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

Percentage Accurate: 95.3% → 98.6%

Time: 13.1s

Alternatives: 17

Speedup: 1.0×

• 26.7% 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: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{-54}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot \left(9 \cdot y\right)\right) \cdot z\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 6e-54)
   (+ (- (* x 2.0) (* (* t (* 9.0 y)) z)) (* a (* 27.0 b)))
   (fma (* a 27.0) b (fma x 2.0 (* (* y z) (* t -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 6e-54) {
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	} else {
		tmp = fma((a * 27.0), b, fma(x, 2.0, ((y * z) * (t * -9.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 6e-54)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(t * Float64(9.0 * y)) * z)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = fma(Float64(a * 27.0), b, fma(x, 2.0, Float64(Float64(y * z) * Float64(t * -9.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 6e-54], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 27.0), $MachinePrecision] * b + N[(x * 2.0 + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.00000000000000018e-54

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. sub-neg 97.2%

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

      3. associate-*l* 97.0%

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

      4. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-*r* 97.2%

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

      5. *-commutative 97.2%

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

      6. associate-*r* 96.6%

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

      7. *-commutative 96.6%

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

   6. Simplified 96.6%

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

   if 6.00000000000000018e-54 < t

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 90.3%

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

      4. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-*r* 90.3%

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

      3. fma-def 90.3%

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

      4. associate-*r* 97.0%

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

      5. fma-neg 97.0%

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

      6. distribute-lft-neg-in 97.0%

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

      7. distribute-lft-neg-in 97.0%

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

      8. distribute-rgt-neg-in 97.0%

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

      9. metadata-eval 97.0%

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

      10. associate-*r* 97.0%

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

      11. *-commutative 97.0%

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

      12. associate-*l* 97.0%

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

      13. associate-*l* 96.9%

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

   5. Applied egg-rr 96.9%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{-54}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot \left(9 \cdot y\right)\right) \cdot z\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\right)\right)\\ \end{array} \]

Alternative 2: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot \left(9 \cdot y\right)\right) \cdot z\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 3.8e-177)
   (+ (- (* x 2.0) (* (* t (* 9.0 y)) z)) (* a (* 27.0 b)))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* 9.0 (* y z)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.8e-177) {
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 3.8d-177) then
        tmp = ((x * 2.0d0) - ((t * (9.0d0 * y)) * z)) + (a * (27.0d0 * b))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (9.0d0 * (y * z))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.8e-177) {
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 3.8e-177:
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 3.8e-177)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(t * Float64(9.0 * y)) * z)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 3.8e-177)
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.8e-177], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.80000000000000004e-177

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. sub-neg 97.4%

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

      3. associate-*l* 96.6%

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

      4. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l* 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*r* 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

   6. Simplified 96.1%

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

   if 3.80000000000000004e-177 < t

   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. Taylor expanded in y around 0 96.7%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.8 \cdot 10^{-177}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot \left(9 \cdot y\right)\right) \cdot z\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(t \cdot z\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1e-124)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* t z) (* 9.0 y))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* 9.0 (* y z)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e-124) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((t * z) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1d-124)) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((t * z) * (9.0d0 * y)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (9.0d0 * (y * z))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e-124) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((t * z) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1e-124:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((t * z) * (9.0 * y)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1e-124)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(t * z) * Float64(9.0 * y))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1e-124)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((t * z) * (9.0 * y)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1e-124], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * z), $MachinePrecision] * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999933e-125

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. sub-neg 96.8%

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

      3. associate-*l* 93.9%

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

      4. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   if -9.99999999999999933e-125 < z

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 97.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(t \cdot z\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 4: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-120}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e-120)
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* 9.0 (* t z))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* 9.0 (* y z)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e-120) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (t * z)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2d-120)) then
        tmp = ((a * (27.0d0 * b)) + (x * 2.0d0)) - (y * (9.0d0 * (t * z)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (9.0d0 * (y * z))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e-120) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (t * z)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2e-120:
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (t * z)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e-120)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(y * Float64(9.0 * Float64(t * z))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2e-120)
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (t * z)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2e-120], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999996e-120

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. sub-neg 96.7%

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

      3. associate-*l* 93.7%

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

      4. associate-*l* 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. Step-by-step derivation

      1. +-commutative 93.7%

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

      2. associate-+r- 93.7%

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

      3. associate-*l* 93.7%

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

   5. Applied egg-rr 93.7%

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

   if -1.99999999999999996e-120 < z

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 97.4%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-120}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 5: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-181}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot \left(9 \cdot y\right)\right) \cdot z\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1e-181)
   (+ (- (* x 2.0) (* (* t (* 9.0 y)) z)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* t (* y (* 9.0 z)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e-181) {
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1d-181) then
        tmp = ((x * 2.0d0) - ((t * (9.0d0 * y)) * z)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (t * (y * (9.0d0 * z)))) + (b * (a * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e-181) {
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1e-181:
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1e-181)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(t * Float64(9.0 * y)) * z)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1e-181)
		tmp = ((x * 2.0) - ((t * (9.0 * y)) * z)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1e-181], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000005e-181

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. sub-neg 97.4%

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

      3. associate-*l* 96.6%

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

      4. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l* 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*r* 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

   6. Simplified 96.1%

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

   if 1.00000000000000005e-181 < t

   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. pow1 96.7%

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

      2. associate-*l* 96.7%

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

   3. Applied egg-rr 96.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{{\left(y \cdot \left(9 \cdot z\right)\right)}^{1}} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-181}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot \left(9 \cdot y\right)\right) \cdot z\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 6: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+54}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= x -1.1e+73)
     (* x 2.0)
     (if (<= x -500000.0)
       t_1
       (if (<= x -2.1e-93)
         (* -9.0 (* z (* t y)))
         (if (<= x -1.5e-199)
           t_1
           (if (<= x -4e-268)
             (* y (* z (* t -9.0)))
             (if (<= x 7.8e+54) (* 27.0 (* a b)) (* x 2.0)))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (x <= -1.1e+73) {
		tmp = x * 2.0;
	} else if (x <= -500000.0) {
		tmp = t_1;
	} else if (x <= -2.1e-93) {
		tmp = -9.0 * (z * (t * y));
	} else if (x <= -1.5e-199) {
		tmp = t_1;
	} else if (x <= -4e-268) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= 7.8e+54) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (x <= (-1.1d+73)) then
        tmp = x * 2.0d0
    else if (x <= (-500000.0d0)) then
        tmp = t_1
    else if (x <= (-2.1d-93)) then
        tmp = (-9.0d0) * (z * (t * y))
    else if (x <= (-1.5d-199)) then
        tmp = t_1
    else if (x <= (-4d-268)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (x <= 7.8d+54) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (x <= -1.1e+73) {
		tmp = x * 2.0;
	} else if (x <= -500000.0) {
		tmp = t_1;
	} else if (x <= -2.1e-93) {
		tmp = -9.0 * (z * (t * y));
	} else if (x <= -1.5e-199) {
		tmp = t_1;
	} else if (x <= -4e-268) {
		tmp = y * (z * (t * -9.0));
	} else if (x <= 7.8e+54) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if x <= -1.1e+73:
		tmp = x * 2.0
	elif x <= -500000.0:
		tmp = t_1
	elif x <= -2.1e-93:
		tmp = -9.0 * (z * (t * y))
	elif x <= -1.5e-199:
		tmp = t_1
	elif x <= -4e-268:
		tmp = y * (z * (t * -9.0))
	elif x <= 7.8e+54:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (x <= -1.1e+73)
		tmp = Float64(x * 2.0);
	elseif (x <= -500000.0)
		tmp = t_1;
	elseif (x <= -2.1e-93)
		tmp = Float64(-9.0 * Float64(z * Float64(t * y)));
	elseif (x <= -1.5e-199)
		tmp = t_1;
	elseif (x <= -4e-268)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (x <= 7.8e+54)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (x <= -1.1e+73)
		tmp = x * 2.0;
	elseif (x <= -500000.0)
		tmp = t_1;
	elseif (x <= -2.1e-93)
		tmp = -9.0 * (z * (t * y));
	elseif (x <= -1.5e-199)
		tmp = t_1;
	elseif (x <= -4e-268)
		tmp = y * (z * (t * -9.0));
	elseif (x <= 7.8e+54)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+73], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -500000.0], t$95$1, If[LessEqual[x, -2.1e-93], N[(-9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e-199], t$95$1, If[LessEqual[x, -4e-268], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+54], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1e73 or 7.8000000000000005e54 < x

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 65.4%

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

   if -1.1e73 < x < -5e5 or -2.1000000000000001e-93 < x < -1.49999999999999992e-199

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-*l* 97.5%

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

      4. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

      4. fma-def 71.5%

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

   6. Applied egg-rr 71.5%

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

   7. Taylor expanded in a around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-*r* 63.8%

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

      3. *-commutative 63.8%

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

   9. Simplified 63.8%

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

   if -5e5 < x < -2.1000000000000001e-93

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around 0 93.5%

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

   5. Taylor expanded in y around inf 67.6%

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

      1. associate-*r* 67.3%

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

      2. metadata-eval 67.3%

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

      3. distribute-lft-neg-in 67.3%

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

      4. *-commutative 67.3%

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

      5. associate-*l* 61.4%

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

      6. *-commutative 61.4%

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

      7. distribute-rgt-neg-in 61.4%

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

      8. metadata-eval 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in y around 0 67.6%

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

      1. associate-*r* 67.7%

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

   10. Simplified 67.7%

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

   if -1.49999999999999992e-199 < x < -3.99999999999999983e-268

   1. Initial program 91.9%

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

      1. sub-neg 91.9%

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

      2. sub-neg 91.9%

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

      3. associate-*l* 99.9%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 99.7%

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

   5. Taylor expanded in y around inf 56.3%

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

      1. associate-*r* 56.2%

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

      2. metadata-eval 56.2%

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

      3. distribute-lft-neg-in 56.2%

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

      4. *-commutative 56.2%

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

      5. associate-*l* 64.2%

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

      6. *-commutative 64.2%

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

      7. distribute-rgt-neg-in 64.2%

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

      8. metadata-eval 64.2%

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

   7. Simplified 64.2%

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

   if -3.99999999999999983e-268 < x < 7.8000000000000005e54

   1. Initial program 96.5%

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

      1. sub-neg 96.5%

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

      2. sub-neg 96.5%

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

      3. associate-*l* 96.0%

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

      4. associate-*l* 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. Taylor expanded in a around 0 96.0%

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

   5. Taylor expanded in a around inf 57.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -500000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-199}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+54}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 7: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+73} \lor \neg \left(x \leq 4.8 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.5e+73) (not (<= x 4.8e+51)))
   (+ (* x 2.0) (* (* y z) (* t -9.0)))
   (- (* 27.0 (* a b)) (* 9.0 (* t (* y z))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.5e+73) || !(x <= 4.8e+51)) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.5d+73)) .or. (.not. (x <= 4.8d+51))) then
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    else
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.5e+73) || !(x <= 4.8e+51)) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.5e+73) or not (x <= 4.8e+51):
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	else:
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.5e+73) || !(x <= 4.8e+51))
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.5e+73) || ~((x <= 4.8e+51)))
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	else
		tmp = (27.0 * (a * b)) - (9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.5e+73], N[Not[LessEqual[x, 4.8e+51]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000005e73 or 4.7999999999999997e51 < x

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-+r- 94.2%

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

      3. associate-*l* 94.2%

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

   5. Applied egg-rr 94.2%

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

   6. Taylor expanded in a around 0 87.7%

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

      1. cancel-sign-sub-inv 87.7%

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

      2. metadata-eval 87.7%

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

      3. associate-*r* 87.7%

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

      4. *-commutative 87.7%

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

   8. Simplified 87.7%

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

   if -1.50000000000000005e73 < x < 4.7999999999999997e51

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. sub-neg 97.3%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around 0 88.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+73} \lor \neg \left(x \leq 4.8 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 8: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. sub-neg 97.2%

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

   2. sub-neg 97.2%

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

   3. associate-*l* 95.2%

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

   4. associate-*l* 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in y around 0 97.5%

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

   1. *-commutative 97.5%

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

   2. associate-*l* 97.5%

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

   3. *-commutative 97.5%

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

   4. associate-*r* 97.5%

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

   5. *-commutative 97.5%

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

   6. associate-*r* 94.4%

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

   7. *-commutative 94.4%

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

6. Simplified 94.4%

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

7. Taylor expanded in t around 0 97.5%

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

   1. associate-*r* 97.5%

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

   2. *-commutative 97.5%

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

   3. associate-*l* 97.5%

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

9. Simplified 97.5%

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

10. Final simplification 97.5%

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

Alternative 9: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

2. Taylor expanded in y around 0 97.1%

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

3. Final simplification 97.1%

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

Alternative 10: 77.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-64} \lor \neg \left(z \leq 8.2 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e-64) (not (<= z 8.2e+33)))
   (+ (* x 2.0) (* (* y z) (* t -9.0)))
   (+ (* x 2.0) (* 27.0 (* a b)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e-64) || !(z <= 8.2e+33)) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.8d-64)) .or. (.not. (z <= 8.2d+33))) then
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e-64) || !(z <= 8.2e+33)) {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.8e-64) or not (z <= 8.2e+33):
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e-64) || !(z <= 8.2e+33))
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.8e-64) || ~((z <= 8.2e+33)))
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e-64], N[Not[LessEqual[z, 8.2e+33]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $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 z < -3.8000000000000002e-64 or 8.1999999999999999e33 < z

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. sub-neg 95.5%

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

      3. associate-*l* 92.1%

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

      4. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. +-commutative 92.1%

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

      2. associate-+r- 92.1%

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

      3. associate-*l* 92.1%

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

   5. Applied egg-rr 92.1%

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

   6. Taylor expanded in a around 0 70.1%

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

      1. cancel-sign-sub-inv 70.1%

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

      2. metadata-eval 70.1%

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

      3. associate-*r* 70.1%

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

      4. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if -3.8000000000000002e-64 < z < 8.1999999999999999e33

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. sub-neg 99.0%

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

      3. associate-*l* 98.5%

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

      4. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 87.8%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-64} \lor \neg \left(z \leq 8.2 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 11: 77.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.1e-60)
   (- (* x 2.0) (* 9.0 (* t (* y z))))
   (if (<= z 8.5e+33)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (+ (* x 2.0) (* (* y z) (* t -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e-60) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else if (z <= 8.5e+33) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.1d-60)) then
        tmp = (x * 2.0d0) - (9.0d0 * (t * (y * z)))
    else if (z <= 8.5d+33) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e-60) {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	} else if (z <= 8.5e+33) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.1e-60:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	elif z <= 8.5e+33:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.1e-60)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(y * z))));
	elseif (z <= 8.5e+33)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.1e-60)
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	elseif (z <= 8.5e+33)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.1e-60], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+33], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0999999999999999e-60

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. sub-neg 96.1%

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

      3. associate-*l* 92.6%

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

      4. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around 0 70.1%

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

   if -1.0999999999999999e-60 < z < 8.4999999999999998e33

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. sub-neg 99.0%

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

      3. associate-*l* 98.5%

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

      4. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 87.8%

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

   if 8.4999999999999998e33 < z

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. sub-neg 94.5%

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

      3. associate-*l* 91.4%

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

      4. 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. Step-by-step derivation

      1. +-commutative 91.5%

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

      2. associate-+r- 91.5%

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

      3. associate-*l* 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in a around 0 70.2%

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

      1. cancel-sign-sub-inv 70.2%

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

      2. metadata-eval 70.2%

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

      3. associate-*r* 70.2%

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

      4. *-commutative 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-60}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+33}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 12: 47.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -430000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.15 \cdot 10^{-94}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= x -1e+73)
     (* x 2.0)
     (if (<= x -430000.0)
       t_1
       (if (<= x -4.15e-94)
         (* -9.0 (* t (* y z)))
         (if (<= x 4.6e+54) t_1 (* x 2.0)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (x <= -1e+73) {
		tmp = x * 2.0;
	} else if (x <= -430000.0) {
		tmp = t_1;
	} else if (x <= -4.15e-94) {
		tmp = -9.0 * (t * (y * z));
	} else if (x <= 4.6e+54) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (x <= (-1d+73)) then
        tmp = x * 2.0d0
    else if (x <= (-430000.0d0)) then
        tmp = t_1
    else if (x <= (-4.15d-94)) then
        tmp = (-9.0d0) * (t * (y * z))
    else if (x <= 4.6d+54) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (x <= -1e+73) {
		tmp = x * 2.0;
	} else if (x <= -430000.0) {
		tmp = t_1;
	} else if (x <= -4.15e-94) {
		tmp = -9.0 * (t * (y * z));
	} else if (x <= 4.6e+54) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if x <= -1e+73:
		tmp = x * 2.0
	elif x <= -430000.0:
		tmp = t_1
	elif x <= -4.15e-94:
		tmp = -9.0 * (t * (y * z))
	elif x <= 4.6e+54:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (x <= -1e+73)
		tmp = Float64(x * 2.0);
	elseif (x <= -430000.0)
		tmp = t_1;
	elseif (x <= -4.15e-94)
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	elseif (x <= 4.6e+54)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (x <= -1e+73)
		tmp = x * 2.0;
	elseif (x <= -430000.0)
		tmp = t_1;
	elseif (x <= -4.15e-94)
		tmp = -9.0 * (t * (y * z));
	elseif (x <= 4.6e+54)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+73], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -430000.0], t$95$1, If[LessEqual[x, -4.15e-94], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+54], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999983e72 or 4.59999999999999988e54 < x

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 65.4%

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

   if -9.99999999999999983e72 < x < -4.3e5 or -4.1499999999999998e-94 < x < 4.59999999999999988e54

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 96.7%

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

      4. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

      4. fma-def 65.0%

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

   6. Applied egg-rr 65.0%

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

   7. Taylor expanded in a around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-*r* 56.7%

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

      3. *-commutative 56.7%

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

   9. Simplified 56.7%

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

   if -4.3e5 < x < -4.1499999999999998e-94

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 67.6%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -430000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq -4.15 \cdot 10^{-94}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 13: 47.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -430000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-94}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= x -1.4e+73)
     (* x 2.0)
     (if (<= x -430000.0)
       t_1
       (if (<= x -7.6e-94)
         (* -9.0 (* z (* t y)))
         (if (<= x 2.45e+54) t_1 (* x 2.0)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (x <= -1.4e+73) {
		tmp = x * 2.0;
	} else if (x <= -430000.0) {
		tmp = t_1;
	} else if (x <= -7.6e-94) {
		tmp = -9.0 * (z * (t * y));
	} else if (x <= 2.45e+54) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (x <= (-1.4d+73)) then
        tmp = x * 2.0d0
    else if (x <= (-430000.0d0)) then
        tmp = t_1
    else if (x <= (-7.6d-94)) then
        tmp = (-9.0d0) * (z * (t * y))
    else if (x <= 2.45d+54) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (x <= -1.4e+73) {
		tmp = x * 2.0;
	} else if (x <= -430000.0) {
		tmp = t_1;
	} else if (x <= -7.6e-94) {
		tmp = -9.0 * (z * (t * y));
	} else if (x <= 2.45e+54) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if x <= -1.4e+73:
		tmp = x * 2.0
	elif x <= -430000.0:
		tmp = t_1
	elif x <= -7.6e-94:
		tmp = -9.0 * (z * (t * y))
	elif x <= 2.45e+54:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (x <= -1.4e+73)
		tmp = Float64(x * 2.0);
	elseif (x <= -430000.0)
		tmp = t_1;
	elseif (x <= -7.6e-94)
		tmp = Float64(-9.0 * Float64(z * Float64(t * y)));
	elseif (x <= 2.45e+54)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (x <= -1.4e+73)
		tmp = x * 2.0;
	elseif (x <= -430000.0)
		tmp = t_1;
	elseif (x <= -7.6e-94)
		tmp = -9.0 * (z * (t * y));
	elseif (x <= 2.45e+54)
		tmp = t_1;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+73], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -430000.0], t$95$1, If[LessEqual[x, -7.6e-94], N[(-9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e+54], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000004e73 or 2.45e54 < x

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 65.4%

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

   if -1.40000000000000004e73 < x < -4.3e5 or -7.59999999999999999e-94 < x < 2.45e54

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 96.7%

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

      4. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. *-commutative 65.0%

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

      3. *-commutative 65.0%

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

      4. fma-def 65.0%

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

   6. Applied egg-rr 65.0%

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

   7. Taylor expanded in a around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-*r* 56.7%

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

      3. *-commutative 56.7%

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

   9. Simplified 56.7%

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

   if -4.3e5 < x < -7.59999999999999999e-94

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around 0 93.5%

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

   5. Taylor expanded in y around inf 67.6%

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

      1. associate-*r* 67.3%

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

      2. metadata-eval 67.3%

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

      3. distribute-lft-neg-in 67.3%

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

      4. *-commutative 67.3%

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

      5. associate-*l* 61.4%

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

      6. *-commutative 61.4%

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

      7. distribute-rgt-neg-in 61.4%

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

      8. metadata-eval 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in y around 0 67.6%

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

      1. associate-*r* 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -430000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-94}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14: 76.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-6}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.85e-6)
   (* -9.0 (* z (* t y)))
   (if (<= z 4.2e+34) (+ (* x 2.0) (* 27.0 (* a b))) (* t (* y (* z -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e-6) {
		tmp = -9.0 * (z * (t * y));
	} else if (z <= 4.2e+34) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.85d-6)) then
        tmp = (-9.0d0) * (z * (t * y))
    else if (z <= 4.2d+34) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t * (y * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e-6) {
		tmp = -9.0 * (z * (t * y));
	} else if (z <= 4.2e+34) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (y * (z * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.85e-6:
		tmp = -9.0 * (z * (t * y))
	elif z <= 4.2e+34:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t * (y * (z * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.85e-6)
		tmp = Float64(-9.0 * Float64(z * Float64(t * y)));
	elseif (z <= 4.2e+34)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.85e-6)
		tmp = -9.0 * (z * (t * y));
	elseif (z <= 4.2e+34)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = t * (y * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.85e-6], N[(-9.0 * N[(z * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+34], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001e-6

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. sub-neg 95.4%

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

      3. associate-*l* 91.1%

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

      4. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in a around 0 91.1%

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

   5. Taylor expanded in y around inf 52.1%

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

      1. associate-*r* 52.1%

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

      2. metadata-eval 52.1%

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

      3. distribute-lft-neg-in 52.1%

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

      4. *-commutative 52.1%

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

      5. associate-*l* 53.7%

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

      6. *-commutative 53.7%

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

      7. distribute-rgt-neg-in 53.7%

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

      8. metadata-eval 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in y around 0 52.1%

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

      1. associate-*r* 55.1%

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

   10. Simplified 55.1%

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

   if -1.8500000000000001e-6 < z < 4.20000000000000035e34

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. sub-neg 99.1%

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

      3. associate-*l* 98.7%

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

      4. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 84.6%

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

   if 4.20000000000000035e34 < z

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. sub-neg 94.5%

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

      3. associate-*l* 91.4%

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

      4. 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. Step-by-step derivation

      1. +-commutative 91.5%

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

      2. associate-+r- 91.5%

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

      3. associate-*l* 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l* 46.6%

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

      3. associate-*r* 46.6%

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

   8. Simplified 46.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-6}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]

Alternative 15: 47.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+73} \lor \neg \left(x \leq 4.8 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.6e+73) (not (<= x 4.8e+54))) (* x 2.0) (* 27.0 (* a b))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.6e+73) || !(x <= 4.8e+54)) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.6d+73)) .or. (.not. (x <= 4.8d+54))) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.6e+73) || !(x <= 4.8e+54)) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.6e+73) or not (x <= 4.8e+54):
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.6e+73) || !(x <= 4.8e+54))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.6e+73) || ~((x <= 4.8e+54)))
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.6e+73], N[Not[LessEqual[x, 4.8e+54]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999991e73 or 4.79999999999999997e54 < x

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 65.4%

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

   if -1.59999999999999991e73 < x < 4.79999999999999997e54

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. sub-neg 97.3%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in a around 0 96.4%

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

   5. Taylor expanded in a around inf 54.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+73} \lor \neg \left(x \leq 4.8 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 16: 47.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+73} \lor \neg \left(x \leq 9.2 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.45e+73) (not (<= x 9.2e+54))) (* x 2.0) (* a (* 27.0 b))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.45e+73) || !(x <= 9.2e+54)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-1.45d+73)) .or. (.not. (x <= 9.2d+54))) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.45e+73) || !(x <= 9.2e+54)) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.45e+73) or not (x <= 9.2e+54):
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.45e+73) || !(x <= 9.2e+54))
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.45e+73) || ~((x <= 9.2e+54)))
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.45e+73], N[Not[LessEqual[x, 9.2e+54]], $MachinePrecision]], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4500000000000001e73 or 9.19999999999999977e54 < x

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. sub-neg 96.9%

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

      3. associate-*l* 93.2%

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

      4. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 65.4%

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

   if -1.4500000000000001e73 < x < 9.19999999999999977e54

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. sub-neg 97.3%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. *-commutative 62.1%

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

      3. *-commutative 62.1%

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

      4. fma-def 62.1%

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

   6. Applied egg-rr 62.1%

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

   7. Taylor expanded in a around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-*r* 53.9%

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

      3. *-commutative 53.9%

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

   9. Simplified 53.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+73} \lor \neg \left(x \leq 9.2 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 17: 31.7% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. sub-neg 97.2%

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

   2. sub-neg 97.2%

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

   3. associate-*l* 95.2%

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

   4. associate-*l* 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in x around inf 31.8%

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

5. Final simplification 31.8%

   \[\leadsto x \cdot 2 \]

Developer target: 94.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

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

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