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

Percentage Accurate: 95.5% → 98.1%

Time: 10.9s

Alternatives: 12

Speedup: 1.0×

• 27.3% 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: 95.5% 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: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-247}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (<= z -2e-247)
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* (* y 9.0) (* z t))))
   (+ (- (* x 2.0) (* t (* y (* z 9.0)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e-247) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((x * 2.0) - (t * (y * (z * 9.0)))) + (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 (z <= (-2d-247)) then
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - ((y * 9.0d0) * (z * t)))
    else
        tmp = ((x * 2.0d0) - (t * (y * (z * 9.0d0)))) + (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 (z <= -2e-247) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)));
	} else {
		tmp = ((x * 2.0) - (t * (y * (z * 9.0)))) + (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 z <= -2e-247:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)))
	else:
		tmp = ((x * 2.0) - (t * (y * (z * 9.0)))) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e-247)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))) + 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 (z <= -2e-247)
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((y * 9.0) * (z * t)));
	else
		tmp = ((x * 2.0) - (t * (y * (z * 9.0)))) + (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[z, -2e-247], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e-247

   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. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. neg-mul-1 97.4%

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

      4. metadata-eval 97.4%

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

      5. metadata-eval 97.4%

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

      6. cancel-sign-sub-inv 97.4%

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

      7. metadata-eval 97.4%

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

      8. *-lft-identity 97.4%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   if -2e-247 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 98.4%

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

      1. associate-*r* 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-*r* 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-247}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 2: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+38} \lor \neg \left(t_1 \leq 3 \cdot 10^{+124}\right):\\ \;\;\;\;t_1 + t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* b (* a 27.0))))
   (if (or (<= t_1 -4e+38) (not (<= t_1 3e+124)))
     (+ t_1 (* t (* z (* y -9.0))))
     (+ (* x 2.0) (* (* y -9.0) (* z t))))))

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 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -4e+38) || !(t_1 <= 3e+124)) {
		tmp = t_1 + (t * (z * (y * -9.0)));
	} else {
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	}
	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 = b * (a * 27.0d0)
    if ((t_1 <= (-4d+38)) .or. (.not. (t_1 <= 3d+124))) then
        tmp = t_1 + (t * (z * (y * (-9.0d0))))
    else
        tmp = (x * 2.0d0) + ((y * (-9.0d0)) * (z * t))
    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 = b * (a * 27.0);
	double tmp;
	if ((t_1 <= -4e+38) || !(t_1 <= 3e+124)) {
		tmp = t_1 + (t * (z * (y * -9.0)));
	} else {
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	}
	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 = b * (a * 27.0)
	tmp = 0
	if (t_1 <= -4e+38) or not (t_1 <= 3e+124):
		tmp = t_1 + (t * (z * (y * -9.0)))
	else:
		tmp = (x * 2.0) + ((y * -9.0) * (z * t))
	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(b * Float64(a * 27.0))
	tmp = 0.0
	if ((t_1 <= -4e+38) || !(t_1 <= 3e+124))
		tmp = Float64(t_1 + Float64(t * Float64(z * Float64(y * -9.0))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * -9.0) * Float64(z * t)));
	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 = b * (a * 27.0);
	tmp = 0.0;
	if ((t_1 <= -4e+38) || ~((t_1 <= 3e+124)))
		tmp = t_1 + (t * (z * (y * -9.0)));
	else
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+38], N[Not[LessEqual[t$95$1, 3e+124]], $MachinePrecision]], N[(t$95$1 + N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * -9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a 27) b) < -3.99999999999999991e38 or 3e124 < (*.f64 (*.f64 a 27) b)

   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. Taylor expanded in y around 0 99.8%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

      1. add-sqr-sqrt 59.5%

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

      2. sqrt-unprod 79.9%

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

      3. swap-sqr 79.9%

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

      4. metadata-eval 79.9%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. metadata-eval 79.9%

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

      6. swap-sqr 79.9%

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

      7. *-commutative 79.9%

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

      8. *-commutative 79.9%

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

      9. sqrt-unprod 28.2%

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

      10. add-sqr-sqrt 77.6%

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

      11. associate-*r* 76.7%

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

      12. *-commutative 76.7%

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

      13. add-sqr-sqrt 52.4%

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

      14. sqrt-unprod 80.9%

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

      15. pow2 80.9%

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

   6. Applied egg-rr 80.9%

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

      1. associate-*r* 81.8%

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

   8. Simplified 81.8%

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

      1. sqrt-pow1 97.9%

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

      2. metadata-eval 97.9%

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

      3. pow1 97.9%

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

   10. Applied egg-rr 97.9%

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

   11. Taylor expanded in x around 0 91.1%

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

       1. associate-*r* 91.1%

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

       2. *-commutative 91.1%

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

       3. *-commutative 91.1%

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

       4. associate-*r* 95.1%

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

       5. *-commutative 95.1%

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

   13. Simplified 95.1%

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

   if -3.99999999999999991e38 < (*.f64 (*.f64 a 27) b) < 3e124

   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. associate-+l- 96.8%

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

      2. sub-neg 96.8%

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

      3. neg-mul-1 96.8%

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

      4. metadata-eval 96.8%

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

      5. metadata-eval 96.8%

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

      6. cancel-sign-sub-inv 96.8%

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

      7. metadata-eval 96.8%

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

      8. *-lft-identity 96.8%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around 0 81.8%

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

      1. cancel-sign-sub-inv 81.8%

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

      2. metadata-eval 81.8%

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

      3. associate-*l* 81.8%

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

      4. *-commutative 81.8%

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

      5. *-commutative 81.8%

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

   6. Applied egg-rr 81.8%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -4 \cdot 10^{+38} \lor \neg \left(b \cdot \left(a \cdot 27\right) \leq 3 \cdot 10^{+124}\right):\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 3: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+38}:\\ \;\;\;\;t_1 + t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;t_1 \leq 3 \cdot 10^{+124}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -4e+38)
     (+ t_1 (* t (* z (* y -9.0))))
     (if (<= t_1 3e+124)
       (+ (* x 2.0) (* (* y -9.0) (* z t)))
       (+ t_1 (* y (* t (* 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 t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -4e+38) {
		tmp = t_1 + (t * (z * (y * -9.0)));
	} else if (t_1 <= 3e+124) {
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	} else {
		tmp = t_1 + (y * (t * (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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (t_1 <= (-4d+38)) then
        tmp = t_1 + (t * (z * (y * (-9.0d0))))
    else if (t_1 <= 3d+124) then
        tmp = (x * 2.0d0) + ((y * (-9.0d0)) * (z * t))
    else
        tmp = t_1 + (y * (t * (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 t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -4e+38) {
		tmp = t_1 + (t * (z * (y * -9.0)));
	} else if (t_1 <= 3e+124) {
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	} else {
		tmp = t_1 + (y * (t * (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):
	t_1 = b * (a * 27.0)
	tmp = 0
	if t_1 <= -4e+38:
		tmp = t_1 + (t * (z * (y * -9.0)))
	elif t_1 <= 3e+124:
		tmp = (x * 2.0) + ((y * -9.0) * (z * t))
	else:
		tmp = t_1 + (y * (t * (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)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -4e+38)
		tmp = Float64(t_1 + Float64(t * Float64(z * Float64(y * -9.0))));
	elseif (t_1 <= 3e+124)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * -9.0) * Float64(z * t)));
	else
		tmp = Float64(t_1 + Float64(y * Float64(t * 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)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (t_1 <= -4e+38)
		tmp = t_1 + (t * (z * (y * -9.0)));
	elseif (t_1 <= 3e+124)
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	else
		tmp = t_1 + (y * (t * (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_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+38], N[(t$95$1 + N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 3e+124], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * -9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -3.99999999999999991e38

   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. Taylor expanded in y around 0 99.8%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

      1. add-sqr-sqrt 59.9%

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

      2. sqrt-unprod 82.0%

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

      3. swap-sqr 82.0%

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

      4. metadata-eval 82.0%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. metadata-eval 82.0%

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

      6. swap-sqr 82.0%

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

      7. *-commutative 82.0%

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

      8. *-commutative 82.0%

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

      9. sqrt-unprod 30.9%

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

      10. add-sqr-sqrt 79.9%

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

      11. associate-*r* 80.0%

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

      12. *-commutative 80.0%

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

      13. add-sqr-sqrt 58.2%

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

      14. sqrt-unprod 87.4%

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

      15. pow2 87.4%

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

   6. Applied egg-rr 87.4%

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

      1. associate-*r* 89.1%

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

   8. Simplified 89.1%

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

      1. sqrt-pow1 99.8%

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

      2. metadata-eval 99.8%

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

      3. pow1 99.8%

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

   10. Applied egg-rr 99.8%

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

   11. Taylor expanded in x around 0 89.3%

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

       1. associate-*r* 89.3%

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

       2. *-commutative 89.3%

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

       3. *-commutative 89.3%

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

       4. associate-*r* 94.3%

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

       5. *-commutative 94.3%

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

   13. Simplified 94.3%

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

   if -3.99999999999999991e38 < (*.f64 (*.f64 a 27) b) < 3e124

   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. associate-+l- 96.8%

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

      2. sub-neg 96.8%

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

      3. neg-mul-1 96.8%

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

      4. metadata-eval 96.8%

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

      5. metadata-eval 96.8%

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

      6. cancel-sign-sub-inv 96.8%

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

      7. metadata-eval 96.8%

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

      8. *-lft-identity 96.8%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around 0 81.8%

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

      1. cancel-sign-sub-inv 81.8%

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

      2. metadata-eval 81.8%

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

      3. associate-*l* 81.8%

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

      4. *-commutative 81.8%

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

      5. *-commutative 81.8%

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

   6. Applied egg-rr 81.8%

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

   if 3e124 < (*.f64 (*.f64 a 27) b)

   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. Taylor expanded in x around 0 93.4%

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

      1. *-commutative 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*r* 93.3%

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

      4. associate-*r* 93.3%

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

      5. *-commutative 93.3%

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

      6. associate-*l* 93.3%

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

      7. *-commutative 93.3%

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

   4. Simplified 93.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -4 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 3 \cdot 10^{+124}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]

Alternative 4: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+38}:\\ \;\;\;\;t_1 + t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;t_1 \leq 3 \cdot 10^{+124}:\\ \;\;\;\;x \cdot 2 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

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 (* b (* a 27.0))) (t_2 (* (* y -9.0) (* z t))))
   (if (<= t_1 -4e+38)
     (+ t_1 (* t (* z (* y -9.0))))
     (if (<= t_1 3e+124) (+ (* x 2.0) t_2) (+ t_1 t_2)))))

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 = b * (a * 27.0);
	double t_2 = (y * -9.0) * (z * t);
	double tmp;
	if (t_1 <= -4e+38) {
		tmp = t_1 + (t * (z * (y * -9.0)));
	} else if (t_1 <= 3e+124) {
		tmp = (x * 2.0) + t_2;
	} else {
		tmp = t_1 + t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (y * (-9.0d0)) * (z * t)
    if (t_1 <= (-4d+38)) then
        tmp = t_1 + (t * (z * (y * (-9.0d0))))
    else if (t_1 <= 3d+124) then
        tmp = (x * 2.0d0) + t_2
    else
        tmp = t_1 + t_2
    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 = b * (a * 27.0);
	double t_2 = (y * -9.0) * (z * t);
	double tmp;
	if (t_1 <= -4e+38) {
		tmp = t_1 + (t * (z * (y * -9.0)));
	} else if (t_1 <= 3e+124) {
		tmp = (x * 2.0) + t_2;
	} else {
		tmp = t_1 + t_2;
	}
	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 = b * (a * 27.0)
	t_2 = (y * -9.0) * (z * t)
	tmp = 0
	if t_1 <= -4e+38:
		tmp = t_1 + (t * (z * (y * -9.0)))
	elif t_1 <= 3e+124:
		tmp = (x * 2.0) + t_2
	else:
		tmp = t_1 + t_2
	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(b * Float64(a * 27.0))
	t_2 = Float64(Float64(y * -9.0) * Float64(z * t))
	tmp = 0.0
	if (t_1 <= -4e+38)
		tmp = Float64(t_1 + Float64(t * Float64(z * Float64(y * -9.0))));
	elseif (t_1 <= 3e+124)
		tmp = Float64(Float64(x * 2.0) + t_2);
	else
		tmp = Float64(t_1 + t_2);
	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 = b * (a * 27.0);
	t_2 = (y * -9.0) * (z * t);
	tmp = 0.0;
	if (t_1 <= -4e+38)
		tmp = t_1 + (t * (z * (y * -9.0)));
	elseif (t_1 <= 3e+124)
		tmp = (x * 2.0) + t_2;
	else
		tmp = t_1 + t_2;
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * -9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+38], N[(t$95$1 + N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 3e+124], N[(N[(x * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a 27) b) < -3.99999999999999991e38

   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. Taylor expanded in y around 0 99.8%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

      1. add-sqr-sqrt 59.9%

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

      2. sqrt-unprod 82.0%

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

      3. swap-sqr 82.0%

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

      4. metadata-eval 82.0%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. metadata-eval 82.0%

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

      6. swap-sqr 82.0%

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

      7. *-commutative 82.0%

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

      8. *-commutative 82.0%

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

      9. sqrt-unprod 30.9%

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

      10. add-sqr-sqrt 79.9%

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

      11. associate-*r* 80.0%

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

      12. *-commutative 80.0%

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

      13. add-sqr-sqrt 58.2%

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

      14. sqrt-unprod 87.4%

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

      15. pow2 87.4%

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

   6. Applied egg-rr 87.4%

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

      1. associate-*r* 89.1%

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

   8. Simplified 89.1%

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

      1. sqrt-pow1 99.8%

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

      2. metadata-eval 99.8%

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

      3. pow1 99.8%

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

   10. Applied egg-rr 99.8%

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

   11. Taylor expanded in x around 0 89.3%

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

       1. associate-*r* 89.3%

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

       2. *-commutative 89.3%

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

       3. *-commutative 89.3%

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

       4. associate-*r* 94.3%

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

       5. *-commutative 94.3%

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

   13. Simplified 94.3%

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

   if -3.99999999999999991e38 < (*.f64 (*.f64 a 27) b) < 3e124

   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. associate-+l- 96.8%

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

      2. sub-neg 96.8%

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

      3. neg-mul-1 96.8%

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

      4. metadata-eval 96.8%

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

      5. metadata-eval 96.8%

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

      6. cancel-sign-sub-inv 96.8%

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

      7. metadata-eval 96.8%

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

      8. *-lft-identity 96.8%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around 0 81.8%

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

      1. cancel-sign-sub-inv 81.8%

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

      2. metadata-eval 81.8%

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

      3. associate-*l* 81.8%

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

      4. *-commutative 81.8%

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

      5. *-commutative 81.8%

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

   6. Applied egg-rr 81.8%

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

   if 3e124 < (*.f64 (*.f64 a 27) b)

   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. Taylor expanded in x around 0 93.4%

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

      1. associate-*r* 93.3%

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

   4. Simplified 93.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -4 \cdot 10^{+38}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 3 \cdot 10^{+124}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 5: 93.4% accurate, 1.0× speedup

Math

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

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) (* (* z 9.0) (* y t)))))

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) - ((z * 9.0) * (y * t)));
}

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) - ((z * 9.0d0) * (y * t)))
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) - ((z * 9.0) * (y * t)));
}

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) - ((z * 9.0) * (y * t)))

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(Float64(z * 9.0) * Float64(y * t))))
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) - ((z * 9.0) * (y * t)));
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[(N[(z * 9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in y around 0 97.9%

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

   1. associate-*r* 97.9%

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

   2. *-commutative 97.9%

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

   3. associate-*r* 97.9%

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

4. Simplified 97.9%

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

   1. add-sqr-sqrt 50.3%

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

   2. sqrt-unprod 73.1%

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

   3. swap-sqr 73.1%

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

   4. metadata-eval 73.1%

      \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. metadata-eval 73.1%

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

   6. swap-sqr 73.1%

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

   7. *-commutative 73.1%

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

   8. *-commutative 73.1%

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

   9. sqrt-unprod 31.3%

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

   10. add-sqr-sqrt 64.9%

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

   11. associate-*r* 64.1%

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

   12. *-commutative 64.1%

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

   13. add-sqr-sqrt 44.5%

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

   14. sqrt-unprod 75.1%

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

   15. pow2 75.1%

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

6. Applied egg-rr 75.1%

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

   1. associate-*r* 76.5%

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

8. Simplified 76.5%

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

   1. sqrt-pow1 96.9%

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

   2. metadata-eval 96.9%

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

   3. pow1 96.9%

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

10. Applied egg-rr 96.9%

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

11. Final simplification 96.9%

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

Alternative 6: 95.6% accurate, 1.0× speedup

Math

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

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

C

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

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) - (t * (y * (z * 9.0d0)))) + (b * (a * 27.0d0))
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) - (t * (y * (z * 9.0)))) + (b * (a * 27.0));
}

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in y around 0 97.9%

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

   1. associate-*r* 97.9%

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

   2. *-commutative 97.9%

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

   3. associate-*r* 97.9%

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

4. Simplified 97.9%

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

5. Final simplification 97.9%

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

Alternative 7: 95.5% accurate, 1.0× speedup

Math

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

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 (* z (* y 9.0))))))

C

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

Fortran

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

Java

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

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 * (z * (y * 9.0))))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Final simplification 97.9%

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

Alternative 8: 77.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+79} \lor \neg \left(y \leq 460000000000\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (or (<= y -1.9e+79) (not (<= y 460000000000.0)))
   (+ (* x 2.0) (* (* y -9.0) (* z t)))
   (+ (* x 2.0) (* b (* a 27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+79) || !(y <= 460000000000.0)) {
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	} else {
		tmp = (x * 2.0) + (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 ((y <= (-1.9d+79)) .or. (.not. (y <= 460000000000.0d0))) then
        tmp = (x * 2.0d0) + ((y * (-9.0d0)) * (z * t))
    else
        tmp = (x * 2.0d0) + (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 ((y <= -1.9e+79) || !(y <= 460000000000.0)) {
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	} else {
		tmp = (x * 2.0) + (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 (y <= -1.9e+79) or not (y <= 460000000000.0):
		tmp = (x * 2.0) + ((y * -9.0) * (z * t))
	else:
		tmp = (x * 2.0) + (b * (a * 27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e+79) || !(y <= 460000000000.0))
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * -9.0) * Float64(z * t)));
	else
		tmp = Float64(Float64(x * 2.0) + 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 ((y <= -1.9e+79) || ~((y <= 460000000000.0)))
		tmp = (x * 2.0) + ((y * -9.0) * (z * t));
	else
		tmp = (x * 2.0) + (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[Or[LessEqual[y, -1.9e+79], N[Not[LessEqual[y, 460000000000.0]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * -9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e79 or 4.6e11 < y

   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. associate-+l- 97.3%

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

      2. sub-neg 97.3%

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

      3. neg-mul-1 97.3%

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

      4. metadata-eval 97.3%

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

      5. metadata-eval 97.3%

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

      6. cancel-sign-sub-inv 97.3%

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

      7. metadata-eval 97.3%

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

      8. *-lft-identity 97.3%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in a around 0 73.0%

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

      1. cancel-sign-sub-inv 73.0%

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

      2. metadata-eval 73.0%

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

      3. associate-*l* 73.0%

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

      4. *-commutative 73.0%

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

      5. *-commutative 73.0%

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

   6. Applied egg-rr 73.0%

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

   if -1.9000000000000001e79 < y < 4.6e11

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 78.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+79} \lor \neg \left(y \leq 460000000000\right):\\ \;\;\;\;x \cdot 2 + \left(y \cdot -9\right) \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 9: 48.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+41} \lor \neg \left(a \leq 1.2 \cdot 10^{-72}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1e+41) (not (<= a 1.2e-72))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+41) || !(a <= 1.2e-72)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1d+41)) .or. (.not. (a <= 1.2d-72))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+41) || !(a <= 1.2e-72)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1e+41) or not (a <= 1.2e-72):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1e+41) || !(a <= 1.2e-72))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1e+41) || ~((a <= 1.2e-72)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1e+41], N[Not[LessEqual[a, 1.2e-72]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000001e41 or 1.2e-72 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 79.0%

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

   3. Taylor expanded in x around 0 56.8%

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

   if -1.00000000000000001e41 < a < 1.2e-72

   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. Taylor expanded in y around 0 96.0%

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

      1. associate-*r* 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-*r* 96.1%

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

   4. Simplified 96.1%

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

      1. add-sqr-sqrt 48.0%

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

      2. sqrt-unprod 65.5%

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

      3. swap-sqr 65.5%

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

      4. metadata-eval 65.5%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. metadata-eval 65.5%

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

      6. swap-sqr 65.5%

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

      7. *-commutative 65.5%

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

      8. *-commutative 65.5%

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

      9. sqrt-unprod 29.1%

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

      10. add-sqr-sqrt 55.0%

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

      11. associate-*r* 55.0%

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

      12. *-commutative 55.0%

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

      13. add-sqr-sqrt 38.9%

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

      14. sqrt-unprod 69.3%

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

      15. pow2 69.3%

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

   6. Applied egg-rr 69.3%

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

      1. associate-*r* 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in x around inf 36.1%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+41} \lor \neg \left(a \leq 1.2 \cdot 10^{-72}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 10: 48.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-74}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 (<= a -2.5e+43)
   (* b (* a 27.0))
   (if (<= a 5.2e-74) (* 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 (a <= -2.5e+43) {
		tmp = b * (a * 27.0);
	} else if (a <= 5.2e-74) {
		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 (a <= (-2.5d+43)) then
        tmp = b * (a * 27.0d0)
    else if (a <= 5.2d-74) 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 (a <= -2.5e+43) {
		tmp = b * (a * 27.0);
	} else if (a <= 5.2e-74) {
		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 a <= -2.5e+43:
		tmp = b * (a * 27.0)
	elif a <= 5.2e-74:
		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 (a <= -2.5e+43)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (a <= 5.2e-74)
		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 (a <= -2.5e+43)
		tmp = b * (a * 27.0);
	elseif (a <= 5.2e-74)
		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[LessEqual[a, -2.5e+43], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-74], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5000000000000002e43

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

      1. add-sqr-sqrt 53.9%

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

      2. sqrt-unprod 86.2%

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

      3. swap-sqr 86.2%

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

      4. metadata-eval 86.2%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. metadata-eval 86.2%

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

      6. swap-sqr 86.2%

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

      7. *-commutative 86.2%

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

      8. *-commutative 86.2%

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

      9. sqrt-unprod 36.0%

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

      10. add-sqr-sqrt 82.0%

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

      11. associate-*r* 82.1%

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

      12. *-commutative 82.1%

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

      13. add-sqr-sqrt 60.1%

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

      14. sqrt-unprod 82.5%

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

      15. pow2 82.5%

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

   6. Applied egg-rr 82.5%

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

      1. associate-*r* 84.4%

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

   8. Simplified 84.4%

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

      1. sqrt-pow1 99.8%

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

      2. metadata-eval 99.8%

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

      3. pow1 99.8%

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

   10. Applied egg-rr 99.8%

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

   11. Taylor expanded in a around inf 65.0%

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

       1. *-commutative 65.0%

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

       2. *-commutative 65.0%

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

       3. associate-*r* 65.1%

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

       4. *-commutative 65.1%

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

   13. Simplified 65.1%

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

   if -2.5000000000000002e43 < a < 5.2000000000000002e-74

   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. Taylor expanded in y around 0 96.0%

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

      1. associate-*r* 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-*r* 96.1%

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

   4. Simplified 96.1%

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

      1. add-sqr-sqrt 47.6%

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

      2. sqrt-unprod 65.0%

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

      3. swap-sqr 65.0%

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

      4. metadata-eval 65.0%

         \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. metadata-eval 65.0%

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

      6. swap-sqr 65.0%

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

      7. *-commutative 65.0%

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

      8. *-commutative 65.0%

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

      9. sqrt-unprod 28.9%

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

      10. add-sqr-sqrt 54.6%

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

      11. associate-*r* 54.6%

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

      12. *-commutative 54.6%

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

      13. add-sqr-sqrt 38.6%

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

      14. sqrt-unprod 68.8%

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

      15. pow2 68.8%

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

   6. Applied egg-rr 68.8%

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

      1. associate-*r* 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in x around inf 35.8%

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

   if 5.2000000000000002e-74 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 76.1%

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

   3. Taylor expanded in x around 0 52.0%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-74}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 11: 64.7% accurate, 1.9× speedup

Math

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

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 (+ (* x 2.0) (* b (* a 27.0))))

C

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

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) + (b * (a * 27.0d0))
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) + (b * (a * 27.0));
}

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) + (b * (a * 27.0))

Julia

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in x around inf 67.3%

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

3. Final simplification 67.3%

   \[\leadsto x \cdot 2 + b \cdot \left(a \cdot 27\right) \]

Alternative 12: 30.8% 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 97.9%

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

2. Taylor expanded in y around 0 97.9%

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

   1. associate-*r* 97.9%

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

   2. *-commutative 97.9%

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

   3. associate-*r* 97.9%

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

4. Simplified 97.9%

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

   1. add-sqr-sqrt 50.3%

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

   2. sqrt-unprod 73.1%

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

   3. swap-sqr 73.1%

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

   4. metadata-eval 73.1%

      \[\leadsto \left(x \cdot 2 - \left(y \cdot \sqrt{\color{blue}{81} \cdot \left(z \cdot z\right)}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   5. metadata-eval 73.1%

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

   6. swap-sqr 73.1%

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

   7. *-commutative 73.1%

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

   8. *-commutative 73.1%

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

   9. sqrt-unprod 31.3%

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

   10. add-sqr-sqrt 64.9%

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

   11. associate-*r* 64.1%

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

   12. *-commutative 64.1%

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

   13. add-sqr-sqrt 44.5%

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

   14. sqrt-unprod 75.1%

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

   15. pow2 75.1%

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

6. Applied egg-rr 75.1%

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

   1. associate-*r* 76.5%

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

8. Simplified 76.5%

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

9. Taylor expanded in x around inf 29.4%

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

10. Final simplification 29.4%

    \[\leadsto x \cdot 2 \]

Developer target: 95.1% 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 2023217 
(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)))