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

Percentage Accurate: 95.8% → 98.5%

Time: 11.7s

Alternatives: 12

Speedup: 0.1×

• 27.5% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{-38}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \mathsf{fma}\left(y \cdot \left(z \cdot 9\right), t, a \cdot \left(b \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.5e-38)
   (+ (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* t (* z -9.0))))
   (- (* x 2.0) (fma (* y (* z 9.0)) t (* a (* b -27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.5e-38) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) + (y * (t * (z * -9.0)));
	} else {
		tmp = (x * 2.0) - fma((y * (z * 9.0)), t, (a * (b * -27.0)));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.5e-38)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) + Float64(y * Float64(t * Float64(z * -9.0))));
	else
		tmp = Float64(Float64(x * 2.0) - fma(Float64(y * Float64(z * 9.0)), t, Float64(a * Float64(b * -27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2.5e-38], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision] * t + N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.50000000000000017e-38

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-*l* 95.1%

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

      3. fma-def 95.1%

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

      4. associate-*l* 95.4%

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

      5. *-commutative 95.4%

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

      6. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

      1. fma-udef 95.4%

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

      2. associate-*r* 95.4%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-*r* 95.1%

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

      6. *-commutative 95.1%

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

      7. cancel-sign-sub-inv 95.1%

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

      8. distribute-lft-neg-in 95.1%

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

      9. associate-+r+ 95.1%

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

      10. associate-*r* 95.1%

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

      11. *-commutative 95.1%

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

      12. associate-*r* 95.4%

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

      13. *-commutative 95.4%

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

      14. associate-*r* 95.4%

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

      15. *-commutative 95.4%

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

      16. distribute-rgt-neg-in 95.4%

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

      17. metadata-eval 95.4%

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

      18. associate-*r* 94.9%

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

      19. *-commutative 94.9%

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

      20. associate-*r* 94.9%

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

   5. Applied egg-rr 94.9%

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

   if 2.50000000000000017e-38 < z

   1. Initial program 96.4%

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

      1. associate-+l- 96.4%

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

      2. sub-neg 96.4%

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

      3. neg-mul-1 96.4%

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

      4. metadata-eval 96.4%

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

      5. metadata-eval 96.4%

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

      6. cancel-sign-sub-inv 96.4%

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

      7. metadata-eval 96.4%

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

      8. *-lft-identity 96.4%

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

      9. associate-*l* 94.2%

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

      10. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

      1. sub-neg 94.2%

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

      2. associate-*r* 96.4%

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

      3. fma-def 97.6%

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

      4. associate-*l* 97.6%

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

      5. distribute-rgt-neg-in 97.6%

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

      6. *-commutative 97.6%

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

      7. distribute-rgt-neg-in 97.6%

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

      8. metadata-eval 97.6%

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

   5. Applied egg-rr 97.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{-38}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \mathsf{fma}\left(y \cdot \left(z \cdot 9\right), t, a \cdot \left(b \cdot -27\right)\right)\\ \end{array} \]

Alternative 2: 95.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. associate-+l- 95.5%

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

   2. fma-neg 95.5%

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

   3. neg-sub0 95.5%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

   4. associate-+l- 95.5%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

   5. neg-sub0 95.5%

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

   6. associate-*l* 95.0%

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

   7. associate-*l* 94.6%

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

   8. distribute-rgt-neg-in 94.6%

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

   9. fma-def 94.6%

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

   10. *-commutative 94.6%

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

   11. distribute-rgt-neg-in 94.6%

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

   12. metadata-eval 94.6%

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

3. Simplified 94.6%

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

4. Final simplification 94.6%

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

Alternative 3: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+253}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* a (* b -27.0)))))
   (if (<= b -6.5e-32)
     t_1
     (if (<= b 2.3e+26)
       (- (* x 2.0) (* y (* 9.0 (* z t))))
       (if (<= b 5.6e+253) (+ (* a (* 27.0 b)) (* y (* -9.0 (* z t)))) t_1)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (b <= -6.5e-32) {
		tmp = t_1;
	} else if (b <= 2.3e+26) {
		tmp = (x * 2.0) - (y * (9.0 * (z * t)));
	} else if (b <= 5.6e+253) {
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (a * (b * (-27.0d0)))
    if (b <= (-6.5d-32)) then
        tmp = t_1
    else if (b <= 2.3d+26) then
        tmp = (x * 2.0d0) - (y * (9.0d0 * (z * t)))
    else if (b <= 5.6d+253) then
        tmp = (a * (27.0d0 * b)) + (y * ((-9.0d0) * (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (b <= -6.5e-32) {
		tmp = t_1;
	} else if (b <= 2.3e+26) {
		tmp = (x * 2.0) - (y * (9.0 * (z * t)));
	} else if (b <= 5.6e+253) {
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (a * (b * -27.0))
	tmp = 0
	if b <= -6.5e-32:
		tmp = t_1
	elif b <= 2.3e+26:
		tmp = (x * 2.0) - (y * (9.0 * (z * t)))
	elif b <= 5.6e+253:
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)))
	tmp = 0.0
	if (b <= -6.5e-32)
		tmp = t_1;
	elseif (b <= 2.3e+26)
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t))));
	elseif (b <= 5.6e+253)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(y * Float64(-9.0 * Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (a * (b * -27.0));
	tmp = 0.0;
	if (b <= -6.5e-32)
		tmp = t_1;
	elseif (b <= 2.3e+26)
		tmp = (x * 2.0) - (y * (9.0 * (z * t)));
	elseif (b <= 5.6e+253)
		tmp = (a * (27.0 * b)) + (y * (-9.0 * (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e-32], t$95$1, If[LessEqual[b, 2.3e+26], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+253], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.49999999999999988e-32 or 5.5999999999999999e253 < b

   1. Initial program 93.2%

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

      1. associate-+l- 93.2%

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

      2. sub-neg 93.2%

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

      3. neg-mul-1 93.2%

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

      4. metadata-eval 93.2%

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

      5. metadata-eval 93.2%

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

      6. cancel-sign-sub-inv 93.2%

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

      7. metadata-eval 93.2%

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

      8. *-lft-identity 93.2%

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

      9. associate-*l* 95.8%

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

      10. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around 0 70.1%

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

      1. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in a around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-*l* 70.1%

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

   9. Simplified 70.1%

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

   if -6.49999999999999988e-32 < b < 2.3000000000000001e26

   1. Initial program 95.0%

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

   2. Taylor expanded in a around 0 83.4%

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

      1. expm1-log1p-u 64.6%

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

      2. expm1-udef 60.9%

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

      3. *-commutative 60.9%

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

      4. associate-*r* 60.8%

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

   4. Applied egg-rr 60.8%

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

      1. expm1-def 64.1%

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

      2. expm1-log1p 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-*l* 83.4%

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

      5. *-commutative 83.4%

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

      6. associate-*l* 83.5%

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

   6. Simplified 83.5%

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

   if 2.3000000000000001e26 < b < 5.5999999999999999e253

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 77.0%

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

      1. cancel-sign-sub-inv 77.0%

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

      2. metadata-eval 77.0%

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

      3. *-commutative 77.0%

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

      4. associate-*r* 77.1%

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

      5. *-commutative 77.1%

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

      6. *-commutative 77.1%

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

      7. associate-*r* 77.1%

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

      8. *-commutative 77.1%

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

      9. associate-*l* 77.1%

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

      10. *-commutative 77.1%

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

      11. associate-*l* 77.1%

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

   4. Applied egg-rr 77.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+253}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 4: 45.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+114} \lor \neg \left(a \leq -6.2 \cdot 10^{+71}\right) \land \left(a \leq -9 \cdot 10^{-77} \lor \neg \left(a \leq 4 \cdot 10^{-197}\right) \land \left(a \leq 3.55 \cdot 10^{-149} \lor \neg \left(a \leq 2.35 \cdot 10^{-62}\right)\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.25e+114)
         (and (not (<= a -6.2e+71))
              (or (<= a -9e-77)
                  (and (not (<= a 4e-197))
                       (or (<= a 3.55e-149) (not (<= a 2.35e-62)))))))
   (* 27.0 (* a b))
   (* x 2.0)))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.25e+114) || (!(a <= -6.2e+71) && ((a <= -9e-77) || (!(a <= 4e-197) && ((a <= 3.55e-149) || !(a <= 2.35e-62)))))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.25d+114)) .or. (.not. (a <= (-6.2d+71))) .and. (a <= (-9d-77)) .or. (.not. (a <= 4d-197)) .and. (a <= 3.55d-149) .or. (.not. (a <= 2.35d-62))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.25e+114) || (!(a <= -6.2e+71) && ((a <= -9e-77) || (!(a <= 4e-197) && ((a <= 3.55e-149) || !(a <= 2.35e-62)))))) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.25e+114) or (not (a <= -6.2e+71) and ((a <= -9e-77) or (not (a <= 4e-197) and ((a <= 3.55e-149) or not (a <= 2.35e-62))))):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.25e+114) || (!(a <= -6.2e+71) && ((a <= -9e-77) || (!(a <= 4e-197) && ((a <= 3.55e-149) || !(a <= 2.35e-62))))))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.25e+114) || (~((a <= -6.2e+71)) && ((a <= -9e-77) || (~((a <= 4e-197)) && ((a <= 3.55e-149) || ~((a <= 2.35e-62)))))))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.25e+114], And[N[Not[LessEqual[a, -6.2e+71]], $MachinePrecision], Or[LessEqual[a, -9e-77], And[N[Not[LessEqual[a, 4e-197]], $MachinePrecision], Or[LessEqual[a, 3.55e-149], N[Not[LessEqual[a, 2.35e-62]], $MachinePrecision]]]]]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25e114 or -6.20000000000000036e71 < a < -9.0000000000000001e-77 or 3.9999999999999999e-197 < a < 3.5500000000000001e-149 or 2.34999999999999992e-62 < a

   1. Initial program 96.8%

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

   2. Taylor expanded in a around inf 50.5%

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

   if -2.25e114 < a < -6.20000000000000036e71 or -9.0000000000000001e-77 < a < 3.9999999999999999e-197 or 3.5500000000000001e-149 < a < 2.34999999999999992e-62

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf 48.4%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+114} \lor \neg \left(a \leq -6.2 \cdot 10^{+71}\right) \land \left(a \leq -9 \cdot 10^{-77} \lor \neg \left(a \leq 4 \cdot 10^{-197}\right) \land \left(a \leq 3.55 \cdot 10^{-149} \lor \neg \left(a \leq 2.35 \cdot 10^{-62}\right)\right)\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 5: 45.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+71}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-197}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-148}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= a -1.8e+114)
     t_1
     (if (<= a -3.4e+71)
       (* x 2.0)
       (if (<= a -1.04e-76)
         t_1
         (if (<= a 3.8e-197)
           (* x 2.0)
           (if (<= a 1.36e-148)
             (* 27.0 (* a b))
             (if (<= a 2.3e-62) (* x 2.0) t_1))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (a <= -1.8e+114) {
		tmp = t_1;
	} else if (a <= -3.4e+71) {
		tmp = x * 2.0;
	} else if (a <= -1.04e-76) {
		tmp = t_1;
	} else if (a <= 3.8e-197) {
		tmp = x * 2.0;
	} else if (a <= 1.36e-148) {
		tmp = 27.0 * (a * b);
	} else if (a <= 2.3e-62) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (a <= (-1.8d+114)) then
        tmp = t_1
    else if (a <= (-3.4d+71)) then
        tmp = x * 2.0d0
    else if (a <= (-1.04d-76)) then
        tmp = t_1
    else if (a <= 3.8d-197) then
        tmp = x * 2.0d0
    else if (a <= 1.36d-148) then
        tmp = 27.0d0 * (a * b)
    else if (a <= 2.3d-62) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (a <= -1.8e+114) {
		tmp = t_1;
	} else if (a <= -3.4e+71) {
		tmp = x * 2.0;
	} else if (a <= -1.04e-76) {
		tmp = t_1;
	} else if (a <= 3.8e-197) {
		tmp = x * 2.0;
	} else if (a <= 1.36e-148) {
		tmp = 27.0 * (a * b);
	} else if (a <= 2.3e-62) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if a <= -1.8e+114:
		tmp = t_1
	elif a <= -3.4e+71:
		tmp = x * 2.0
	elif a <= -1.04e-76:
		tmp = t_1
	elif a <= 3.8e-197:
		tmp = x * 2.0
	elif a <= 1.36e-148:
		tmp = 27.0 * (a * b)
	elif a <= 2.3e-62:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (a <= -1.8e+114)
		tmp = t_1;
	elseif (a <= -3.4e+71)
		tmp = Float64(x * 2.0);
	elseif (a <= -1.04e-76)
		tmp = t_1;
	elseif (a <= 3.8e-197)
		tmp = Float64(x * 2.0);
	elseif (a <= 1.36e-148)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (a <= 2.3e-62)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (a <= -1.8e+114)
		tmp = t_1;
	elseif (a <= -3.4e+71)
		tmp = x * 2.0;
	elseif (a <= -1.04e-76)
		tmp = t_1;
	elseif (a <= 3.8e-197)
		tmp = x * 2.0;
	elseif (a <= 1.36e-148)
		tmp = 27.0 * (a * b);
	elseif (a <= 2.3e-62)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+114], t$95$1, If[LessEqual[a, -3.4e+71], N[(x * 2.0), $MachinePrecision], If[LessEqual[a, -1.04e-76], t$95$1, If[LessEqual[a, 3.8e-197], N[(x * 2.0), $MachinePrecision], If[LessEqual[a, 1.36e-148], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-62], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8e114 or -3.3999999999999998e71 < a < -1.04e-76 or 2.3e-62 < a

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-*l* 96.4%

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

      3. fma-def 96.4%

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

      4. associate-*l* 95.8%

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

      5. *-commutative 95.8%

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

      6. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

      1. fma-udef 95.8%

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

      2. associate-*r* 95.8%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-*r* 96.4%

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

      6. *-commutative 96.4%

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

      7. cancel-sign-sub-inv 96.4%

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

      8. distribute-lft-neg-in 96.4%

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

      9. associate-+r+ 96.4%

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

      10. associate-*r* 96.4%

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

      11. *-commutative 96.4%

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

      12. associate-*r* 95.8%

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

      13. *-commutative 95.8%

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

      14. associate-*r* 95.8%

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

      15. *-commutative 95.8%

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

      16. distribute-rgt-neg-in 95.8%

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

      17. metadata-eval 95.8%

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

      18. associate-*r* 95.8%

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

      19. *-commutative 95.8%

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

      20. associate-*r* 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in a around inf 53.0%

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

      1. associate-*r* 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-*r* 53.1%

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

   8. Simplified 53.1%

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

   if -1.8e114 < a < -3.3999999999999998e71 or -1.04e-76 < a < 3.7999999999999999e-197 or 1.36e-148 < a < 2.3e-62

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf 48.4%

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

   if 3.7999999999999999e-197 < a < 1.36e-148

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 27.9%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+71}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-197}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-148}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 6: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. +-commutative 95.5%

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

   2. associate-*l* 95.5%

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

   3. fma-def 95.5%

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

   4. associate-*l* 95.0%

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

   5. *-commutative 95.0%

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

   6. associate-*l* 95.0%

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

3. Simplified 95.0%

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

   1. fma-udef 95.0%

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

   2. associate-*r* 95.0%

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

   3. associate-*r* 95.0%

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

   4. *-commutative 95.0%

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

   5. associate-*r* 95.5%

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

   6. *-commutative 95.5%

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

   7. cancel-sign-sub-inv 95.5%

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

   8. distribute-lft-neg-in 95.5%

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

   9. associate-+r+ 95.5%

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

   10. associate-*r* 95.5%

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

   11. *-commutative 95.5%

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

   12. associate-*r* 95.0%

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

   13. *-commutative 95.0%

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

   14. associate-*r* 95.0%

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

   15. *-commutative 95.0%

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

   16. distribute-rgt-neg-in 95.0%

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

   17. metadata-eval 95.0%

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

   18. associate-*r* 94.6%

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

   19. *-commutative 94.6%

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

   20. associate-*r* 94.6%

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

5. Applied egg-rr 94.6%

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

6. Final simplification 94.6%

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

Alternative 7: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-245}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))) (t_2 (* -9.0 (* y (* z t)))))
   (if (<= z -3.7e-31)
     t_2
     (if (<= z -9e-190)
       t_1
       (if (<= z 5e-245) (* x 2.0) (if (<= z 6e-82) t_1 t_2))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -3.7e-31) {
		tmp = t_2;
	} else if (z <= -9e-190) {
		tmp = t_1;
	} else if (z <= 5e-245) {
		tmp = x * 2.0;
	} else if (z <= 6e-82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    t_2 = (-9.0d0) * (y * (z * t))
    if (z <= (-3.7d-31)) then
        tmp = t_2
    else if (z <= (-9d-190)) then
        tmp = t_1
    else if (z <= 5d-245) then
        tmp = x * 2.0d0
    else if (z <= 6d-82) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -3.7e-31) {
		tmp = t_2;
	} else if (z <= -9e-190) {
		tmp = t_1;
	} else if (z <= 5e-245) {
		tmp = x * 2.0;
	} else if (z <= 6e-82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if z <= -3.7e-31:
		tmp = t_2
	elif z <= -9e-190:
		tmp = t_1
	elif z <= 5e-245:
		tmp = x * 2.0
	elif z <= 6e-82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	t_2 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (z <= -3.7e-31)
		tmp = t_2;
	elseif (z <= -9e-190)
		tmp = t_1;
	elseif (z <= 5e-245)
		tmp = Float64(x * 2.0);
	elseif (z <= 6e-82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	t_2 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (z <= -3.7e-31)
		tmp = t_2;
	elseif (z <= -9e-190)
		tmp = t_1;
	elseif (z <= 5e-245)
		tmp = x * 2.0;
	elseif (z <= 6e-82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-31], t$95$2, If[LessEqual[z, -9e-190], t$95$1, If[LessEqual[z, 5e-245], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6e-82], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6999999999999998e-31 or 5.9999999999999998e-82 < z

   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. Taylor expanded in y around inf 48.5%

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

   if -3.6999999999999998e-31 < z < -9.00000000000000042e-190 or 4.9999999999999997e-245 < z < 5.9999999999999998e-82

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-*l* 97.6%

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

      3. fma-def 97.6%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-*r* 99.7%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 97.5%

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

      6. *-commutative 97.5%

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

      7. cancel-sign-sub-inv 97.5%

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

      8. distribute-lft-neg-in 97.5%

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

      9. associate-+r+ 97.5%

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

      10. associate-*r* 97.6%

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

      11. *-commutative 97.6%

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

      12. associate-*r* 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-*r* 99.8%

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

      15. *-commutative 99.8%

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

      16. distribute-rgt-neg-in 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-*r* 99.8%

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

      19. *-commutative 99.8%

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

      20. associate-*r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 45.0%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*r* 45.0%

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

   8. Simplified 45.0%

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

   if -9.00000000000000042e-190 < z < 4.9999999999999997e-245

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 45.4%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-31}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-245}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 8: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-240}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= z -5e-31)
     (* (* z t) (* y -9.0))
     (if (<= z -9e-190)
       t_1
       (if (<= z 3.3e-240)
         (* x 2.0)
         (if (<= z 8e-82) t_1 (* -9.0 (* y (* z t)))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -5e-31) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= -9e-190) {
		tmp = t_1;
	} else if (z <= 3.3e-240) {
		tmp = x * 2.0;
	} else if (z <= 8e-82) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (y * (z * t));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-5d-31)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (z <= (-9d-190)) then
        tmp = t_1
    else if (z <= 3.3d-240) then
        tmp = x * 2.0d0
    else if (z <= 8d-82) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (y * (z * t))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -5e-31) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= -9e-190) {
		tmp = t_1;
	} else if (z <= 3.3e-240) {
		tmp = x * 2.0;
	} else if (z <= 8e-82) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (y * (z * t));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -5e-31:
		tmp = (z * t) * (y * -9.0)
	elif z <= -9e-190:
		tmp = t_1
	elif z <= 3.3e-240:
		tmp = x * 2.0
	elif z <= 8e-82:
		tmp = t_1
	else:
		tmp = -9.0 * (y * (z * t))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -5e-31)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (z <= -9e-190)
		tmp = t_1;
	elseif (z <= 3.3e-240)
		tmp = Float64(x * 2.0);
	elseif (z <= 8e-82)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -5e-31)
		tmp = (z * t) * (y * -9.0);
	elseif (z <= -9e-190)
		tmp = t_1;
	elseif (z <= 3.3e-240)
		tmp = x * 2.0;
	elseif (z <= 8e-82)
		tmp = t_1;
	else
		tmp = -9.0 * (y * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-31], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-190], t$95$1, If[LessEqual[z, 3.3e-240], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 8e-82], t$95$1, N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5e-31

   1. Initial program 89.4%

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

   2. Taylor expanded in y around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. *-commutative 43.8%

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

      3. *-commutative 43.8%

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

      4. associate-*l* 43.8%

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

      5. *-commutative 43.8%

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

   4. Simplified 43.8%

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

   if -5e-31 < z < -9.00000000000000042e-190 or 3.3000000000000002e-240 < z < 8e-82

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-*l* 97.6%

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

      3. fma-def 97.6%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-*r* 99.7%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 97.5%

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

      6. *-commutative 97.5%

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

      7. cancel-sign-sub-inv 97.5%

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

      8. distribute-lft-neg-in 97.5%

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

      9. associate-+r+ 97.5%

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

      10. associate-*r* 97.6%

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

      11. *-commutative 97.6%

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

      12. associate-*r* 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-*r* 99.8%

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

      15. *-commutative 99.8%

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

      16. distribute-rgt-neg-in 99.8%

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

      17. metadata-eval 99.8%

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

      18. associate-*r* 99.8%

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

      19. *-commutative 99.8%

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

      20. associate-*r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 45.0%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*r* 45.0%

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

   8. Simplified 45.0%

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

   if -9.00000000000000042e-190 < z < 3.3000000000000002e-240

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 45.4%

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

   if 8e-82 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in y around inf 51.7%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-240}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+78} \lor \neg \left(y \leq 5.8 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.22e+78) (not (<= y 5.8e-152)))
   (+ (* x 2.0) (* -9.0 (* t (* y z))))
   (- (* x 2.0) (* a (* b -27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.22e+78) || !(y <= 5.8e-152)) {
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.22d+78)) .or. (.not. (y <= 5.8d-152))) then
        tmp = (x * 2.0d0) + ((-9.0d0) * (t * (y * z)))
    else
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.22e+78) || !(y <= 5.8e-152)) {
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.22e+78) or not (y <= 5.8e-152):
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)))
	else:
		tmp = (x * 2.0) - (a * (b * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.22e+78) || !(y <= 5.8e-152))
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(t * Float64(y * z))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.22e+78) || ~((y <= 5.8e-152)))
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	else
		tmp = (x * 2.0) - (a * (b * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.22e+78], N[Not[LessEqual[y, 5.8e-152]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22000000000000006e78 or 5.8000000000000003e-152 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in a around 0 71.9%

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

      1. cancel-sign-sub-inv 71.9%

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

      2. metadata-eval 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*r* 68.2%

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

   4. Applied egg-rr 68.2%

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

   if -1.22000000000000006e78 < y < 5.8000000000000003e-152

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. sub-neg 98.0%

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

      3. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. metadata-eval 98.0%

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

      8. *-lft-identity 98.0%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 78.4%

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

      1. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in a around 0 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l* 78.4%

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

   9. Simplified 78.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+78} \lor \neg \left(y \leq 5.8 \cdot 10^{-152}\right):\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 10: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.1 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.1e+77)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= y 3.4e-152)
     (- (* x 2.0) (* a (* b -27.0)))
     (+ (* x 2.0) (* -9.0 (* t (* y z)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.1e+77) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (y <= 3.4e-152) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.1d+77)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (y <= 3.4d-152) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((-9.0d0) * (t * (y * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.1e+77) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (y <= 3.4e-152) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.1e+77:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif y <= 3.4e-152:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.1e+77)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (y <= 3.4e-152)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(t * Float64(y * z))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.1e+77)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (y <= 3.4e-152)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (x * 2.0) + (-9.0 * (t * (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.1e+77], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-152], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.10000000000000014e77

   1. Initial program 93.4%

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

   2. Taylor expanded in a around 0 76.3%

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

   if -9.10000000000000014e77 < y < 3.39999999999999984e-152

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. sub-neg 98.0%

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

      3. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. metadata-eval 98.0%

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

      8. *-lft-identity 98.0%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 78.4%

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

      1. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in a around 0 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l* 78.4%

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

   9. Simplified 78.4%

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

   if 3.39999999999999984e-152 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in a around 0 69.4%

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

      1. cancel-sign-sub-inv 69.4%

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

      2. metadata-eval 69.4%

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

      3. *-commutative 69.4%

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

      4. associate-*r* 66.0%

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

   4. Applied egg-rr 66.0%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.1 \cdot 10^{+77}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 11: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+33} \lor \neg \left(z \leq 1050000000000\right):\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e+33) (not (<= z 1050000000000.0)))
   (* (* z t) (* y -9.0))
   (- (* x 2.0) (* a (* b -27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+33) || !(z <= 1050000000000.0)) {
		tmp = (z * t) * (y * -9.0);
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.1d+33)) .or. (.not. (z <= 1050000000000.0d0))) then
        tmp = (z * t) * (y * (-9.0d0))
    else
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+33) || !(z <= 1050000000000.0)) {
		tmp = (z * t) * (y * -9.0);
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e+33) or not (z <= 1050000000000.0):
		tmp = (z * t) * (y * -9.0)
	else:
		tmp = (x * 2.0) - (a * (b * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e+33) || !(z <= 1050000000000.0))
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e+33) || ~((z <= 1050000000000.0)))
		tmp = (z * t) * (y * -9.0);
	else
		tmp = (x * 2.0) - (a * (b * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e+33], N[Not[LessEqual[z, 1050000000000.0]], $MachinePrecision]], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000001e33 or 1.05e12 < z

   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. Taylor expanded in y around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. *-commutative 50.5%

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

      3. *-commutative 50.5%

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

      4. associate-*l* 50.5%

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

      5. *-commutative 50.5%

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

   4. Simplified 50.5%

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

   if -2.1000000000000001e33 < z < 1.05e12

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. sub-neg 98.0%

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

      3. neg-mul-1 98.0%

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

      4. metadata-eval 98.0%

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

      5. metadata-eval 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. metadata-eval 98.0%

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

      8. *-lft-identity 98.0%

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

      9. associate-*l* 99.1%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 80.8%

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

      1. *-commutative 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in a around 0 80.8%

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

      1. *-commutative 80.8%

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

      2. associate-*l* 80.8%

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

   9. Simplified 80.8%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+33} \lor \neg \left(z \leq 1050000000000\right):\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 12: 31.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Taylor expanded in x around inf 30.2%

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

3. Final simplification 30.2%

   \[\leadsto x \cdot 2 \]

Developer target: 95.4% 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 2023258 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

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

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