. associate-+l- 91.1%

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

      6. associate-*l* 91.1%

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

      7. *-commutative 91.1%

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

      8. *-commutative 91.1%

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

      9. associate-*l* 94.8%

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

      10. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 67.8%

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

   if -3.65000000000000012e73 < y < 2.60000000000000003e-160

   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. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. *-commutative 99.8%

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

      4. cancel-sign-sub-inv 99.8%

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

      5. associate-*r* 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. cancel-sign-sub-inv 99.8%

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

      9. associate-+r- 99.8%

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

      10. associate-*l* 99.8%

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

      11. fma-define 99.8%

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

      12. cancel-sign-sub-inv 99.8%

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

      13. fma-define 99.8%

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

      14. *-commutative 99.8%

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

      15. distribute-rgt-neg-in 99.8%

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

      16. distribute-lft-neg-out 99.8%

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

      17. associate-*r* 99.8%

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

      18. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 77.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+73} \lor \neg \left(y \leq 2.6 \cdot 10^{-160}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+72}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-160}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.8e+72)
   (- (* x 2.0) (* 9.0 (* t (* z y))))
   (if (<= y 2.6e-160)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (- (* x 2.0) (* z (* y (* t 9.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.8e+72) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (y <= 2.6e-160) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.8d+72)) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    else if (y <= 2.6d-160) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (z * (y * (t * 9.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.8e+72) {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	} else if (y <= 2.6e-160) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.8e+72:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	elif y <= 2.6e-160:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (z * (y * (t * 9.0)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.8e+72)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	elseif (y <= 2.6e-160)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(z * Float64(y * Float64(t * 9.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.8e+72)
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	elseif (y <= 2.6e-160)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (z * (y * (t * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.8e+72], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-160], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(y * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.79999999999999984e72

   1. Initial program 87.4%

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

      1. associate-+l- 87.4%

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

      2. *-commutative 87.4%

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

      3. *-commutative 87.4%

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

      4. associate-*l* 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate-*l* 87.4%

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

      7. *-commutative 87.4%

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

      8. *-commutative 87.4%

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

      9. associate-*l* 97.3%

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

      10. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around 0 80.4%

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

   if -7.79999999999999984e72 < y < 2.60000000000000003e-160

   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. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. *-commutative 99.8%

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

      4. cancel-sign-sub-inv 99.8%

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

      5. associate-*r* 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. cancel-sign-sub-inv 99.8%

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

      9. associate-+r- 99.8%

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

      10. associate-*l* 99.8%

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

      11. fma-define 99.8%

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

      12. cancel-sign-sub-inv 99.8%

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

      13. fma-define 99.8%

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

      14. *-commutative 99.8%

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

      15. distribute-rgt-neg-in 99.8%

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

      16. distribute-lft-neg-out 99.8%

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

      17. associate-*r* 99.8%

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

      18. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 77.4%

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

   if 2.60000000000000003e-160 < y

   1. Initial program 92.6%

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

      1. associate-+l- 92.6%

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

      2. *-commutative 92.6%

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

      3. *-commutative 92.6%

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

      4. associate-*l* 92.6%

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

      5. associate-+l- 92.6%

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

      6. associate-*l* 92.6%

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

      7. *-commutative 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-*l* 93.7%

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

      10. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around 0 62.5%

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

      1. pow1 62.5%

         \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}^{1}} \]

      2. *-commutative 62.5%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)}^{1} \]

      3. associate-*r* 61.5%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right)}^{1} \]

      4. *-commutative 61.5%

         \[\leadsto 2 \cdot x - {\left(9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right)}^{1} \]

   7. Applied egg-rr 61.5%

      \[\leadsto 2 \cdot x - \color{blue}{{\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}^{1}} \]
   8. Step-by-step derivation

      1. unpow1 61.5%

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

      2. associate-*r* 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*r* 60.8%

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

      5. *-commutative 60.8%

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

      6. *-commutative 60.8%

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

      7. *-commutative 60.8%

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

      8. associate-*l* 60.8%

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

   9. Simplified 60.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+72}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-160}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-58} \lor \neg \left(b \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e-58) (not (<= b 1.9e+35))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e-58) || !(b <= 1.9e+35)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.3d-58)) .or. (.not. (b <= 1.9d+35))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e-58) || !(b <= 1.9e+35)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e-58) or not (b <= 1.9e+35):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e-58) || !(b <= 1.9e+35))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e-58) || ~((b <= 1.9e+35)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e-58], N[Not[LessEqual[b, 1.9e+35]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.30000000000000003e-58 or 1.9e35 < b

   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. +-commutative 93.8%

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

      2. associate-+r- 93.8%

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

      3. *-commutative 93.8%

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

      4. cancel-sign-sub-inv 93.8%

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

      5. associate-*r* 93.9%

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

      6. distribute-lft-neg-in 93.9%

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

      7. *-commutative 93.9%

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

      8. cancel-sign-sub-inv 93.9%

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

      9. associate-+r- 93.9%

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

      10. associate-*l* 93.9%

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

      11. fma-define 96.2%

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

      12. cancel-sign-sub-inv 96.2%

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

      13. fma-define 96.2%

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

      14. *-commutative 96.2%

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

      15. distribute-rgt-neg-in 96.2%

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

      16. distribute-lft-neg-out 96.2%

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

      17. associate-*r* 96.0%

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

      18. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in a around inf 50.2%

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

   if -1.30000000000000003e-58 < b < 1.9e35

   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. +-commutative 96.7%

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

      2. associate-+r- 96.7%

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

      3. *-commutative 96.7%

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

      4. cancel-sign-sub-inv 96.7%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 96.0%

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

      11. fma-define 96.0%

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

      12. cancel-sign-sub-inv 96.0%

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

      13. fma-define 96.0%

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

      14. *-commutative 96.0%

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

      15. distribute-rgt-neg-in 96.0%

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

      16. distribute-lft-neg-out 96.0%

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

      17. associate-*r* 96.7%

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

      18. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 58.8%

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

   6. Taylor expanded in x around inf 48.5%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-58} \lor \neg \left(b \leq 1.9 \cdot 10^{+35}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.8e-57)
   (* a (* 27.0 b))
   (if (<= b 5.9e+34) (* x 2.0) (* b (* a 27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.8e-57) {
		tmp = a * (27.0 * b);
	} else if (b <= 5.9e+34) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.8d-57)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 5.9d+34) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.8e-57) {
		tmp = a * (27.0 * b);
	} else if (b <= 5.9e+34) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.8e-57:
		tmp = a * (27.0 * b)
	elif b <= 5.9e+34:
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.8e-57)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 5.9e+34)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.8e-57)
		tmp = a * (27.0 * b);
	elseif (b <= 5.9e+34)
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.8e-57], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e+34], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.7999999999999997e-57

   1. Initial program 93.6%

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

      1. +-commutative 93.6%

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

      2. associate-+r- 93.6%

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

      3. *-commutative 93.6%

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

      4. cancel-sign-sub-inv 93.6%

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

      5. associate-*r* 92.6%

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

      6. distribute-lft-neg-in 92.6%

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

      7. *-commutative 92.6%

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

      8. cancel-sign-sub-inv 92.6%

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

      9. associate-+r- 92.6%

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

      10. associate-*l* 92.7%

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

      11. fma-define 95.1%

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

      12. cancel-sign-sub-inv 95.1%

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

      13. fma-define 95.1%

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

      14. *-commutative 95.1%

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

      15. distribute-rgt-neg-in 95.1%

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

      16. distribute-lft-neg-out 95.1%

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

      17. associate-*r* 96.1%

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

      18. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 63.8%

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

   6. Taylor expanded in a around inf 53.4%

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

   7. Taylor expanded in x around 0 44.8%

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

   if -3.7999999999999997e-57 < b < 5.8999999999999999e34

   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. +-commutative 96.7%

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

      2. associate-+r- 96.7%

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

      3. *-commutative 96.7%

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

      4. cancel-sign-sub-inv 96.7%

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

      5. associate-*r* 96.0%

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

      6. distribute-lft-neg-in 96.0%

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

      7. *-commutative 96.0%

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

      8. cancel-sign-sub-inv 96.0%

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

      9. associate-+r- 96.0%

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

      10. associate-*l* 96.0%

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

      11. fma-define 96.0%

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

      12. cancel-sign-sub-inv 96.0%

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

      13. fma-define 96.0%

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

      14. *-commutative 96.0%

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

      15. distribute-rgt-neg-in 96.0%

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

      16. distribute-lft-neg-out 96.0%

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

      17. associate-*r* 96.7%

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

      18. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 58.8%

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

   6. Taylor expanded in x around inf 48.5%

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

   if 5.8999999999999999e34 < b

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-+r- 94.1%

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

      3. *-commutative 94.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 94.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 96.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 96.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 96.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 96.0%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 96.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 95.9%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 97.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-define 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. *-commutative 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

      15. distribute-rgt-neg-in 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

      16. distribute-lft-neg-out 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

      17. associate-*r* 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

      18. associate-*l* 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 58.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} \]

      2. *-commutative 58.7%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot 27 \]

      3. associate-*r* 58.8%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot 27\right)} \]

      4. *-commutative 58.8%

         \[\leadsto b \cdot \color{blue}{\left(27 \cdot a\right)} \]

   7. Simplified 58.8%

      \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e-57)
   (* a (* 27.0 b))
   (if (<= b 5.5e+33) (* x 2.0) (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e-57) {
		tmp = a * (27.0 * b);
	} else if (b <= 5.5e+33) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.6d-57)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 5.5d+33) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e-57) {
		tmp = a * (27.0 * b);
	} else if (b <= 5.5e+33) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e-57:
		tmp = a * (27.0 * b)
	elif b <= 5.5e+33:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e-57)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 5.5e+33)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.6e-57)
		tmp = a * (27.0 * b);
	elseif (b <= 5.5e+33)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e-57], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+33], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.6000000000000002e-57

   1. Initial program 93.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 93.6%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 93.6%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 93.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 93.6%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 92.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 92.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 92.6%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 92.6%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 92.6%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 92.7%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 95.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 95.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-define 95.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. *-commutative 95.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

      15. distribute-rgt-neg-in 95.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

      16. distribute-lft-neg-out 95.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

      17. associate-*r* 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

      18. associate-*l* 96.2%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.8%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   6. Taylor expanded in a around inf 53.4%

      \[\leadsto \color{blue}{a \cdot \left(2 \cdot \frac{x}{a} + 27 \cdot b\right)} \]

   7. Taylor expanded in x around 0 44.8%

      \[\leadsto a \cdot \color{blue}{\left(27 \cdot b\right)} \]

   if -3.6000000000000002e-57 < b < 5.5000000000000006e33

   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. +-commutative 96.7%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 96.7%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 96.7%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 96.7%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 96.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 96.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 96.0%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 96.0%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 96.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 96.0%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 96.0%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-define 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. *-commutative 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

      15. distribute-rgt-neg-in 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

      16. distribute-lft-neg-out 96.0%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

      17. associate-*r* 96.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

      18. associate-*l* 96.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 59.2%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

   6. Taylor expanded in x around inf 48.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 5.5000000000000006e33 < b

   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. +-commutative 94.3%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 94.3%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 94.3%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 94.3%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 96.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 96.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 96.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 96.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 96.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 96.0%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 97.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-define 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. *-commutative 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

      15. distribute-rgt-neg-in 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

      16. distribute-lft-neg-out 97.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

      17. associate-*r* 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

      18. associate-*l* 96.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 57.6%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+201}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.25e+201) (* (* z t) (* y -9.0)) (+ (* x 2.0) (* 27.0 (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+201) {
		tmp = (z * t) * (y * -9.0);
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.25d+201)) then
        tmp = (z * t) * (y * (-9.0d0))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.25e+201) {
		tmp = (z * t) * (y * -9.0);
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.25e+201:
		tmp = (z * t) * (y * -9.0)
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.25e+201)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.25e+201)
		tmp = (z * t) * (y * -9.0);
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.25e+201], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25000000000000005e201

   1. Initial program 82.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 82.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 82.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 82.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 82.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 82.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 82.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 82.5%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 82.5%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 82.5%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 82.5%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 87.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 87.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-define 87.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. *-commutative 87.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

      15. distribute-rgt-neg-in 87.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

      16. distribute-lft-neg-out 87.1%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

      17. associate-*r* 86.6%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

      18. associate-*l* 86.7%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.8%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot -9} \]

      2. associate-*r* 60.7%

         \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]

      3. associate-*l* 60.8%

         \[\leadsto t \cdot \color{blue}{\left(y \cdot \left(z \cdot -9\right)\right)} \]

   7. Simplified 60.8%

      \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(z \cdot -9\right)\right)} \]

   8. Taylor expanded in t around 0 60.8%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

      2. associate-*r* 69.4%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} \]

      3. *-commutative 69.4%

         \[\leadsto -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right) \]

      4. associate-*l* 69.3%

         \[\leadsto \color{blue}{\left(-9 \cdot \left(z \cdot t\right)\right) \cdot y} \]

      5. *-commutative 69.3%

         \[\leadsto \color{blue}{\left(\left(z \cdot t\right) \cdot -9\right)} \cdot y \]

      6. associate-*l* 69.4%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot \left(-9 \cdot y\right)} \]

      7. *-commutative 69.4%

         \[\leadsto \left(z \cdot t\right) \cdot \color{blue}{\left(y \cdot -9\right)} \]

      8. *-commutative 69.4%

         \[\leadsto \color{blue}{\left(t \cdot z\right)} \cdot \left(y \cdot -9\right) \]

   10. Simplified 69.4%

       \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot \left(y \cdot -9\right)} \]

   if -2.25000000000000005e201 < y

   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. +-commutative 96.4%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-+r- 96.4%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      3. *-commutative 96.4%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      4. cancel-sign-sub-inv 96.4%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      5. associate-*r* 96.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

      6. distribute-lft-neg-in 96.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

      7. *-commutative 96.1%

         \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

      8. cancel-sign-sub-inv 96.1%

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

      9. associate-+r- 96.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      10. associate-*l* 96.1%

          \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

      11. fma-define 96.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

      12. cancel-sign-sub-inv 96.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

      13. fma-define 96.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

      14. *-commutative 96.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

      15. distribute-rgt-neg-in 96.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

      16. distribute-lft-neg-out 96.9%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

      17. associate-*r* 97.3%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

      18. associate-*l* 97.3%

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.9%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+201}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.7% accurate, 5.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 95.2%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 95.2%

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

   2. associate-+r- 95.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

   3. *-commutative 95.2%

      \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

   4. cancel-sign-sub-inv 95.2%

      \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

   5. associate-*r* 94.9%

      \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(\left(-t\right) \cdot \left(y \cdot 9\right)\right) \cdot z} \]

   6. distribute-lft-neg-in 94.9%

      \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \color{blue}{\left(-t \cdot \left(y \cdot 9\right)\right)} \cdot z \]

   7. *-commutative 94.9%

      \[\leadsto \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) + \left(-\color{blue}{\left(y \cdot 9\right) \cdot t}\right) \cdot z \]

   8. cancel-sign-sub-inv 94.9%

      \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z} \]

   9. associate-+r- 94.9%

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

   10. associate-*l* 94.9%

       \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right) \]

   11. fma-define 96.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot t\right) \cdot z\right)} \]

   12. cancel-sign-sub-inv 96.1%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{x \cdot 2 + \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z}\right) \]

   13. fma-define 96.1%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-\left(y \cdot 9\right) \cdot t\right) \cdot z\right)}\right) \]

   14. *-commutative 96.1%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(y \cdot 9\right)}\right) \cdot z\right)\right) \]

   15. distribute-rgt-neg-in 96.1%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{\left(t \cdot \left(-y \cdot 9\right)\right)} \cdot z\right)\right) \]

   16. distribute-lft-neg-out 96.1%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \left(t \cdot \color{blue}{\left(\left(-y\right) \cdot 9\right)}\right) \cdot z\right)\right) \]

   17. associate-*r* 96.4%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(\left(-y\right) \cdot 9\right) \cdot z\right)}\right)\right) \]

   18. associate-*l* 96.4%

       \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(\left(-y\right) \cdot \left(9 \cdot z\right)\right)}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 63.8%

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]

6. Taylor expanded in x around inf 34.0%

   \[\leadsto \color{blue}{2 \cdot x} \]

7. Final simplification 34.0%

   \[\leadsto x \cdot 2 \]
8. Add Preprocessing

Developer Target 1: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))