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

Percentage Accurate: 95.8% → 98.4%

Time: 24.0s

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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-265}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, \mathsf{fma}\left(y, \left(z \cdot -9\right) \cdot t, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t \cdot 9, z \cdot y, \mathsf{fma}\left(a, b \cdot 27, x \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9.2e-265)
   (fma (* a b) 27.0 (fma y (* (* z -9.0) t) (* x 2.0)))
   (fma (- (* t 9.0)) (* z y) (fma a (* b 27.0) (* x 2.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.2e-265) {
		tmp = fma((a * b), 27.0, fma(y, ((z * -9.0) * t), (x * 2.0)));
	} else {
		tmp = fma(-(t * 9.0), (z * y), fma(a, (b * 27.0), (x * 2.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.2e-265)
		tmp = fma(Float64(a * b), 27.0, fma(y, Float64(Float64(z * -9.0) * t), Float64(x * 2.0)));
	else
		tmp = fma(Float64(-Float64(t * 9.0)), Float64(z * y), fma(a, Float64(b * 27.0), Float64(x * 2.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.2e-265], N[(N[(a * b), $MachinePrecision] * 27.0 + N[(y * N[(N[(z * -9.0), $MachinePrecision] * t), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[(t * 9.0), $MachinePrecision]) * N[(z * y), $MachinePrecision] + N[(a * N[(b * 27.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999996e-265

   1. Initial program 93.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. associate-*l* N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. associate-*l* N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-commutative N/A

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

      16. distribute-rgt-neg-in N/A

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

      17. *-lowering-*.f64 N/A

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

      18. metadata-eval N/A

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

      19. *-lowering-*.f64 92.9

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

   4. Applied egg-rr 92.9%

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

   if -9.1999999999999996e-265 < z

   1. Initial program 91.8%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. neg-lowering-neg.f64 N/A

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

      14. *-commutative N/A

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

      15. *-lowering-*.f64 N/A

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

      16. associate-*l* N/A

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

      17. accelerator-lowering-fma.f64 N/A

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

      18. *-lowering-*.f64 N/A

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

      19. *-lowering-*.f64 92.6

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

   4. Applied egg-rr 92.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-265}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, 27, \mathsf{fma}\left(y, \left(z \cdot -9\right) \cdot t, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t \cdot 9, z \cdot y, \mathsf{fma}\left(a, b \cdot 27, x \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \left(a \cdot b\right) \cdot 27\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-271}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (* (* a b) 27.0)))
   (if (<= t_1 -5e+64)
     t_2
     (if (<= t_1 5e-271)
       (* x 2.0)
       (if (<= t_1 2e+74) (* z (* -9.0 (* y t))) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (a * b) * 27.0;
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = t_2;
	} else if (t_1 <= 5e-271) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+74) {
		tmp = z * (-9.0 * (y * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (a * b) * 27.0d0
    if (t_1 <= (-5d+64)) then
        tmp = t_2
    else if (t_1 <= 5d-271) then
        tmp = x * 2.0d0
    else if (t_1 <= 2d+74) then
        tmp = z * ((-9.0d0) * (y * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (a * b) * 27.0;
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = t_2;
	} else if (t_1 <= 5e-271) {
		tmp = x * 2.0;
	} else if (t_1 <= 2e+74) {
		tmp = z * (-9.0 * (y * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = (a * b) * 27.0
	tmp = 0
	if t_1 <= -5e+64:
		tmp = t_2
	elif t_1 <= 5e-271:
		tmp = x * 2.0
	elif t_1 <= 2e+74:
		tmp = z * (-9.0 * (y * t))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(Float64(a * b) * 27.0)
	tmp = 0.0
	if (t_1 <= -5e+64)
		tmp = t_2;
	elseif (t_1 <= 5e-271)
		tmp = Float64(x * 2.0);
	elseif (t_1 <= 2e+74)
		tmp = Float64(z * Float64(-9.0 * Float64(y * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = (a * b) * 27.0;
	tmp = 0.0;
	if (t_1 <= -5e+64)
		tmp = t_2;
	elseif (t_1 <= 5e-271)
		tmp = x * 2.0;
	elseif (t_1 <= 2e+74)
		tmp = z * (-9.0 * (y * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+64], t$95$2, If[LessEqual[t$95$1, 5e-271], N[(x * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+74], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e64 or 1.9999999999999999e74 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 75.7

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

   5. Simplified 75.7%

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

   if -5e64 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 5.0000000000000002e-271

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 52.6

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

   5. Simplified 52.6%

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

   if 5.0000000000000002e-271 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e74

   1. Initial program 93.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 93.1

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 46.8

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

   7. Simplified 46.8%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 52.1

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

   9. Applied egg-rr 52.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 5 \cdot 10^{-271}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z y) (* -9.0 t))) (t_2 (* t (* z (* y 9.0)))))
   (if (<= t_2 -5e+117)
     t_1
     (if (<= t_2 2e+116) (fma 27.0 (* a b) (* x 2.0)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * y) * (-9.0 * t);
	double t_2 = t * (z * (y * 9.0));
	double tmp;
	if (t_2 <= -5e+117) {
		tmp = t_1;
	} else if (t_2 <= 2e+116) {
		tmp = fma(27.0, (a * b), (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * y) * Float64(-9.0 * t))
	t_2 = Float64(t * Float64(z * Float64(y * 9.0)))
	tmp = 0.0
	if (t_2 <= -5e+117)
		tmp = t_1;
	elseif (t_2 <= 2e+116)
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+117], t$95$1, If[LessEqual[t$95$2, 2e+116], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -4.99999999999999983e117 or 2.00000000000000003e116 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 81.2%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 87.9

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

   4. Applied egg-rr 87.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 68.6

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

   7. Simplified 68.6%

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

   if -4.99999999999999983e117 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.00000000000000003e116

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 88.0

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

   5. Simplified 88.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq -5 \cdot 10^{+117}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ \mathbf{elif}\;t \cdot \left(z \cdot \left(y \cdot 9\right)\right) \leq 2 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= t_1 -5e+64)
     (fma t (* -9.0 (* z y)) (* (* a b) 27.0))
     (if (<= t_1 2e+74)
       (fma -9.0 (* y (* z t)) (* x 2.0))
       (fma 27.0 (* a b) (* x 2.0))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = fma(t, (-9.0 * (z * y)), ((a * b) * 27.0));
	} else if (t_1 <= 2e+74) {
		tmp = fma(-9.0, (y * (z * t)), (x * 2.0));
	} else {
		tmp = fma(27.0, (a * b), (x * 2.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (t_1 <= -5e+64)
		tmp = fma(t, Float64(-9.0 * Float64(z * y)), Float64(Float64(a * b) * 27.0));
	elseif (t_1 <= 2e+74)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), Float64(x * 2.0));
	else
		tmp = fma(27.0, Float64(a * b), Float64(x * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+64], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+74], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e64

   1. Initial program 92.6%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 89.3

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

   5. Simplified 89.3%

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

   if -5e64 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e74

   1. Initial program 94.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 94.5

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

   4. Applied egg-rr 94.5%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 87.0

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

   7. Simplified 87.0%

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

   if 1.9999999999999999e74 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 87.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 84.9

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

   5. Simplified 84.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), \left(a \cdot b\right) \cdot 27\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (fma 27.0 (* a b) (* x 2.0))))
   (if (<= t_1 -5e+64)
     t_2
     (if (<= t_1 2e+74) (fma -9.0 (* y (* z t)) (* x 2.0)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = fma(27.0, (a * b), (x * 2.0));
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = t_2;
	} else if (t_1 <= 2e+74) {
		tmp = fma(-9.0, (y * (z * t)), (x * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = fma(27.0, Float64(a * b), Float64(x * 2.0))
	tmp = 0.0
	if (t_1 <= -5e+64)
		tmp = t_2;
	elseif (t_1 <= 2e+74)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), Float64(x * 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+64], t$95$2, If[LessEqual[t$95$1, 2e+74], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e64 or 1.9999999999999999e74 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 90.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 85.0

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

   5. Simplified 85.0%

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

   if -5e64 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e74

   1. Initial program 94.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 94.5

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

   4. Applied egg-rr 94.5%

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

   5. Taylor expanded in a around 0

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

      1. *-lowering-*.f64 87.0

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

   7. Simplified 87.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (fma 27.0 (* a b) (* x 2.0))))
   (if (<= t_1 -5e+64)
     t_2
     (if (<= t_1 2e+74) (fma -9.0 (* t (* z y)) (* x 2.0)) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = fma(27.0, (a * b), (x * 2.0));
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = t_2;
	} else if (t_1 <= 2e+74) {
		tmp = fma(-9.0, (t * (z * y)), (x * 2.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = fma(27.0, Float64(a * b), Float64(x * 2.0))
	tmp = 0.0
	if (t_1 <= -5e+64)
		tmp = t_2;
	elseif (t_1 <= 2e+74)
		tmp = fma(-9.0, Float64(t * Float64(z * y)), Float64(x * 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+64], t$95$2, If[LessEqual[t$95$1, 2e+74], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e64 or 1.9999999999999999e74 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 90.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 85.0

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

   5. Simplified 85.0%

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

   if -5e64 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.9999999999999999e74

   1. Initial program 94.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 94.5

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

   4. Applied egg-rr 94.5%

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

   5. Taylor expanded in a around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 86.5

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

   7. Simplified 86.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(z \cdot y\right), x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := \left(a \cdot b\right) \cdot 27\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (* (* a b) 27.0)))
   (if (<= t_1 -5e+64) t_2 (if (<= t_1 1e+24) (* x 2.0) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (a * b) * 27.0;
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = t_2;
	} else if (t_1 <= 1e+24) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (a * b) * 27.0d0
    if (t_1 <= (-5d+64)) then
        tmp = t_2
    else if (t_1 <= 1d+24) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = (a * b) * 27.0;
	double tmp;
	if (t_1 <= -5e+64) {
		tmp = t_2;
	} else if (t_1 <= 1e+24) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = (a * b) * 27.0
	tmp = 0
	if t_1 <= -5e+64:
		tmp = t_2
	elif t_1 <= 1e+24:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(Float64(a * b) * 27.0)
	tmp = 0.0
	if (t_1 <= -5e+64)
		tmp = t_2;
	elseif (t_1 <= 1e+24)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = (a * b) * 27.0;
	tmp = 0.0;
	if (t_1 <= -5e+64)
		tmp = t_2;
	elseif (t_1 <= 1e+24)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+64], t$95$2, If[LessEqual[t$95$1, 1e+24], N[(x * 2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -5e64 or 9.9999999999999998e23 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 91.4%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 71.7

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

   5. Simplified 71.7%

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

   if -5e64 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 9.9999999999999998e23

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 48.5

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

   5. Simplified 48.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot 27\right) \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;b \cdot \left(a \cdot 27\right) \leq 10^{+24}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-57}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-168}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-154}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 10^{-73}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.6e-57)
   (* (* z t) (* y -9.0))
   (if (<= z -7.6e-168)
     (* (* a b) 27.0)
     (if (<= z 1.02e-154)
       (* x 2.0)
       (if (<= z 1e-73) (* a (* b 27.0)) (* (* z y) (* -9.0 t)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.6e-57) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= -7.6e-168) {
		tmp = (a * b) * 27.0;
	} else if (z <= 1.02e-154) {
		tmp = x * 2.0;
	} else if (z <= 1e-73) {
		tmp = a * (b * 27.0);
	} else {
		tmp = (z * y) * (-9.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.6d-57)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (z <= (-7.6d-168)) then
        tmp = (a * b) * 27.0d0
    else if (z <= 1.02d-154) then
        tmp = x * 2.0d0
    else if (z <= 1d-73) then
        tmp = a * (b * 27.0d0)
    else
        tmp = (z * y) * ((-9.0d0) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.6e-57) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= -7.6e-168) {
		tmp = (a * b) * 27.0;
	} else if (z <= 1.02e-154) {
		tmp = x * 2.0;
	} else if (z <= 1e-73) {
		tmp = a * (b * 27.0);
	} else {
		tmp = (z * y) * (-9.0 * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.6e-57:
		tmp = (z * t) * (y * -9.0)
	elif z <= -7.6e-168:
		tmp = (a * b) * 27.0
	elif z <= 1.02e-154:
		tmp = x * 2.0
	elif z <= 1e-73:
		tmp = a * (b * 27.0)
	else:
		tmp = (z * y) * (-9.0 * t)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.6e-57)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (z <= -7.6e-168)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (z <= 1.02e-154)
		tmp = Float64(x * 2.0);
	elseif (z <= 1e-73)
		tmp = Float64(a * Float64(b * 27.0));
	else
		tmp = Float64(Float64(z * y) * Float64(-9.0 * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.6e-57)
		tmp = (z * t) * (y * -9.0);
	elseif (z <= -7.6e-168)
		tmp = (a * b) * 27.0;
	elseif (z <= 1.02e-154)
		tmp = x * 2.0;
	elseif (z <= 1e-73)
		tmp = a * (b * 27.0);
	else
		tmp = (z * y) * (-9.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.6e-57], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-168], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[z, 1.02e-154], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1e-73], N[(a * N[(b * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * N[(-9.0 * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6e-57

   1. Initial program 89.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 88.1

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 52.2

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

   7. Simplified 52.2%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 51.1

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

   9. Applied egg-rr 51.1%

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

   if -1.6e-57 < z < -7.6000000000000001e-168

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 46.8

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

   5. Simplified 46.8%

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

   if -7.6000000000000001e-168 < z < 1.01999999999999992e-154

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 53.7

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

   5. Simplified 53.7%

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

   if 1.01999999999999992e-154 < z < 9.99999999999999997e-74

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 46.2

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

   5. Simplified 46.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 46.3

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

   7. Applied egg-rr 46.3%

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

   if 9.99999999999999997e-74 < z

   1. Initial program 87.2%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 93.9

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 38.8

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

   7. Simplified 38.8%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(-9 \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-57}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-168}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-154}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 10^{-73}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(-9 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-168}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-155}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.6e-63)
   (* (* z t) (* y -9.0))
   (if (<= z -7.5e-168)
     (* (* a b) 27.0)
     (if (<= z 5.2e-155)
       (* x 2.0)
       (if (<= z 4.6e-73) (* a (* b 27.0)) (* t (* -9.0 (* z y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.6e-63) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= -7.5e-168) {
		tmp = (a * b) * 27.0;
	} else if (z <= 5.2e-155) {
		tmp = x * 2.0;
	} else if (z <= 4.6e-73) {
		tmp = a * (b * 27.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.6d-63)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (z <= (-7.5d-168)) then
        tmp = (a * b) * 27.0d0
    else if (z <= 5.2d-155) then
        tmp = x * 2.0d0
    else if (z <= 4.6d-73) then
        tmp = a * (b * 27.0d0)
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.6e-63) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= -7.5e-168) {
		tmp = (a * b) * 27.0;
	} else if (z <= 5.2e-155) {
		tmp = x * 2.0;
	} else if (z <= 4.6e-73) {
		tmp = a * (b * 27.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.6e-63:
		tmp = (z * t) * (y * -9.0)
	elif z <= -7.5e-168:
		tmp = (a * b) * 27.0
	elif z <= 5.2e-155:
		tmp = x * 2.0
	elif z <= 4.6e-73:
		tmp = a * (b * 27.0)
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.6e-63)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (z <= -7.5e-168)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (z <= 5.2e-155)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.6e-73)
		tmp = Float64(a * Float64(b * 27.0));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.6e-63)
		tmp = (z * t) * (y * -9.0);
	elseif (z <= -7.5e-168)
		tmp = (a * b) * 27.0;
	elseif (z <= 5.2e-155)
		tmp = x * 2.0;
	elseif (z <= 4.6e-73)
		tmp = a * (b * 27.0);
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.6e-63], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-168], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[z, 5.2e-155], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.6e-73], N[(a * N[(b * 27.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.59999999999999987e-63

   1. Initial program 89.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 88.1

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 52.2

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

   7. Simplified 52.2%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 51.1

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

   9. Applied egg-rr 51.1%

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

   if -6.59999999999999987e-63 < z < -7.4999999999999995e-168

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 46.8

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

   5. Simplified 46.8%

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

   if -7.4999999999999995e-168 < z < 5.20000000000000016e-155

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 53.7

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

   5. Simplified 53.7%

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

   if 5.20000000000000016e-155 < z < 4.59999999999999977e-73

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 46.2

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

   5. Simplified 46.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 46.3

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

   7. Applied egg-rr 46.3%

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

   if 4.59999999999999977e-73 < z

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 38.8

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

   5. Simplified 38.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-168}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-155}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-168}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-155}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.35e-62)
   (* y (* -9.0 (* z t)))
   (if (<= z -4e-168)
     (* (* a b) 27.0)
     (if (<= z 1.56e-155)
       (* x 2.0)
       (if (<= z 4.2e-71) (* a (* b 27.0)) (* t (* -9.0 (* z y))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e-62) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= -4e-168) {
		tmp = (a * b) * 27.0;
	} else if (z <= 1.56e-155) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-71) {
		tmp = a * (b * 27.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.35d-62)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= (-4d-168)) then
        tmp = (a * b) * 27.0d0
    else if (z <= 1.56d-155) then
        tmp = x * 2.0d0
    else if (z <= 4.2d-71) then
        tmp = a * (b * 27.0d0)
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e-62) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= -4e-168) {
		tmp = (a * b) * 27.0;
	} else if (z <= 1.56e-155) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-71) {
		tmp = a * (b * 27.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.35e-62:
		tmp = y * (-9.0 * (z * t))
	elif z <= -4e-168:
		tmp = (a * b) * 27.0
	elif z <= 1.56e-155:
		tmp = x * 2.0
	elif z <= 4.2e-71:
		tmp = a * (b * 27.0)
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.35e-62)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= -4e-168)
		tmp = Float64(Float64(a * b) * 27.0);
	elseif (z <= 1.56e-155)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.2e-71)
		tmp = Float64(a * Float64(b * 27.0));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.35e-62)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= -4e-168)
		tmp = (a * b) * 27.0;
	elseif (z <= 1.56e-155)
		tmp = x * 2.0;
	elseif (z <= 4.2e-71)
		tmp = a * (b * 27.0);
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.35e-62], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-168], N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision], If[LessEqual[z, 1.56e-155], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.2e-71], N[(a * N[(b * 27.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.34999999999999992e-62

   1. Initial program 89.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 88.1

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 52.2

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

   7. Simplified 52.2%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 49.8

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

   9. Applied egg-rr 49.8%

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

   if -2.34999999999999992e-62 < z < -4.0000000000000002e-168

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 46.8

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

   5. Simplified 46.8%

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

   if -4.0000000000000002e-168 < z < 1.56e-155

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 53.7

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

   5. Simplified 53.7%

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

   if 1.56e-155 < z < 4.2000000000000002e-71

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 49.3

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

   5. Simplified 49.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 49.5

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

   7. Applied egg-rr 49.5%

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

   if 4.2000000000000002e-71 < z

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 39.2

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

   5. Simplified 39.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-168}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-155}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, b \cdot 27, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 7.6e+81)
   (fma -9.0 (* y (* z t)) (fma a (* b 27.0) (* x 2.0)))
   (fma t (* -9.0 (* z y)) (* (* a b) 27.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 7.6e+81) {
		tmp = fma(-9.0, (y * (z * t)), fma(a, (b * 27.0), (x * 2.0)));
	} else {
		tmp = fma(t, (-9.0 * (z * y)), ((a * b) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 7.6e+81)
		tmp = fma(-9.0, Float64(y * Float64(z * t)), fma(a, Float64(b * 27.0), Float64(x * 2.0)));
	else
		tmp = fma(t, Float64(-9.0 * Float64(z * y)), Float64(Float64(a * b) * 27.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 7.6e+81], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * 27.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.599999999999999e81

   1. Initial program 95.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. distribute-lft-neg-in N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   if 7.599999999999999e81 < z

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 62.6

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

   5. Simplified 62.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(-9, y \cdot \left(z \cdot t\right), \mathsf{fma}\left(a, b \cdot 27, x \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), \left(a \cdot b\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.6% accurate, 6.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 33.3

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

5. Simplified 33.3%

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

6. Final simplification 33.3%

   \[\leadsto x \cdot 2 \]
7. Add Preprocessing

Developer Target 1: 95.2% 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 2024201 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

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