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

Percentage Accurate: 95.5% → 98.5%

Time: 17.9s

Alternatives: 17

Speedup: 0.9×

• 27.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= z 5e-75)
     (fma x 2.0 (fma y (* -9.0 (* z t)) t_1))
     (fma x 2.0 (fma t (* -9.0 (* z y)) 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 = b * (a * 27.0);
	double tmp;
	if (z <= 5e-75) {
		tmp = fma(x, 2.0, fma(y, (-9.0 * (z * t)), t_1));
	} else {
		tmp = fma(x, 2.0, fma(t, (-9.0 * (z * y)), 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(b * Float64(a * 27.0))
	tmp = 0.0
	if (z <= 5e-75)
		tmp = fma(x, 2.0, fma(y, Float64(-9.0 * Float64(z * t)), t_1));
	else
		tmp = fma(x, 2.0, fma(t, Float64(-9.0 * Float64(z * y)), t_1));
	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_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 5e-75], N[(x * 2.0 + N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 4.99999999999999979e-75

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. fma-neg 96.1%

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

      3. neg-sub0 96.1%

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

      4. associate-+l- 96.1%

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

      5. neg-sub0 96.1%

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

      6. associate-*l* 95.5%

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

      7. associate-*l* 95.4%

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

      8. distribute-rgt-neg-in 95.4%

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

      9. fma-def 96.6%

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

      10. *-commutative 96.6%

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

      11. distribute-rgt-neg-in 96.6%

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

      12. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

   if 4.99999999999999979e-75 < z

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. fma-neg 91.5%

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

      3. neg-sub0 91.5%

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

      4. associate-+l- 91.5%

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

      5. neg-sub0 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-neg-in 91.5%

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

      8. fma-def 91.5%

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

      9. *-commutative 91.5%

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

      10. associate-*r* 91.5%

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

      11. distribute-rgt-neg-in 91.5%

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

      12. *-commutative 91.5%

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

      13. metadata-eval 91.5%

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

   3. Simplified 91.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), b \cdot \left(a \cdot 27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= z 5e-75)
     (+ (- (* x 2.0) (* y (* 9.0 (* z t)))) t_1)
     (fma x 2.0 (fma t (* -9.0 (* z y)) 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 = b * (a * 27.0);
	double tmp;
	if (z <= 5e-75) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + t_1;
	} else {
		tmp = fma(x, 2.0, fma(t, (-9.0 * (z * y)), 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(b * Float64(a * 27.0))
	tmp = 0.0
	if (z <= 5e-75)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))) + t_1);
	else
		tmp = fma(x, 2.0, fma(t, Float64(-9.0 * Float64(z * y)), t_1));
	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_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 5e-75], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x * 2.0 + N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 4.99999999999999979e-75

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 95.5%

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

      1. *-commutative 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

      5. *-commutative 95.4%

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

   4. Simplified 95.4%

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

   if 4.99999999999999979e-75 < z

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. fma-neg 91.5%

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

      3. neg-sub0 91.5%

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

      4. associate-+l- 91.5%

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

      5. neg-sub0 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-neg-in 91.5%

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

      8. fma-def 91.5%

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

      9. *-commutative 91.5%

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

      10. associate-*r* 91.5%

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

      11. distribute-rgt-neg-in 91.5%

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

      12. *-commutative 91.5%

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

      13. metadata-eval 91.5%

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

   3. Simplified 91.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -9 \cdot \left(z \cdot y\right), b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.2e-73)
   (+ (- (* x 2.0) (* y (* 9.0 (* z t)))) (* b (* a 27.0)))
   (fma x 2.0 (+ (* t (* y (* z -9.0))) (* a (* 27.0 b))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.2e-73) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (b * (a * 27.0));
	} else {
		tmp = fma(x, 2.0, ((t * (y * (z * -9.0))) + (a * (27.0 * b))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.2e-73)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))) + Float64(b * Float64(a * 27.0)));
	else
		tmp = fma(x, 2.0, Float64(Float64(t * Float64(y * Float64(z * -9.0))) + Float64(a * Float64(27.0 * b))));
	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, 1.2e-73], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.20000000000000003e-73

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 95.5%

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

      1. *-commutative 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 95.4%

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

      4. *-commutative 95.4%

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

      5. *-commutative 95.4%

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

   4. Simplified 95.4%

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

   if 1.20000000000000003e-73 < z

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. fma-neg 91.5%

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

      3. neg-sub0 91.5%

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

      4. associate-+l- 91.5%

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

      5. neg-sub0 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-neg-in 91.5%

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

      8. fma-def 91.5%

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

      9. *-commutative 91.5%

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

      10. associate-*r* 91.5%

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

      11. distribute-rgt-neg-in 91.5%

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

      12. *-commutative 91.5%

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

      13. metadata-eval 91.5%

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

   3. Simplified 91.5%

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

      1. fma-udef 91.5%

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

      2. associate-*l* 91.5%

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

      3. associate-*r* 92.6%

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

   5. Applied egg-rr 92.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\right)\\ \end{array} \]

Alternative 4: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 35000000000:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (- (* x 2.0) (* 9.0 (* y (* z t)))))
        (t_2 (- (* x 2.0) (* b (* a -27.0)))))
   (if (<= b -1.7e-46)
     t_2
     (if (<= b 6.4e-6)
       t_1
       (if (<= b 35000000000.0)
         (- (* x 2.0) (* (* a b) -27.0))
         (if (<= b 3.3e+78) 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 = (x * 2.0) - (9.0 * (y * (z * t)));
	double t_2 = (x * 2.0) - (b * (a * -27.0));
	double tmp;
	if (b <= -1.7e-46) {
		tmp = t_2;
	} else if (b <= 6.4e-6) {
		tmp = t_1;
	} else if (b <= 35000000000.0) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else if (b <= 3.3e+78) {
		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 = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    t_2 = (x * 2.0d0) - (b * (a * (-27.0d0)))
    if (b <= (-1.7d-46)) then
        tmp = t_2
    else if (b <= 6.4d-6) then
        tmp = t_1
    else if (b <= 35000000000.0d0) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else if (b <= 3.3d+78) 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 = (x * 2.0) - (9.0 * (y * (z * t)));
	double t_2 = (x * 2.0) - (b * (a * -27.0));
	double tmp;
	if (b <= -1.7e-46) {
		tmp = t_2;
	} else if (b <= 6.4e-6) {
		tmp = t_1;
	} else if (b <= 35000000000.0) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else if (b <= 3.3e+78) {
		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 = (x * 2.0) - (9.0 * (y * (z * t)))
	t_2 = (x * 2.0) - (b * (a * -27.0))
	tmp = 0
	if b <= -1.7e-46:
		tmp = t_2
	elif b <= 6.4e-6:
		tmp = t_1
	elif b <= 35000000000.0:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	elif b <= 3.3e+78:
		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(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))))
	t_2 = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)))
	tmp = 0.0
	if (b <= -1.7e-46)
		tmp = t_2;
	elseif (b <= 6.4e-6)
		tmp = t_1;
	elseif (b <= 35000000000.0)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	elseif (b <= 3.3e+78)
		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 = (x * 2.0) - (9.0 * (y * (z * t)));
	t_2 = (x * 2.0) - (b * (a * -27.0));
	tmp = 0.0;
	if (b <= -1.7e-46)
		tmp = t_2;
	elseif (b <= 6.4e-6)
		tmp = t_1;
	elseif (b <= 35000000000.0)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	elseif (b <= 3.3e+78)
		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[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e-46], t$95$2, If[LessEqual[b, 6.4e-6], t$95$1, If[LessEqual[b, 35000000000.0], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+78], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.69999999999999998e-46 or 3.3e78 < b

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. sub-neg 93.6%

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

      3. neg-mul-1 93.6%

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

      4. metadata-eval 93.6%

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

      5. metadata-eval 93.6%

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

      6. cancel-sign-sub-inv 93.6%

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

      7. metadata-eval 93.6%

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

      8. *-lft-identity 93.6%

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

      9. associate-*l* 96.3%

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

      10. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-*l* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in a around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*l* 77.8%

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

   9. Simplified 77.8%

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

   if -1.69999999999999998e-46 < b < 6.3999999999999997e-6 or 3.5e10 < b < 3.3e78

   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 a around 0 76.7%

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

   if 6.3999999999999997e-6 < b < 3.5e10

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. sub-neg 99.1%

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

      3. neg-mul-1 99.1%

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

      4. metadata-eval 99.1%

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

      5. metadata-eval 99.1%

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

      6. cancel-sign-sub-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. *-lft-identity 99.1%

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

      9. associate-*l* 80.2%

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

      10. associate-*l* 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in y around 0 80.3%

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

      1. *-commutative 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 35000000000:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+78}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \]

Alternative 5: 97.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.35e+69)
   (+ (- (* x 2.0) (* y (* 9.0 (* z t)))) (* b (* a 27.0)))
   (- (* 27.0 (* a b)) (* 9.0 (* t (* z y))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.35e+69) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (b * (a * 27.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.35d+69) then
        tmp = ((x * 2.0d0) - (y * (9.0d0 * (z * t)))) + (b * (a * 27.0d0))
    else
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.35e+69) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (b * (a * 27.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.35e+69:
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (b * (a * 27.0))
	else:
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.35e+69)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.35e+69)
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (b * (a * 27.0));
	else
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.35e+69], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.3499999999999999e69

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 95.7%

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

      1. *-commutative 95.7%

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

      2. *-commutative 95.7%

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

      3. associate-*r* 95.6%

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

      4. *-commutative 95.6%

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

      5. *-commutative 95.6%

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

   4. Simplified 95.6%

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

   if 1.3499999999999999e69 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in x around 0 69.9%

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

      1. expm1-log1p-u 42.1%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      2. expm1-udef 42.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(t \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 42.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   4. Applied egg-rr 42.0%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 42.1%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 69.9%

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

      3. associate-*r* 72.1%

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

   6. Simplified 72.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 6: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq 1.3 \cdot 10^{-15}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + t_1\\ \end{array} \end{array} \]

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 (* b (* a 27.0))))
   (if (<= z 1.3e-15)
     (+ (- (* x 2.0) (* y (* 9.0 (* z t)))) t_1)
     (+ (- (* x 2.0) (* t (* z (* y 9.0)))) 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 = b * (a * 27.0);
	double tmp;
	if (z <= 1.3e-15) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + t_1;
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + 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 = b * (a * 27.0d0)
    if (z <= 1.3d-15) then
        tmp = ((x * 2.0d0) - (y * (9.0d0 * (z * t)))) + t_1
    else
        tmp = ((x * 2.0d0) - (t * (z * (y * 9.0d0)))) + 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 = b * (a * 27.0);
	double tmp;
	if (z <= 1.3e-15) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + t_1;
	} else {
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + 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 = b * (a * 27.0)
	tmp = 0
	if z <= 1.3e-15:
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + t_1
	else:
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + 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(b * Float64(a * 27.0))
	tmp = 0.0
	if (z <= 1.3e-15)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))) + t_1);
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0)))) + 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 = b * (a * 27.0);
	tmp = 0.0;
	if (z <= 1.3e-15)
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + t_1;
	else
		tmp = ((x * 2.0) - (t * (z * (y * 9.0)))) + 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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 1.3e-15], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.30000000000000002e-15

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 95.8%

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

      1. *-commutative 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. *-commutative 95.8%

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

   4. Simplified 95.8%

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

   if 1.30000000000000002e-15 < z

   1. Initial program 89.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.3 \cdot 10^{-15}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 7: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-291}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 39000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* -9.0 (* y (* z t)))) (t_2 (* b (* a 27.0))))
   (if (<= b -3.8e-59)
     t_2
     (if (<= b -5.2e-291)
       (* x 2.0)
       (if (<= b 2.3e-5)
         t_1
         (if (<= b 39000000000.0)
           (* 27.0 (* a b))
           (if (<= b 2e+79) 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 = -9.0 * (y * (z * t));
	double t_2 = b * (a * 27.0);
	double tmp;
	if (b <= -3.8e-59) {
		tmp = t_2;
	} else if (b <= -5.2e-291) {
		tmp = x * 2.0;
	} else if (b <= 2.3e-5) {
		tmp = t_1;
	} else if (b <= 39000000000.0) {
		tmp = 27.0 * (a * b);
	} else if (b <= 2e+79) {
		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 = (-9.0d0) * (y * (z * t))
    t_2 = b * (a * 27.0d0)
    if (b <= (-3.8d-59)) then
        tmp = t_2
    else if (b <= (-5.2d-291)) then
        tmp = x * 2.0d0
    else if (b <= 2.3d-5) then
        tmp = t_1
    else if (b <= 39000000000.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 2d+79) 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 = -9.0 * (y * (z * t));
	double t_2 = b * (a * 27.0);
	double tmp;
	if (b <= -3.8e-59) {
		tmp = t_2;
	} else if (b <= -5.2e-291) {
		tmp = x * 2.0;
	} else if (b <= 2.3e-5) {
		tmp = t_1;
	} else if (b <= 39000000000.0) {
		tmp = 27.0 * (a * b);
	} else if (b <= 2e+79) {
		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 = -9.0 * (y * (z * t))
	t_2 = b * (a * 27.0)
	tmp = 0
	if b <= -3.8e-59:
		tmp = t_2
	elif b <= -5.2e-291:
		tmp = x * 2.0
	elif b <= 2.3e-5:
		tmp = t_1
	elif b <= 39000000000.0:
		tmp = 27.0 * (a * b)
	elif b <= 2e+79:
		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(-9.0 * Float64(y * Float64(z * t)))
	t_2 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (b <= -3.8e-59)
		tmp = t_2;
	elseif (b <= -5.2e-291)
		tmp = Float64(x * 2.0);
	elseif (b <= 2.3e-5)
		tmp = t_1;
	elseif (b <= 39000000000.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 2e+79)
		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 = -9.0 * (y * (z * t));
	t_2 = b * (a * 27.0);
	tmp = 0.0;
	if (b <= -3.8e-59)
		tmp = t_2;
	elseif (b <= -5.2e-291)
		tmp = x * 2.0;
	elseif (b <= 2.3e-5)
		tmp = t_1;
	elseif (b <= 39000000000.0)
		tmp = 27.0 * (a * b);
	elseif (b <= 2e+79)
		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[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e-59], t$95$2, If[LessEqual[b, -5.2e-291], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 2.3e-5], t$95$1, If[LessEqual[b, 39000000000.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+79], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.79999999999999983e-59 or 1.99999999999999993e79 < b

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. expm1-log1p-u 54.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} - 1\right)} \]

      3. associate-*r* 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(9 \cdot y\right) \cdot \left(t \cdot z\right)}\right)} - 1\right) \]

      4. *-commutative 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   4. Applied egg-rr 53.0%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 54.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*l* 72.9%

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

      5. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in a around inf 58.8%

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

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   if -3.79999999999999983e-59 < b < -5.1999999999999997e-291

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. fma-neg 95.9%

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

      3. neg-sub0 95.9%

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

      4. associate-+l- 95.9%

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

      5. neg-sub0 95.9%

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

      6. associate-*l* 94.3%

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

      7. associate-*l* 94.2%

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

      8. distribute-rgt-neg-in 94.2%

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

      9. fma-def 94.2%

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

      10. *-commutative 94.2%

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

      11. distribute-rgt-neg-in 94.2%

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

      12. metadata-eval 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 39.0%

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

   if -5.1999999999999997e-291 < b < 2.3e-5 or 3.9e10 < b < 1.99999999999999993e79

   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. Taylor expanded in y around 0 93.1%

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

      1. *-commutative 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*r* 93.0%

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

      4. *-commutative 93.0%

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

      5. *-commutative 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in y around inf 49.1%

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

   if 2.3e-5 < b < 3.9e10

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*r* 80.2%

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

      4. *-commutative 80.2%

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

      5. *-commutative 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in a around inf 60.4%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-291}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-5}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 39000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+79}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 8: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-291}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 46000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* b (* a 27.0))))
   (if (<= b -1.02e-57)
     t_1
     (if (<= b -4.6e-291)
       (* x 2.0)
       (if (<= b 1.4e-5)
         (* -9.0 (* y (* z t)))
         (if (<= b 46000000000.0)
           (* 27.0 (* a b))
           (if (<= b 1.5e+79) (* t (* -9.0 (* z y))) 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 = b * (a * 27.0);
	double tmp;
	if (b <= -1.02e-57) {
		tmp = t_1;
	} else if (b <= -4.6e-291) {
		tmp = x * 2.0;
	} else if (b <= 1.4e-5) {
		tmp = -9.0 * (y * (z * t));
	} else if (b <= 46000000000.0) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.5e+79) {
		tmp = t * (-9.0 * (z * y));
	} 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 = b * (a * 27.0d0)
    if (b <= (-1.02d-57)) then
        tmp = t_1
    else if (b <= (-4.6d-291)) then
        tmp = x * 2.0d0
    else if (b <= 1.4d-5) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (b <= 46000000000.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 1.5d+79) then
        tmp = t * ((-9.0d0) * (z * y))
    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 = b * (a * 27.0);
	double tmp;
	if (b <= -1.02e-57) {
		tmp = t_1;
	} else if (b <= -4.6e-291) {
		tmp = x * 2.0;
	} else if (b <= 1.4e-5) {
		tmp = -9.0 * (y * (z * t));
	} else if (b <= 46000000000.0) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.5e+79) {
		tmp = t * (-9.0 * (z * y));
	} 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 = b * (a * 27.0)
	tmp = 0
	if b <= -1.02e-57:
		tmp = t_1
	elif b <= -4.6e-291:
		tmp = x * 2.0
	elif b <= 1.4e-5:
		tmp = -9.0 * (y * (z * t))
	elif b <= 46000000000.0:
		tmp = 27.0 * (a * b)
	elif b <= 1.5e+79:
		tmp = t * (-9.0 * (z * y))
	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(b * Float64(a * 27.0))
	tmp = 0.0
	if (b <= -1.02e-57)
		tmp = t_1;
	elseif (b <= -4.6e-291)
		tmp = Float64(x * 2.0);
	elseif (b <= 1.4e-5)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (b <= 46000000000.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 1.5e+79)
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	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 = b * (a * 27.0);
	tmp = 0.0;
	if (b <= -1.02e-57)
		tmp = t_1;
	elseif (b <= -4.6e-291)
		tmp = x * 2.0;
	elseif (b <= 1.4e-5)
		tmp = -9.0 * (y * (z * t));
	elseif (b <= 46000000000.0)
		tmp = 27.0 * (a * b);
	elseif (b <= 1.5e+79)
		tmp = t * (-9.0 * (z * y));
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e-57], t$95$1, If[LessEqual[b, -4.6e-291], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1.4e-5], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 46000000000.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+79], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.02e-57 or 1.49999999999999987e79 < b

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. expm1-log1p-u 54.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} - 1\right)} \]

      3. associate-*r* 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(9 \cdot y\right) \cdot \left(t \cdot z\right)}\right)} - 1\right) \]

      4. *-commutative 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   4. Applied egg-rr 53.0%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 54.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*l* 72.9%

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

      5. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in a around inf 58.8%

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

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   if -1.02e-57 < b < -4.6000000000000001e-291

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. fma-neg 95.9%

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

      3. neg-sub0 95.9%

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

      4. associate-+l- 95.9%

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

      5. neg-sub0 95.9%

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

      6. associate-*l* 94.3%

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

      7. associate-*l* 94.2%

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

      8. distribute-rgt-neg-in 94.2%

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

      9. fma-def 94.2%

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

      10. *-commutative 94.2%

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

      11. distribute-rgt-neg-in 94.2%

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

      12. metadata-eval 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 39.0%

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

   if -4.6000000000000001e-291 < b < 1.39999999999999998e-5

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*r* 91.8%

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

      4. *-commutative 91.8%

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

      5. *-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around inf 50.2%

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

   if 1.39999999999999998e-5 < b < 4.6e10

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*r* 80.2%

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

      4. *-commutative 80.2%

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

      5. *-commutative 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in a around inf 60.4%

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

   if 4.6e10 < b < 1.49999999999999987e79

   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 y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 43.4%

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

      1. *-commutative 43.4%

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

      2. associate-*l* 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in y around 0 43.4%

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

      1. *-commutative 43.4%

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

      2. associate-*r* 43.3%

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

      3. *-commutative 43.3%

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

      4. associate-*l* 43.4%

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

      5. *-commutative 43.4%

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

   10. Simplified 43.4%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-291}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 46000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 9: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-292}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 0.000205:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 52000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* b (* a 27.0))))
   (if (<= b -3.15e-55)
     t_1
     (if (<= b -8e-292)
       (* x 2.0)
       (if (<= b 0.000205)
         (* y (* t (* z -9.0)))
         (if (<= b 52000000000.0)
           (* 27.0 (* a b))
           (if (<= b 1.4e+79) (* t (* -9.0 (* z y))) 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 = b * (a * 27.0);
	double tmp;
	if (b <= -3.15e-55) {
		tmp = t_1;
	} else if (b <= -8e-292) {
		tmp = x * 2.0;
	} else if (b <= 0.000205) {
		tmp = y * (t * (z * -9.0));
	} else if (b <= 52000000000.0) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.4e+79) {
		tmp = t * (-9.0 * (z * y));
	} 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 = b * (a * 27.0d0)
    if (b <= (-3.15d-55)) then
        tmp = t_1
    else if (b <= (-8d-292)) then
        tmp = x * 2.0d0
    else if (b <= 0.000205d0) then
        tmp = y * (t * (z * (-9.0d0)))
    else if (b <= 52000000000.0d0) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 1.4d+79) then
        tmp = t * ((-9.0d0) * (z * y))
    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 = b * (a * 27.0);
	double tmp;
	if (b <= -3.15e-55) {
		tmp = t_1;
	} else if (b <= -8e-292) {
		tmp = x * 2.0;
	} else if (b <= 0.000205) {
		tmp = y * (t * (z * -9.0));
	} else if (b <= 52000000000.0) {
		tmp = 27.0 * (a * b);
	} else if (b <= 1.4e+79) {
		tmp = t * (-9.0 * (z * y));
	} 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 = b * (a * 27.0)
	tmp = 0
	if b <= -3.15e-55:
		tmp = t_1
	elif b <= -8e-292:
		tmp = x * 2.0
	elif b <= 0.000205:
		tmp = y * (t * (z * -9.0))
	elif b <= 52000000000.0:
		tmp = 27.0 * (a * b)
	elif b <= 1.4e+79:
		tmp = t * (-9.0 * (z * y))
	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(b * Float64(a * 27.0))
	tmp = 0.0
	if (b <= -3.15e-55)
		tmp = t_1;
	elseif (b <= -8e-292)
		tmp = Float64(x * 2.0);
	elseif (b <= 0.000205)
		tmp = Float64(y * Float64(t * Float64(z * -9.0)));
	elseif (b <= 52000000000.0)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 1.4e+79)
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	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 = b * (a * 27.0);
	tmp = 0.0;
	if (b <= -3.15e-55)
		tmp = t_1;
	elseif (b <= -8e-292)
		tmp = x * 2.0;
	elseif (b <= 0.000205)
		tmp = y * (t * (z * -9.0));
	elseif (b <= 52000000000.0)
		tmp = 27.0 * (a * b);
	elseif (b <= 1.4e+79)
		tmp = t * (-9.0 * (z * y));
	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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.15e-55], t$95$1, If[LessEqual[b, -8e-292], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 0.000205], N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 52000000000.0], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+79], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.1499999999999999e-55 or 1.4000000000000001e79 < b

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. expm1-log1p-u 54.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} - 1\right)} \]

      3. associate-*r* 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(9 \cdot y\right) \cdot \left(t \cdot z\right)}\right)} - 1\right) \]

      4. *-commutative 53.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   4. Applied egg-rr 53.0%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 54.0%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*l* 72.9%

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

      5. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in a around inf 58.8%

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

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   if -3.1499999999999999e-55 < b < -8.0000000000000004e-292

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. fma-neg 95.9%

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

      3. neg-sub0 95.9%

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

      4. associate-+l- 95.9%

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

      5. neg-sub0 95.9%

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

      6. associate-*l* 94.3%

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

      7. associate-*l* 94.2%

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

      8. distribute-rgt-neg-in 94.2%

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

      9. fma-def 94.2%

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

      10. *-commutative 94.2%

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

      11. distribute-rgt-neg-in 94.2%

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

      12. metadata-eval 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 39.0%

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

   if -8.0000000000000004e-292 < b < 2.05e-4

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*r* 91.8%

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

      4. *-commutative 91.8%

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

      5. *-commutative 91.8%

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

   4. Simplified 91.8%

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

   5. Taylor expanded in y around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 50.1%

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

   7. Simplified 50.1%

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

   8. Taylor expanded in t around 0 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*r* 50.2%

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

   10. Simplified 50.2%

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

   if 2.05e-4 < b < 5.2e10

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*r* 80.2%

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

      4. *-commutative 80.2%

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

      5. *-commutative 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in a around inf 60.4%

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

   if 5.2e10 < b < 1.4000000000000001e79

   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 y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 43.4%

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

      1. *-commutative 43.4%

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

      2. associate-*l* 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in y around 0 43.4%

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

      1. *-commutative 43.4%

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

      2. associate-*r* 43.3%

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

      3. *-commutative 43.3%

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

      4. associate-*l* 43.4%

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

      5. *-commutative 43.4%

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

   10. Simplified 43.4%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-292}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 0.000205:\\ \;\;\;\;y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;b \leq 52000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 10: 78.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-146} \lor \neg \left(z \leq 3.7 \cdot 10^{-100}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.8e-146) (not (<= z 3.7e-100)))
   (+ (* a (* 27.0 b)) (* -9.0 (* y (* z t))))
   (- (* x 2.0) (* b (* a -27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e-146) || !(z <= 3.7e-100)) {
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (b * (a * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.8d-146)) .or. (.not. (z <= 3.7d-100))) then
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (y * (z * t)))
    else
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e-146) || !(z <= 3.7e-100)) {
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (b * (a * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.8e-146) or not (z <= 3.7e-100):
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) - (b * (a * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.8e-146) || !(z <= 3.7e-100))
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.8e-146) || ~((z <= 3.7e-100)))
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) - (b * (a * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.8e-146], N[Not[LessEqual[z, 3.7e-100]], $MachinePrecision]], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000001e-146 or 3.70000000000000018e-100 < z

   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 x around 0 72.8%

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

      1. cancel-sign-sub-inv 72.8%

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

      2. associate-*r* 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-*r* 72.8%

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

      5. metadata-eval 72.8%

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

      6. *-commutative 72.8%

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

   4. Applied egg-rr 72.8%

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

   if -6.8000000000000001e-146 < z < 3.70000000000000018e-100

   1. Initial program 98.6%

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

      1. associate-+l- 98.6%

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

      2. sub-neg 98.6%

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

      3. neg-mul-1 98.6%

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

      4. metadata-eval 98.6%

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

      5. metadata-eval 98.6%

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

      6. cancel-sign-sub-inv 98.6%

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

      7. metadata-eval 98.6%

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

      8. *-lft-identity 98.6%

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

      9. associate-*l* 98.6%

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

      10. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l* 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in a around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 83.5%

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

   9. Simplified 83.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-146} \lor \neg \left(z \leq 3.7 \cdot 10^{-100}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \]

Alternative 11: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e-145)
   (+ (* a (* 27.0 b)) (* -9.0 (* y (* z t))))
   (if (<= z 1.35e-94)
     (- (* x 2.0) (* b (* a -27.0)))
     (- (* 27.0 (* a b)) (* 9.0 (* t (* z y)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e-145) {
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)));
	} else if (z <= 1.35e-94) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.3d-145)) then
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (y * (z * t)))
    else if (z <= 1.35d-94) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e-145) {
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)));
	} else if (z <= 1.35e-94) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e-145:
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)))
	elif z <= 1.35e-94:
		tmp = (x * 2.0) - (b * (a * -27.0))
	else:
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e-145)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 1.35e-94)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3e-145)
		tmp = (a * (27.0 * b)) + (-9.0 * (y * (z * t)));
	elseif (z <= 1.35e-94)
		tmp = (x * 2.0) - (b * (a * -27.0));
	else
		tmp = (27.0 * (a * b)) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e-145], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-94], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000007e-145

   1. Initial program 94.0%

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

   2. Taylor expanded in x around 0 74.7%

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

      1. cancel-sign-sub-inv 74.7%

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

      2. associate-*r* 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*r* 74.7%

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

      5. metadata-eval 74.7%

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

      6. *-commutative 74.7%

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

   4. Applied egg-rr 74.7%

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

   if -2.30000000000000007e-145 < z < 1.3500000000000001e-94

   1. Initial program 98.6%

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

      1. associate-+l- 98.6%

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

      2. sub-neg 98.6%

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

      3. neg-mul-1 98.6%

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

      4. metadata-eval 98.6%

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

      5. metadata-eval 98.6%

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

      6. cancel-sign-sub-inv 98.6%

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

      7. metadata-eval 98.6%

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

      8. *-lft-identity 98.6%

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

      9. associate-*l* 98.6%

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

      10. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l* 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in a around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 83.5%

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

   9. Simplified 83.5%

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

   if 1.3500000000000001e-94 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in x around 0 70.5%

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

      1. expm1-log1p-u 40.4%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      2. expm1-udef 38.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(t \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 38.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   4. Applied egg-rr 38.7%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 40.4%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 70.5%

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

      3. associate-*r* 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 12: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e-57)
   (* -9.0 (* y (* z t)))
   (if (<= z 5.2e+43) (- (* x 2.0) (* a (* b -27.0))) (* t (* -9.0 (* z y))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e-57) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 5.2e+43) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.9d-57)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 5.2d+43) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e-57) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 5.2e+43) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9e-57:
		tmp = -9.0 * (y * (z * t))
	elif z <= 5.2e+43:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e-57)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 5.2e+43)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.9e-57)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 5.2e+43)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e-57], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+43], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-57

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 91.4%

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

      1. *-commutative 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*r* 91.3%

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

      4. *-commutative 91.3%

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

      5. *-commutative 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in y around inf 50.7%

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

   if -1.8999999999999999e-57 < z < 5.20000000000000042e43

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. neg-mul-1 98.4%

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

      4. metadata-eval 98.4%

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

      5. metadata-eval 98.4%

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

      6. cancel-sign-sub-inv 98.4%

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

      7. metadata-eval 98.4%

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

      8. *-lft-identity 98.4%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l* 78.5%

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

   6. Simplified 78.5%

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

   if 5.20000000000000042e43 < z

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-*r* 91.0%

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

      4. *-commutative 91.0%

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

      5. *-commutative 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around inf 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*l* 47.9%

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

   7. Simplified 47.9%

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

   8. Taylor expanded in y around 0 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*r* 49.8%

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

      3. *-commutative 49.8%

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

      4. associate-*l* 49.8%

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

      5. *-commutative 49.8%

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

   10. Simplified 49.8%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 13: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.1e-57)
   (* -9.0 (* y (* z t)))
   (if (<= z 4.5e+45) (- (* x 2.0) (* b (* a -27.0))) (* t (* -9.0 (* z y))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e-57) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 4.5e+45) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.1d-57)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 4.5d+45) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e-57) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 4.5e+45) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.1e-57:
		tmp = -9.0 * (y * (z * t))
	elif z <= 4.5e+45:
		tmp = (x * 2.0) - (b * (a * -27.0))
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.1e-57)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 4.5e+45)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.1e-57)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 4.5e+45)
		tmp = (x * 2.0) - (b * (a * -27.0));
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.1e-57], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+45], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e-57

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 91.4%

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

      1. *-commutative 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*r* 91.3%

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

      4. *-commutative 91.3%

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

      5. *-commutative 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in y around inf 50.7%

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

   if -2.0999999999999999e-57 < z < 4.4999999999999998e45

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. neg-mul-1 98.4%

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

      4. metadata-eval 98.4%

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

      5. metadata-eval 98.4%

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

      6. cancel-sign-sub-inv 98.4%

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

      7. metadata-eval 98.4%

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

      8. *-lft-identity 98.4%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l* 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in a around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*l* 78.5%

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

   9. Simplified 78.5%

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

   if 4.4999999999999998e45 < z

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-*r* 91.0%

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

      4. *-commutative 91.0%

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

      5. *-commutative 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around inf 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*l* 47.9%

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

   7. Simplified 47.9%

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

   8. Taylor expanded in y around 0 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*r* 49.8%

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

      3. *-commutative 49.8%

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

      4. associate-*l* 49.8%

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

      5. *-commutative 49.8%

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

   10. Simplified 49.8%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 14: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.1e-57)
   (* -9.0 (* y (* z t)))
   (if (<= z 1.7e+45) (- (* x 2.0) (* (* a b) -27.0)) (* t (* -9.0 (* z y))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e-57) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 1.7e+45) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.1d-57)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 1.7d+45) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e-57) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 1.7e+45) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.1e-57:
		tmp = -9.0 * (y * (z * t))
	elif z <= 1.7e+45:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.1e-57)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 1.7e+45)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.1e-57)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 1.7e+45)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.1e-57], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+45], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e-57

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 91.4%

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

      1. *-commutative 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*r* 91.3%

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

      4. *-commutative 91.3%

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

      5. *-commutative 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in y around inf 50.7%

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

   if -2.0999999999999999e-57 < z < 1.7e45

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. neg-mul-1 98.4%

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

      4. metadata-eval 98.4%

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

      5. metadata-eval 98.4%

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

      6. cancel-sign-sub-inv 98.4%

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

      7. metadata-eval 98.4%

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

      8. *-lft-identity 98.4%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 79.2%

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

      1. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   if 1.7e45 < z

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-*r* 91.0%

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

      4. *-commutative 91.0%

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

      5. *-commutative 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around inf 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*l* 47.9%

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

   7. Simplified 47.9%

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

   8. Taylor expanded in y around 0 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*r* 49.8%

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

      3. *-commutative 49.8%

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

      4. associate-*l* 49.8%

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

      5. *-commutative 49.8%

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

   10. Simplified 49.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-57}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 15: 47.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-56} \lor \neg \left(b \leq 2.6 \cdot 10^{-28}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.2e-56) (not (<= b 2.6e-28))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.2e-56) || !(b <= 2.6e-28)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.2d-56)) .or. (.not. (b <= 2.6d-28))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.2e-56) || !(b <= 2.6e-28)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.2e-56) or not (b <= 2.6e-28):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.2e-56) || !(b <= 2.6e-28))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.2e-56) || ~((b <= 2.6e-28)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.2e-56], N[Not[LessEqual[b, 2.6e-28]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.19999999999999956e-56 or 2.6e-28 < b

   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 y around 0 95.0%

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

      1. *-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 94.9%

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

      4. *-commutative 94.9%

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

      5. *-commutative 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in a around inf 55.2%

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

   if -7.19999999999999956e-56 < b < 2.6e-28

   1. Initial program 96.3%

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

      1. associate-+l- 96.3%

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

      2. fma-neg 96.3%

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

      3. neg-sub0 96.3%

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

      4. associate-+l- 96.3%

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

      5. neg-sub0 96.3%

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

      6. associate-*l* 94.1%

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

      7. associate-*l* 94.0%

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

      8. distribute-rgt-neg-in 94.0%

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

      9. fma-def 94.1%

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

      10. *-commutative 94.1%

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

      11. distribute-rgt-neg-in 94.1%

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

      12. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 37.4%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{-56} \lor \neg \left(b \leq 2.6 \cdot 10^{-28}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 16: 47.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-25}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.3e-60)
   (* b (* a 27.0))
   (if (<= b 3e-25) (* x 2.0) (* 27.0 (* a b)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e-60) {
		tmp = b * (a * 27.0);
	} else if (b <= 3e-25) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.3d-60)) then
        tmp = b * (a * 27.0d0)
    else if (b <= 3d-25) then
        tmp = x * 2.0d0
    else
        tmp = 27.0d0 * (a * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e-60) {
		tmp = b * (a * 27.0);
	} else if (b <= 3e-25) {
		tmp = x * 2.0;
	} else {
		tmp = 27.0 * (a * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.3e-60:
		tmp = b * (a * 27.0)
	elif b <= 3e-25:
		tmp = x * 2.0
	else:
		tmp = 27.0 * (a * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.3e-60)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (b <= 3e-25)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(27.0 * Float64(a * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.3e-60)
		tmp = b * (a * 27.0);
	elseif (b <= 3e-25)
		tmp = x * 2.0;
	else
		tmp = 27.0 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.3e-60], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-25], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2999999999999999e-60

   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 x around 0 78.0%

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

      1. expm1-log1p-u 54.4%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right)} \]

      2. expm1-udef 53.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} - 1\right)} \]

      3. associate-*r* 53.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(9 \cdot y\right) \cdot \left(t \cdot z\right)}\right)} - 1\right) \]

      4. *-commutative 53.7%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   4. Applied egg-rr 53.7%

      \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   5. Step-by-step derivation

      1. expm1-def 54.4%

         \[\leadsto 27 \cdot \left(a \cdot b\right) - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*l* 74.1%

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

      5. *-commutative 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in a around inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. *-commutative 55.9%

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

   9. Simplified 55.9%

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

   if -1.2999999999999999e-60 < b < 2.9999999999999998e-25

   1. Initial program 96.3%

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

      1. associate-+l- 96.3%

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

      2. fma-neg 96.3%

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

      3. neg-sub0 96.3%

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

      4. associate-+l- 96.3%

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

      5. neg-sub0 96.3%

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

      6. associate-*l* 94.1%

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

      7. associate-*l* 94.0%

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

      8. distribute-rgt-neg-in 94.0%

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

      9. fma-def 94.1%

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

      10. *-commutative 94.1%

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

      11. distribute-rgt-neg-in 94.1%

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

      12. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 37.4%

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

   if 2.9999999999999998e-25 < b

   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 y around 0 92.8%

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

      1. *-commutative 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*r* 92.8%

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

      4. *-commutative 92.8%

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

      5. *-commutative 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in a around inf 53.1%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-25}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 17: 30.5% 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 94.7%

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

   1. associate-+l- 94.7%

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

   2. fma-neg 94.7%

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

   3. neg-sub0 94.7%

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

   4. associate-+l- 94.7%

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

   5. neg-sub0 94.7%

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

   6. associate-*l* 94.6%

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

   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 95.4%

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

   10. *-commutative 95.4%

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

   11. distribute-rgt-neg-in 95.4%

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

   12. metadata-eval 95.4%

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

3. Simplified 95.4%

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

4. Taylor expanded in x around inf 27.3%

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

5. Final simplification 27.3%

   \[\leadsto x \cdot 2 \]

Developer target: 95.0% 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 2023181 
(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)))