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

Percentage Accurate: 95.0% → 98.3%

Time: 14.3s

Alternatives: 12

Speedup: 0.9×

• 27.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.0% 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: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 -5e-137)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* t (* z -9.0)))))
   (+ (- (* x 2.0) (* t (* z (* y 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 <= -5e-137) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (t * (z * -9.0)))));
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 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 <= -5e-137)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(z * -9.0)))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5e-137], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 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 < -5.00000000000000001e-137

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-+r- 95.9%

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

      3. cancel-sign-sub-inv 95.9%

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

      4. *-commutative 95.9%

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

      5. distribute-rgt-neg-out 95.9%

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

      6. associate-*r* 97.8%

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

      7. *-commutative 97.8%

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

      8. distribute-rgt-neg-in 97.8%

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

      9. associate-+r+ 97.8%

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

      10. sub-neg 97.8%

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

      11. associate-*l* 97.8%

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

      12. fma-def 97.8%

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

      13. fma-neg 97.8%

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

      14. associate-*l* 97.8%

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

      15. *-commutative 97.8%

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

      16. associate-*r* 95.8%

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

      17. distribute-rgt-neg-in 95.8%

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

   3. Simplified 95.9%

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

   if -5.00000000000000001e-137 < z

   1. Initial program 98.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= (* y 9.0) -5e-40)
     (+ t_1 (- (* x 2.0) (* (* y 9.0) (* z t))))
     (+ t_1 (+ (* x 2.0) (* z (* y (* t -9.0))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if ((y * 9.0) <= -5e-40) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = t_1 + ((x * 2.0) + (z * (y * (t * -9.0))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if ((y * 9.0d0) <= (-5d-40)) then
        tmp = t_1 + ((x * 2.0d0) - ((y * 9.0d0) * (z * t)))
    else
        tmp = t_1 + ((x * 2.0d0) + (z * (y * (t * (-9.0d0)))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if ((y * 9.0) <= -5e-40) {
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	} else {
		tmp = t_1 + ((x * 2.0) + (z * (y * (t * -9.0))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if (y * 9.0) <= -5e-40:
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)))
	else:
		tmp = t_1 + ((x * 2.0) + (z * (y * (t * -9.0))))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (Float64(y * 9.0) <= -5e-40)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if ((y * 9.0) <= -5e-40)
		tmp = t_1 + ((x * 2.0) - ((y * 9.0) * (z * t)));
	else
		tmp = t_1 + ((x * 2.0) + (z * (y * (t * -9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * 9.0), $MachinePrecision], -5e-40], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -4.99999999999999965e-40

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. distribute-lft-neg-in 95.0%

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

      3. associate-*l* 95.0%

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

      4. *-commutative 95.0%

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

      5. *-commutative 95.0%

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

      6. cancel-sign-sub-inv 95.0%

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

      7. *-commutative 95.0%

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

      8. *-commutative 95.0%

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

      9. associate-*l* 95.0%

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

      10. associate-*l* 97.4%

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

      11. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   if -4.99999999999999965e-40 < (*.f64 y 9)

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. cancel-sign-sub-inv 98.1%

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

      4. *-commutative 98.1%

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

      5. distribute-rgt-neg-out 98.1%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

      8. distribute-rgt-neg-in 96.1%

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

      9. associate-+r+ 96.1%

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

      10. sub-neg 96.1%

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

      11. +-commutative 96.1%

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

      12. associate-+l- 96.1%

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

      13. fma-neg 96.1%

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

      14. associate-*l* 94.4%

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

      15. fma-neg 94.4%

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

      16. *-commutative 94.4%

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

      17. fma-neg 94.4%

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

   3. Simplified 96.1%

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

      1. fma-udef 96.1%

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

      2. fma-udef 96.1%

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

      3. associate-*r* 96.1%

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

      4. associate-+r+ 96.1%

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

   5. Applied egg-rr 96.1%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 230000000:\\ \;\;\;\;\left(x \cdot 2 + a \cdot \left(27 \cdot b\right)\right) + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

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 (<= t 230000000.0)
   (+ (+ (* x 2.0) (* a (* 27.0 b))) (* (* y t) (* z -9.0)))
   (+ (- (* x 2.0) (* t (* z (* y 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 (t <= 230000000.0) {
		tmp = ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -9.0));
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 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 (t <= 230000000.0d0) then
        tmp = ((x * 2.0d0) + (a * (27.0d0 * b))) + ((y * t) * (z * (-9.0d0)))
    else
        tmp = ((x * 2.0d0) - (t * (z * (y * 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 (t <= 230000000.0) {
		tmp = ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -9.0));
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 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 t <= 230000000.0:
		tmp = ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -9.0))
	else:
		tmp = ((x * 2.0) - (t * (z * (y * 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 (t <= 230000000.0)
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b))) + Float64(Float64(y * t) * Float64(z * -9.0)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 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 (t <= 230000000.0)
		tmp = ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -9.0));
	else
		tmp = ((x * 2.0) - (t * (z * (y * 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[t, 230000000.0], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.3e8

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. cancel-sign-sub-inv 96.0%

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

      4. *-commutative 96.0%

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

      5. distribute-rgt-neg-out 96.0%

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

      6. associate-*r* 96.1%

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

      7. *-commutative 96.1%

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

      8. distribute-rgt-neg-in 96.1%

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

      9. associate-+r+ 96.1%

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

      10. sub-neg 96.1%

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

      11. associate-*l* 96.1%

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

      12. fma-def 96.1%

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

      13. fma-neg 96.1%

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

      14. associate-*l* 96.1%

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

      15. *-commutative 96.1%

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

      16. associate-*r* 96.1%

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

      17. distribute-rgt-neg-in 96.1%

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

   3. Simplified 96.2%

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

      1. fma-udef 96.2%

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

      2. fma-udef 96.2%

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

      3. associate-+r+ 96.2%

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

      4. associate-*r* 96.1%

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

      5. *-commutative 96.1%

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

   5. Applied egg-rr 96.1%

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

   if 2.3e8 < t

   1. Initial program 99.8%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 230000000:\\ \;\;\;\;\left(x \cdot 2 + a \cdot \left(27 \cdot b\right)\right) + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 4: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-245}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot 2 + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e-245)
   (+ (* x 2.0) (* 27.0 (* a b)))
   (if (<= b 4.2e+59)
     (+ (* x 2.0) (* y (* -9.0 (* z t))))
     (+ (* a (* 27.0 b)) (* t (* y (* z -9.0)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e-245) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (b <= 4.2e+59) {
		tmp = (x * 2.0) + (y * (-9.0 * (z * t)));
	} else {
		tmp = (a * (27.0 * b)) + (t * (y * (z * -9.0)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.8d-245)) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else if (b <= 4.2d+59) then
        tmp = (x * 2.0d0) + (y * ((-9.0d0) * (z * t)))
    else
        tmp = (a * (27.0d0 * b)) + (t * (y * (z * (-9.0d0))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e-245) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (b <= 4.2e+59) {
		tmp = (x * 2.0) + (y * (-9.0 * (z * t)));
	} else {
		tmp = (a * (27.0 * b)) + (t * (y * (z * -9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e-245:
		tmp = (x * 2.0) + (27.0 * (a * b))
	elif b <= 4.2e+59:
		tmp = (x * 2.0) + (y * (-9.0 * (z * t)))
	else:
		tmp = (a * (27.0 * b)) + (t * (y * (z * -9.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e-245)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	elseif (b <= 4.2e+59)
		tmp = Float64(Float64(x * 2.0) + Float64(y * Float64(-9.0 * Float64(z * t))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(t * Float64(y * Float64(z * -9.0))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e-245)
		tmp = (x * 2.0) + (27.0 * (a * b));
	elseif (b <= 4.2e+59)
		tmp = (x * 2.0) + (y * (-9.0 * (z * t)));
	else
		tmp = (a * (27.0 * b)) + (t * (y * (z * -9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e-245], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+59], N[(N[(x * 2.0), $MachinePrecision] + N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.7999999999999999e-245

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-lft-neg-in 98.2%

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

      3. associate-*l* 98.2%

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

      4. *-commutative 98.2%

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

      5. *-commutative 98.2%

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

      6. cancel-sign-sub-inv 98.2%

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

      7. *-commutative 98.2%

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

      8. *-commutative 98.2%

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

      9. associate-*l* 98.2%

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

      10. associate-*l* 95.8%

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

      11. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around 0 64.5%

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

   if -6.7999999999999999e-245 < b < 4.19999999999999968e59

   1. Initial program 96.5%

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

      1. sub-neg 96.5%

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

      2. distribute-lft-neg-in 96.5%

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

      3. associate-*l* 96.5%

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

      4. *-commutative 96.5%

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

      5. *-commutative 96.5%

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

      6. cancel-sign-sub-inv 96.5%

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

      7. *-commutative 96.5%

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

      8. *-commutative 96.5%

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

      9. associate-*l* 96.5%

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

      10. associate-*l* 94.1%

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

      11. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in a around 0 86.3%

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

      1. expm1-log1p-u 66.0%

         \[\leadsto 2 \cdot x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 61.6%

         \[\leadsto 2 \cdot x - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} \]

      3. *-commutative 61.6%

         \[\leadsto 2 \cdot x - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 9}\right)} - 1\right) \]

   6. Applied egg-rr 61.6%

      \[\leadsto 2 \cdot x - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 9\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 66.0%

         \[\leadsto 2 \cdot x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 9\right)\right)} \]

      2. expm1-log1p 86.3%

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

      3. associate-*l* 86.4%

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

      4. associate-*l* 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in t around 0 86.3%

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

       1. *-commutative 86.3%

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

       2. associate-*r* 86.4%

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

       3. *-commutative 86.4%

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

       4. associate-*l* 86.5%

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

   11. Simplified 86.5%

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

       1. sub-neg 86.5%

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

       2. distribute-rgt-neg-in 86.5%

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

       3. associate-*r* 86.4%

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

       4. *-commutative 86.4%

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

       5. distribute-rgt-neg-in 86.4%

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

       6. metadata-eval 86.4%

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

       7. *-commutative 86.4%

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

       8. associate-*r* 86.4%

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

       9. *-commutative 86.4%

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

       10. +-commutative 86.4%

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

       11. *-commutative 86.4%

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

       12. associate-*r* 84.0%

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

       13. associate-*r* 84.0%

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

       14. *-commutative 84.0%

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

   13. Applied egg-rr 84.0%

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

   if 4.19999999999999968e59 < b

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. distribute-lft-neg-in 96.0%

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

      3. associate-*l* 95.9%

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

      4. *-commutative 95.9%

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

      5. *-commutative 95.9%

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

      6. cancel-sign-sub-inv 95.9%

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

      7. *-commutative 95.9%

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

      8. *-commutative 95.9%

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

      9. associate-*l* 96.0%

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

      10. associate-*l* 96.4%

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

      11. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in x around 0 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l* 94.2%

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

      3. associate-*l* 94.1%

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

   6. Simplified 94.1%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-245}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot 2 + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \end{array} \]

Alternative 5: 93.0% accurate, 1.0× speedup

Math

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

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) (* a (* 27.0 b))) (* (* 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) {
	return ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -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 = ((x * 2.0d0) + (a * (27.0d0 * b))) + ((y * t) * (z * (-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 ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -9.0));
}

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) + (a * (27.0 * b))) + ((y * t) * (z * -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(Float64(x * 2.0) + Float64(a * Float64(27.0 * b))) + Float64(Float64(y * t) * Float64(z * -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 = ((x * 2.0) + (a * (27.0 * b))) + ((y * t) * (z * -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[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. associate-+r- 97.2%

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

   3. cancel-sign-sub-inv 97.2%

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

   4. *-commutative 97.2%

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

   5. distribute-rgt-neg-out 97.2%

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

   6. associate-*r* 96.1%

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

   7. *-commutative 96.1%

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

   8. distribute-rgt-neg-in 96.1%

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

   9. associate-+r+ 96.1%

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

   10. sub-neg 96.1%

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

   11. associate-*l* 96.1%

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

   12. fma-def 96.1%

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

   13. fma-neg 96.1%

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

   14. associate-*l* 96.1%

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

   15. *-commutative 96.1%

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

   16. associate-*r* 95.3%

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

   17. distribute-rgt-neg-in 95.3%

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

3. Simplified 95.4%

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

   1. fma-udef 95.4%

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

   2. fma-udef 95.4%

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

   3. associate-+r+ 95.4%

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

   4. associate-*r* 96.1%

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

   5. *-commutative 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 6: 72.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-245} \lor \neg \left(b \leq 5.6 \cdot 10^{+201}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.8e-245) (not (<= b 5.6e+201)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (+ (* 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 tmp;
	if ((b <= -6.8e-245) || !(b <= 5.6e+201)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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) :: tmp
    if ((b <= (-6.8d-245)) .or. (.not. (b <= 5.6d+201))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    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 tmp;
	if ((b <= -6.8e-245) || !(b <= 5.6e+201)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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):
	tmp = 0
	if (b <= -6.8e-245) or not (b <= 5.6e+201):
		tmp = (x * 2.0) + (27.0 * (a * b))
	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)
	tmp = 0.0
	if ((b <= -6.8e-245) || !(b <= 5.6e+201))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(y * Float64(-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)
	tmp = 0.0;
	if ((b <= -6.8e-245) || ~((b <= 5.6e+201)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	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_] := If[Or[LessEqual[b, -6.8e-245], N[Not[LessEqual[b, 5.6e+201]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.7999999999999999e-245 or 5.6000000000000001e201 < b

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-lft-neg-in 97.8%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

      5. *-commutative 97.8%

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

      6. cancel-sign-sub-inv 97.8%

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

      7. *-commutative 97.8%

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

      8. *-commutative 97.8%

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

      9. associate-*l* 97.8%

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

      10. associate-*l* 96.5%

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

      11. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 68.0%

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

   if -6.7999999999999999e-245 < b < 5.6000000000000001e201

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. distribute-lft-neg-in 96.4%

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

      3. associate-*l* 96.4%

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

      4. *-commutative 96.4%

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

      5. *-commutative 96.4%

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

      6. cancel-sign-sub-inv 96.4%

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

      7. *-commutative 96.4%

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

      8. *-commutative 96.4%

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

      9. associate-*l* 96.4%

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

      10. associate-*l* 93.9%

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

      11. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in a around 0 76.5%

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

      1. expm1-log1p-u 54.8%

         \[\leadsto 2 \cdot x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 50.9%

         \[\leadsto 2 \cdot x - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} \]

      3. *-commutative 50.9%

         \[\leadsto 2 \cdot x - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot 9}\right)} - 1\right) \]

   6. Applied egg-rr 50.9%

      \[\leadsto 2 \cdot x - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 9\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 54.8%

         \[\leadsto 2 \cdot x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 9\right)\right)} \]

      2. expm1-log1p 76.5%

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

      3. associate-*l* 76.6%

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

      4. associate-*l* 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in t around 0 76.5%

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

       1. *-commutative 76.5%

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

       2. associate-*r* 76.6%

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

       3. *-commutative 76.6%

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

       4. associate-*l* 76.6%

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

   11. Simplified 76.6%

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

       1. sub-neg 76.6%

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

       2. distribute-rgt-neg-in 76.6%

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

       3. associate-*r* 76.6%

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

       4. *-commutative 76.6%

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

       5. distribute-rgt-neg-in 76.6%

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

       6. metadata-eval 76.6%

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

       7. *-commutative 76.6%

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

       8. associate-*r* 76.6%

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

       9. *-commutative 76.6%

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

       10. +-commutative 76.6%

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

       11. *-commutative 76.6%

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

       12. associate-*r* 74.1%

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

       13. associate-*r* 74.1%

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

       14. *-commutative 74.1%

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

   13. Applied egg-rr 74.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-245} \lor \neg \left(b \leq 5.6 \cdot 10^{+201}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 47.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq 8.2 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= t 8.2e-303)
     t_1
     (if (<= t 1.15e-76)
       (* x 2.0)
       (if (<= t 1.4e+52) t_1 (* -9.0 (* t (* z y))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (t <= 8.2e-303) {
		tmp = t_1;
	} else if (t <= 1.15e-76) {
		tmp = x * 2.0;
	} else if (t <= 1.4e+52) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (t <= 8.2d-303) then
        tmp = t_1
    else if (t <= 1.15d-76) then
        tmp = x * 2.0d0
    else if (t <= 1.4d+52) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (t * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (t <= 8.2e-303) {
		tmp = t_1;
	} else if (t <= 1.15e-76) {
		tmp = x * 2.0;
	} else if (t <= 1.4e+52) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if t <= 8.2e-303:
		tmp = t_1
	elif t <= 1.15e-76:
		tmp = x * 2.0
	elif t <= 1.4e+52:
		tmp = t_1
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (t <= 8.2e-303)
		tmp = t_1;
	elseif (t <= 1.15e-76)
		tmp = Float64(x * 2.0);
	elseif (t <= 1.4e+52)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (t <= 8.2e-303)
		tmp = t_1;
	elseif (t <= 1.15e-76)
		tmp = x * 2.0;
	elseif (t <= 1.4e+52)
		tmp = t_1;
	else
		tmp = -9.0 * (t * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 8.2e-303], t$95$1, If[LessEqual[t, 1.15e-76], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 1.4e+52], t$95$1, N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 8.20000000000000037e-303 or 1.15000000000000003e-76 < t < 1.4e52

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r- 96.5%

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

      3. cancel-sign-sub-inv 96.5%

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

      4. *-commutative 96.5%

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

      5. distribute-rgt-neg-out 96.5%

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

      6. associate-*r* 95.8%

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

      7. *-commutative 95.8%

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

      8. distribute-rgt-neg-in 95.8%

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

      9. associate-+r+ 95.8%

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

      10. sub-neg 95.8%

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

      11. associate-*l* 95.8%

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

      12. fma-def 95.8%

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

      13. fma-neg 95.8%

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

      14. associate-*l* 95.8%

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

      15. *-commutative 95.8%

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

      16. associate-*r* 95.2%

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

      17. distribute-rgt-neg-in 95.2%

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

   3. Simplified 95.2%

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

      1. fma-udef 95.2%

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

      2. fma-udef 95.2%

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

      3. associate-+r+ 95.2%

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

      4. associate-*r* 95.8%

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

      5. *-commutative 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in a around inf 38.2%

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

   if 8.20000000000000037e-303 < t < 1.15000000000000003e-76

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-+r- 95.6%

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

      3. cancel-sign-sub-inv 95.6%

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

      4. *-commutative 95.6%

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

      5. distribute-rgt-neg-out 95.6%

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

      6. associate-*r* 97.7%

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

      7. *-commutative 97.7%

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

      8. distribute-rgt-neg-in 97.7%

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

      9. associate-+r+ 97.7%

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

      10. sub-neg 97.7%

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

      11. associate-*l* 97.9%

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

      12. fma-def 97.9%

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

      13. fma-neg 97.9%

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

      14. associate-*l* 97.7%

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

      15. *-commutative 97.7%

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

      16. associate-*r* 99.9%

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

      17. distribute-rgt-neg-in 99.9%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

      4. associate-*r* 97.9%

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

      5. *-commutative 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in x around inf 51.7%

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

   if 1.4e52 < t

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-lft-neg-in 99.9%

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

      3. associate-*l* 99.9%

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

      4. *-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. *-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 92.7%

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

      11. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 73.9%

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

   5. Taylor expanded in a around 0 56.3%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{-303}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 8: 47.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq 1.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= t 1.4e-305)
     t_1
     (if (<= t 1.15e-76)
       (* x 2.0)
       (if (<= t 3e+53) t_1 (* t (* -9.0 (* z y))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (t <= 1.4e-305) {
		tmp = t_1;
	} else if (t <= 1.15e-76) {
		tmp = x * 2.0;
	} else if (t <= 3e+53) {
		tmp = t_1;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (t <= 1.4d-305) then
        tmp = t_1
    else if (t <= 1.15d-76) then
        tmp = x * 2.0d0
    else if (t <= 3d+53) then
        tmp = t_1
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (t <= 1.4e-305) {
		tmp = t_1;
	} else if (t <= 1.15e-76) {
		tmp = x * 2.0;
	} else if (t <= 3e+53) {
		tmp = t_1;
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if t <= 1.4e-305:
		tmp = t_1
	elif t <= 1.15e-76:
		tmp = x * 2.0
	elif t <= 3e+53:
		tmp = t_1
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (t <= 1.4e-305)
		tmp = t_1;
	elseif (t <= 1.15e-76)
		tmp = Float64(x * 2.0);
	elseif (t <= 3e+53)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (t <= 1.4e-305)
		tmp = t_1;
	elseif (t <= 1.15e-76)
		tmp = x * 2.0;
	elseif (t <= 3e+53)
		tmp = t_1;
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 1.4e-305], t$95$1, If[LessEqual[t, 1.15e-76], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 3e+53], t$95$1, N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.40000000000000007e-305 or 1.15000000000000003e-76 < t < 2.99999999999999998e53

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r- 96.5%

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

      3. cancel-sign-sub-inv 96.5%

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

      4. *-commutative 96.5%

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

      5. distribute-rgt-neg-out 96.5%

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

      6. associate-*r* 95.8%

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

      7. *-commutative 95.8%

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

      8. distribute-rgt-neg-in 95.8%

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

      9. associate-+r+ 95.8%

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

      10. sub-neg 95.8%

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

      11. associate-*l* 95.8%

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

      12. fma-def 95.8%

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

      13. fma-neg 95.8%

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

      14. associate-*l* 95.8%

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

      15. *-commutative 95.8%

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

      16. associate-*r* 95.2%

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

      17. distribute-rgt-neg-in 95.2%

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

   3. Simplified 95.2%

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

      1. fma-udef 95.2%

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

      2. fma-udef 95.2%

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

      3. associate-+r+ 95.2%

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

      4. associate-*r* 95.8%

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

      5. *-commutative 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in a around inf 38.2%

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

   if 1.40000000000000007e-305 < t < 1.15000000000000003e-76

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-+r- 95.6%

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

      3. cancel-sign-sub-inv 95.6%

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

      4. *-commutative 95.6%

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

      5. distribute-rgt-neg-out 95.6%

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

      6. associate-*r* 97.7%

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

      7. *-commutative 97.7%

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

      8. distribute-rgt-neg-in 97.7%

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

      9. associate-+r+ 97.7%

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

      10. sub-neg 97.7%

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

      11. associate-*l* 97.9%

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

      12. fma-def 97.9%

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

      13. fma-neg 97.9%

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

      14. associate-*l* 97.7%

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

      15. *-commutative 97.7%

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

      16. associate-*r* 99.9%

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

      17. distribute-rgt-neg-in 99.9%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

      4. associate-*r* 97.9%

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

      5. *-commutative 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in x around inf 51.7%

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

   if 2.99999999999999998e53 < t

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-lft-neg-in 99.9%

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

      3. associate-*l* 99.9%

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

      4. *-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. *-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 92.7%

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

      11. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 73.9%

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

   5. Taylor expanded in a around 0 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*l* 56.5%

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

      3. *-commutative 56.5%

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

   7. Simplified 56.5%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{-305}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+53}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 9: 47.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq 2.85 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

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 (* 27.0 (* a b))))
   (if (<= t 2.85e-294)
     t_1
     (if (<= t 1.2e-76)
       (* x 2.0)
       (if (<= t 3.4e+52) t_1 (* 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) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (t <= 2.85e-294) {
		tmp = t_1;
	} else if (t <= 1.2e-76) {
		tmp = x * 2.0;
	} else if (t <= 3.4e+52) {
		tmp = t_1;
	} else {
		tmp = t * (z * (y * -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 = 27.0d0 * (a * b)
    if (t <= 2.85d-294) then
        tmp = t_1
    else if (t <= 1.2d-76) then
        tmp = x * 2.0d0
    else if (t <= 3.4d+52) then
        tmp = t_1
    else
        tmp = t * (z * (y * (-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 = 27.0 * (a * b);
	double tmp;
	if (t <= 2.85e-294) {
		tmp = t_1;
	} else if (t <= 1.2e-76) {
		tmp = x * 2.0;
	} else if (t <= 3.4e+52) {
		tmp = t_1;
	} else {
		tmp = t * (z * (y * -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 = 27.0 * (a * b)
	tmp = 0
	if t <= 2.85e-294:
		tmp = t_1
	elif t <= 1.2e-76:
		tmp = x * 2.0
	elif t <= 3.4e+52:
		tmp = t_1
	else:
		tmp = t * (z * (y * -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(27.0 * Float64(a * b))
	tmp = 0.0
	if (t <= 2.85e-294)
		tmp = t_1;
	elseif (t <= 1.2e-76)
		tmp = Float64(x * 2.0);
	elseif (t <= 3.4e+52)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(z * Float64(y * -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 = 27.0 * (a * b);
	tmp = 0.0;
	if (t <= 2.85e-294)
		tmp = t_1;
	elseif (t <= 1.2e-76)
		tmp = x * 2.0;
	elseif (t <= 3.4e+52)
		tmp = t_1;
	else
		tmp = t * (z * (y * -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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2.85e-294], t$95$1, If[LessEqual[t, 1.2e-76], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 3.4e+52], t$95$1, N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.85000000000000016e-294 or 1.20000000000000007e-76 < t < 3.4e52

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-+r- 95.9%

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

      3. cancel-sign-sub-inv 95.9%

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

      4. *-commutative 95.9%

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

      5. distribute-rgt-neg-out 95.9%

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

      6. associate-*r* 95.9%

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

      7. *-commutative 95.9%

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

      8. distribute-rgt-neg-in 95.9%

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

      9. associate-+r+ 95.9%

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

      10. sub-neg 95.9%

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

      11. associate-*l* 95.9%

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

      12. fma-def 95.9%

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

      13. fma-neg 95.9%

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

      14. associate-*l* 95.9%

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

      15. *-commutative 95.9%

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

      16. associate-*r* 95.3%

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

      17. distribute-rgt-neg-in 95.3%

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

   3. Simplified 95.3%

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

      1. fma-udef 95.3%

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

      2. fma-udef 95.3%

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

      3. associate-+r+ 95.3%

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

      4. associate-*r* 95.9%

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

      5. *-commutative 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in a around inf 37.5%

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

   if 2.85000000000000016e-294 < t < 1.20000000000000007e-76

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. cancel-sign-sub-inv 97.5%

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

      4. *-commutative 97.5%

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

      5. distribute-rgt-neg-out 97.5%

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

      6. associate-*r* 97.6%

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

      7. *-commutative 97.6%

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

      8. distribute-rgt-neg-in 97.6%

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

      9. associate-+r+ 97.6%

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

      10. sub-neg 97.6%

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

      11. associate-*l* 97.7%

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

      12. fma-def 97.7%

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

      13. fma-neg 97.7%

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

      14. associate-*l* 97.6%

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

      15. *-commutative 97.6%

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

      16. associate-*r* 99.9%

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

      17. distribute-rgt-neg-in 99.9%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

      4. associate-*r* 97.7%

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

      5. *-commutative 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in x around inf 50.6%

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

   if 3.4e52 < t

   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. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-lft-neg-in 99.9%

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

      3. associate-*l* 99.9%

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

      4. *-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. *-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 92.7%

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

      11. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 73.9%

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

   5. Taylor expanded in a around 0 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*l* 56.5%

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

      3. *-commutative 56.5%

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

   7. Simplified 56.5%

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

      1. *-commutative 56.5%

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

      2. metadata-eval 56.5%

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

      3. distribute-rgt-neg-in 56.5%

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

      4. *-commutative 56.5%

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

      5. associate-*r* 56.5%

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

      6. neg-sub0 56.5%

         \[\leadsto t \cdot \color{blue}{\left(0 - z \cdot \left(y \cdot 9\right)\right)} \]

   9. Applied egg-rr 56.5%

      \[\leadsto t \cdot \color{blue}{\left(0 - z \cdot \left(y \cdot 9\right)\right)} \]
   10. Step-by-step derivation

       1. neg-sub0 56.5%

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

       2. distribute-rgt-neg-in 56.5%

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

       3. distribute-rgt-neg-in 56.5%

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

       4. metadata-eval 56.5%

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

       5. *-commutative 56.5%

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

   11. Simplified 56.5%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.85 \cdot 10^{-294}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+52}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 10: 68.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+172}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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 (<= y -5.9e+172) (* -9.0 (* t (* z y))) (+ (* 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 (y <= -5.9e+172) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.9d+172)) then
        tmp = (-9.0d0) * (t * (z * y))
    else
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.9e+172) {
		tmp = -9.0 * (t * (z * y));
	} else {
		tmp = (x * 2.0) + (27.0 * (a * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.9e+172:
		tmp = -9.0 * (t * (z * y))
	else:
		tmp = (x * 2.0) + (27.0 * (a * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.9e+172)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

MATLAB

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 <= -5.9e+172)
		tmp = -9.0 * (t * (z * y));
	else
		tmp = (x * 2.0) + (27.0 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.9e+172], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8999999999999998e172

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. distribute-lft-neg-in 93.2%

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

      3. associate-*l* 93.1%

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

      4. *-commutative 93.1%

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

      5. *-commutative 93.1%

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

      6. cancel-sign-sub-inv 93.1%

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

      7. *-commutative 93.1%

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

      8. *-commutative 93.1%

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

      9. associate-*l* 93.2%

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

      10. associate-*l* 93.0%

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

      11. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around 0 82.9%

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

   5. Taylor expanded in a around 0 70.8%

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

   if -5.8999999999999998e172 < y

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. distribute-lft-neg-in 97.7%

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

      3. associate-*l* 97.7%

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

      4. *-commutative 97.7%

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

      5. *-commutative 97.7%

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

      6. cancel-sign-sub-inv 97.7%

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

      7. *-commutative 97.7%

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

      8. *-commutative 97.7%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 95.6%

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

      11. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 64.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+172}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 11: 47.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{-63} \lor \neg \left(b \leq 4.5 \cdot 10^{+59}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 (<= b -1.22e-63) (not (<= b 4.5e+59))) (* 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 ((b <= -1.22e-63) || !(b <= 4.5e+59)) {
		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 ((b <= (-1.22d-63)) .or. (.not. (b <= 4.5d+59))) 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 ((b <= -1.22e-63) || !(b <= 4.5e+59)) {
		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 (b <= -1.22e-63) or not (b <= 4.5e+59):
		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 ((b <= -1.22e-63) || !(b <= 4.5e+59))
		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 ((b <= -1.22e-63) || ~((b <= 4.5e+59)))
		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[b, -1.22e-63], N[Not[LessEqual[b, 4.5e+59]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2199999999999999e-63 or 4.49999999999999959e59 < b

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. cancel-sign-sub-inv 98.2%

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

      4. *-commutative 98.2%

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

      5. distribute-rgt-neg-out 98.2%

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

      6. associate-*r* 95.3%

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

      7. *-commutative 95.3%

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

      8. distribute-rgt-neg-in 95.3%

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

      9. associate-+r+ 95.3%

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

      10. sub-neg 95.3%

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

      11. associate-*l* 95.3%

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

      12. fma-def 95.4%

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

      13. fma-neg 95.4%

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

      14. associate-*l* 95.4%

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

      15. *-commutative 95.4%

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

      16. associate-*r* 95.3%

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

      17. distribute-rgt-neg-in 95.3%

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

   3. Simplified 95.3%

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

      1. fma-udef 95.3%

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

      2. fma-udef 95.3%

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

      3. associate-+r+ 95.3%

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

      4. associate-*r* 95.4%

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

      5. *-commutative 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in a around inf 56.1%

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

   if -1.2199999999999999e-63 < b < 4.49999999999999959e59

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. associate-+r- 96.2%

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

      3. cancel-sign-sub-inv 96.2%

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

      4. *-commutative 96.2%

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

      5. distribute-rgt-neg-out 96.2%

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

      6. associate-*r* 96.9%

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

      7. *-commutative 96.9%

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

      8. distribute-rgt-neg-in 96.9%

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

      9. associate-+r+ 96.9%

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

      10. sub-neg 96.9%

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

      11. associate-*l* 96.9%

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

      12. fma-def 96.9%

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

      13. fma-neg 96.9%

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

      14. associate-*l* 96.9%

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

      15. *-commutative 96.9%

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

      16. associate-*r* 95.3%

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

      17. distribute-rgt-neg-in 95.3%

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

   3. Simplified 95.5%

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

      1. fma-udef 95.5%

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

      2. fma-udef 95.5%

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

      3. associate-+r+ 95.5%

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

      4. associate-*r* 96.9%

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

      5. *-commutative 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in x around inf 41.0%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{-63} \lor \neg \left(b \leq 4.5 \cdot 10^{+59}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 12: 30.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. associate-+r- 97.2%

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

   3. cancel-sign-sub-inv 97.2%

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

   4. *-commutative 97.2%

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

   5. distribute-rgt-neg-out 97.2%

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

   6. associate-*r* 96.1%

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

   7. *-commutative 96.1%

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

   8. distribute-rgt-neg-in 96.1%

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

   9. associate-+r+ 96.1%

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

   10. sub-neg 96.1%

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

   11. associate-*l* 96.1%

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

   12. fma-def 96.1%

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

   13. fma-neg 96.1%

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

   14. associate-*l* 96.1%

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

   15. *-commutative 96.1%

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

   16. associate-*r* 95.3%

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

   17. distribute-rgt-neg-in 95.3%

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

3. Simplified 95.4%

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

   1. fma-udef 95.4%

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

   2. fma-udef 95.4%

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

   3. associate-+r+ 95.4%

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

   4. associate-*r* 96.1%

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

   5. *-commutative 96.1%

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

5. Applied egg-rr 96.1%

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

6. Taylor expanded in x around inf 29.4%

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

7. Final simplification 29.4%

   \[\leadsto x \cdot 2 \]

Developer target: 94.5% 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 2023275 
(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)))