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

Percentage Accurate: 95.3% → 98.9%

Time: 12.7s

Alternatives: 14

Speedup: 0.9×

• 26.8% 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: 95.3% 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: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(z \cdot y\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3e-12)
   (fma a (* 27.0 b) (- (* x 2.0) (* (* y (* z t)) 9.0)))
   (fma x 2.0 (fma t (* (* z y) -9.0) (* b (* a 27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3e-12) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - ((y * (z * t)) * 9.0)));
	} else {
		tmp = fma(x, 2.0, fma(t, ((z * y) * -9.0), (b * (a * 27.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3e-12)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(Float64(y * Float64(z * t)) * 9.0)));
	else
		tmp = fma(x, 2.0, fma(t, Float64(Float64(z * y) * -9.0), Float64(b * Float64(a * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3e-12], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(t * N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.0000000000000001e-12

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. associate-*l* 94.4%

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

      3. fma-def 94.9%

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

      4. associate-*l* 96.0%

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

      5. *-commutative 96.0%

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

      6. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   if 3.0000000000000001e-12 < z

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. fma-neg 89.1%

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

      3. neg-sub0 89.1%

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

      4. associate-+l- 89.1%

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

      5. neg-sub0 89.1%

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

      6. *-commutative 89.1%

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

      7. distribute-rgt-neg-in 89.1%

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

      8. fma-def 90.7%

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

      9. *-commutative 90.7%

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

      10. associate-*r* 90.7%

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

      11. distribute-rgt-neg-in 90.7%

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

      12. *-commutative 90.7%

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

      13. metadata-eval 90.7%

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

   3. Simplified 90.7%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(z \cdot y\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9 + a \cdot \left(b \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1e-12)
   (fma a (* 27.0 b) (- (* x 2.0) (* (* y (* z t)) 9.0)))
   (- (* x 2.0) (+ (* (* t (* z y)) 9.0) (* a (* b -27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1e-12) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - ((y * (z * t)) * 9.0)));
	} else {
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1e-12)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(Float64(y * Float64(z * t)) * 9.0)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(Float64(t * Float64(z * y)) * 9.0) + Float64(a * Float64(b * -27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1e-12], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] + N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.9999999999999998e-13

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. associate-*l* 94.4%

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

      3. fma-def 94.9%

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

      4. associate-*l* 96.0%

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

      5. *-commutative 96.0%

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

      6. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   if 9.9999999999999998e-13 < z

   1. Initial program 89.1%

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

      1. associate-+l- 89.1%

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

      2. sub-neg 89.1%

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

      3. neg-mul-1 89.1%

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

      4. metadata-eval 89.1%

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

      5. metadata-eval 89.1%

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

      6. cancel-sign-sub-inv 89.1%

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

      7. metadata-eval 89.1%

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

      8. *-lft-identity 89.1%

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

      9. associate-*l* 87.8%

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

      10. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

      1. sub-neg 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-*r* 87.8%

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

      4. associate-*r* 89.2%

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

      5. distribute-rgt-neg-in 89.2%

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

      6. *-commutative 89.2%

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

      7. distribute-rgt-neg-in 89.2%

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

      8. metadata-eval 89.2%

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

   5. Applied egg-rr 89.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9 + a \cdot \left(b \cdot -27\right)\right)\\ \end{array} \]

Alternative 3: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \end{array} \end{array} \]

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 (* z (* y 9.0))))
   (if (<= t_1 5e+275)
     (+ (* b (* a 27.0)) (- (* x 2.0) (* t t_1)))
     (- (* 27.0 (* a b)) (* (* y (* z t)) 9.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 5e+275) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * t_1));
	} else {
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y * 9.0d0)
    if (t_1 <= 5d+275) then
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * t_1))
    else
        tmp = (27.0d0 * (a * b)) - ((y * (z * t)) * 9.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y * 9.0);
	double tmp;
	if (t_1 <= 5e+275) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * t_1));
	} else {
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (y * 9.0)
	tmp = 0
	if t_1 <= 5e+275:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * t_1))
	else:
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= 5e+275)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * t_1)));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(Float64(y * Float64(z * t)) * 9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y * 9.0);
	tmp = 0.0;
	if (t_1 <= 5e+275)
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * t_1));
	else
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+275], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 5.0000000000000003e275

   1. Initial program 95.8%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 y 9) z)

   1. Initial program 49.7%

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

   2. Taylor expanded in x around 0 82.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \end{array} \]

Alternative 4: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x \cdot 2 - \left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9 + a \cdot \left(b \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \end{array} \end{array} \]

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 (* y 9.0)) 5e+275)
   (- (* x 2.0) (+ (* (* t (* z y)) 9.0) (* a (* b -27.0))))
   (- (* 27.0 (* a b)) (* (* y (* z t)) 9.0))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 5e+275) {
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	} else {
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z * (y * 9.0d0)) <= 5d+275) then
        tmp = (x * 2.0d0) - (((t * (z * y)) * 9.0d0) + (a * (b * (-27.0d0))))
    else
        tmp = (27.0d0 * (a * b)) - ((y * (z * t)) * 9.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * (y * 9.0)) <= 5e+275) {
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	} else {
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z * (y * 9.0)) <= 5e+275:
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)))
	else:
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * Float64(y * 9.0)) <= 5e+275)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(Float64(t * Float64(z * y)) * 9.0) + Float64(a * Float64(b * -27.0))));
	else
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(Float64(y * Float64(z * t)) * 9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z * (y * 9.0)) <= 5e+275)
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	else
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision], 5e+275], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] + N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 5.0000000000000003e275

   1. Initial program 95.8%

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

      1. associate-+l- 95.8%

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

      2. sub-neg 95.8%

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

      3. neg-mul-1 95.8%

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

      4. metadata-eval 95.8%

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

      5. metadata-eval 95.8%

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

      6. cancel-sign-sub-inv 95.8%

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

      7. metadata-eval 95.8%

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

      8. *-lft-identity 95.8%

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

      9. associate-*l* 93.6%

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

      10. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

      1. sub-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*r* 93.6%

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

      4. associate-*r* 96.2%

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

      5. distribute-rgt-neg-in 96.2%

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

      6. *-commutative 96.2%

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

      7. distribute-rgt-neg-in 96.2%

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

      8. metadata-eval 96.2%

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

   5. Applied egg-rr 96.2%

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

   if 5.0000000000000003e275 < (*.f64 (*.f64 y 9) z)

   1. Initial program 49.7%

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

   2. Taylor expanded in x around 0 82.6%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot 9\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x \cdot 2 - \left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9 + a \cdot \left(b \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 0.0004:\\ \;\;\;\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9 + a \cdot \left(b \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 0.0004)
   (- (* x 2.0) (- (* (* y 9.0) (* z t)) (* a (* 27.0 b))))
   (- (* x 2.0) (+ (* (* t (* z y)) 9.0) (* a (* b -27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 0.0004) {
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)));
	} else {
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 0.0004d0) then
        tmp = (x * 2.0d0) - (((y * 9.0d0) * (z * t)) - (a * (27.0d0 * b)))
    else
        tmp = (x * 2.0d0) - (((t * (z * y)) * 9.0d0) + (a * (b * (-27.0d0))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 0.0004) {
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)));
	} else {
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 0.0004:
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)))
	else:
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 0.0004)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * Float64(z * t)) - Float64(a * Float64(27.0 * b))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(Float64(t * Float64(z * y)) * 9.0) + Float64(a * Float64(b * -27.0))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 0.0004)
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)));
	else
		tmp = (x * 2.0) - (((t * (z * y)) * 9.0) + (a * (b * -27.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 0.0004], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] + N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.00000000000000019e-4

   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. Step-by-step derivation

      1. associate-+l- 94.0%

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

      2. sub-neg 94.0%

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

      3. neg-mul-1 94.0%

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

      4. metadata-eval 94.0%

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

      5. metadata-eval 94.0%

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

      6. cancel-sign-sub-inv 94.0%

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

      7. metadata-eval 94.0%

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

      8. *-lft-identity 94.0%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 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%

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

   if 4.00000000000000019e-4 < z

   1. Initial program 88.9%

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

      1. associate-+l- 88.9%

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

      2. sub-neg 88.9%

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

      3. neg-mul-1 88.9%

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

      4. metadata-eval 88.9%

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

      5. metadata-eval 88.9%

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

      6. cancel-sign-sub-inv 88.9%

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

      7. metadata-eval 88.9%

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

      8. *-lft-identity 88.9%

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

      9. associate-*l* 87.6%

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

      10. associate-*l* 87.6%

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

   3. Simplified 87.6%

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

      1. sub-neg 87.6%

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

      2. *-commutative 87.6%

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

      3. associate-*r* 87.6%

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

      4. associate-*r* 89.0%

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

      5. distribute-rgt-neg-in 89.0%

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

      6. *-commutative 89.0%

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

      7. distribute-rgt-neg-in 89.0%

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

      8. metadata-eval 89.0%

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

   5. Applied egg-rr 89.0%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.0004:\\ \;\;\;\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(\left(t \cdot \left(z \cdot y\right)\right) \cdot 9 + a \cdot \left(b \cdot -27\right)\right)\\ \end{array} \]

Alternative 6: 47.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-290}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-227}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 100000:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -9.0 (* y (* z t)))))
   (if (<= b -1.08e+18)
     (* a (* 27.0 b))
     (if (<= b 9e-290)
       (* x 2.0)
       (if (<= b 1.75e-255)
         t_1
         (if (<= b 1.35e-227)
           (* x 2.0)
           (if (<= b 2.5e-171)
             t_1
             (if (<= b 100000.0) (* 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 t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (b <= -1.08e+18) {
		tmp = a * (27.0 * b);
	} else if (b <= 9e-290) {
		tmp = x * 2.0;
	} else if (b <= 1.75e-255) {
		tmp = t_1;
	} else if (b <= 1.35e-227) {
		tmp = x * 2.0;
	} else if (b <= 2.5e-171) {
		tmp = t_1;
	} else if (b <= 100000.0) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    if (b <= (-1.08d+18)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 9d-290) then
        tmp = x * 2.0d0
    else if (b <= 1.75d-255) then
        tmp = t_1
    else if (b <= 1.35d-227) then
        tmp = x * 2.0d0
    else if (b <= 2.5d-171) then
        tmp = t_1
    else if (b <= 100000.0d0) 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 t_1 = -9.0 * (y * (z * t));
	double tmp;
	if (b <= -1.08e+18) {
		tmp = a * (27.0 * b);
	} else if (b <= 9e-290) {
		tmp = x * 2.0;
	} else if (b <= 1.75e-255) {
		tmp = t_1;
	} else if (b <= 1.35e-227) {
		tmp = x * 2.0;
	} else if (b <= 2.5e-171) {
		tmp = t_1;
	} else if (b <= 100000.0) {
		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):
	t_1 = -9.0 * (y * (z * t))
	tmp = 0
	if b <= -1.08e+18:
		tmp = a * (27.0 * b)
	elif b <= 9e-290:
		tmp = x * 2.0
	elif b <= 1.75e-255:
		tmp = t_1
	elif b <= 1.35e-227:
		tmp = x * 2.0
	elif b <= 2.5e-171:
		tmp = t_1
	elif b <= 100000.0:
		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)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (b <= -1.08e+18)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 9e-290)
		tmp = Float64(x * 2.0);
	elseif (b <= 1.75e-255)
		tmp = t_1;
	elseif (b <= 1.35e-227)
		tmp = Float64(x * 2.0);
	elseif (b <= 2.5e-171)
		tmp = t_1;
	elseif (b <= 100000.0)
		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)
	t_1 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (b <= -1.08e+18)
		tmp = a * (27.0 * b);
	elseif (b <= 9e-290)
		tmp = x * 2.0;
	elseif (b <= 1.75e-255)
		tmp = t_1;
	elseif (b <= 1.35e-227)
		tmp = x * 2.0;
	elseif (b <= 2.5e-171)
		tmp = t_1;
	elseif (b <= 100000.0)
		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_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.08e+18], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-290], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1.75e-255], t$95$1, If[LessEqual[b, 1.35e-227], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 2.5e-171], t$95$1, If[LessEqual[b, 100000.0], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.08e18

   1. Initial program 92.8%

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

      1. associate-+l- 92.8%

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

      2. sub-neg 92.8%

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

      3. neg-mul-1 92.8%

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

      4. metadata-eval 92.8%

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

      5. metadata-eval 92.8%

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

      6. cancel-sign-sub-inv 92.8%

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

      7. metadata-eval 92.8%

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

      8. *-lft-identity 92.8%

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

      9. associate-*l* 86.5%

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

      10. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-*r* 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in x around 0 43.5%

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

      1. *-commutative 43.5%

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

      2. associate-*l* 43.5%

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

   9. Simplified 43.5%

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

   if -1.08e18 < b < 9e-290 or 1.74999999999999989e-255 < b < 1.35e-227 or 2.49999999999999996e-171 < b < 1e5

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 55.6%

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

   if 9e-290 < b < 1.74999999999999989e-255 or 1.35e-227 < b < 2.49999999999999996e-171

   1. Initial program 89.4%

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

   2. Taylor expanded in y around inf 59.9%

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

   if 1e5 < b

   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. Step-by-step derivation

      1. associate-+l- 91.8%

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

      2. sub-neg 91.8%

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

      3. neg-mul-1 91.8%

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

      4. metadata-eval 91.8%

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

      5. metadata-eval 91.8%

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

      6. cancel-sign-sub-inv 91.8%

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

      7. metadata-eval 91.8%

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

      8. *-lft-identity 91.8%

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

      9. associate-*l* 98.2%

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

      10. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*r* 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in x around 0 58.8%

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

      1. *-commutative 58.8%

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

   9. Simplified 58.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-290}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-227}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-171}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 100000:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-37} \lor \neg \left(z \leq 6.3 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot 2 + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-37) (not (<= z 6.3e-62)))
   (+ (* x 2.0) (* z (* -9.0 (* y t))))
   (- (* x 2.0) (* a (* b -27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-37) || !(z <= 6.3e-62)) {
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)));
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3d-37)) .or. (.not. (z <= 6.3d-62))) then
        tmp = (x * 2.0d0) + (z * ((-9.0d0) * (y * t)))
    else
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-37) || !(z <= 6.3e-62)) {
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)));
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e-37) or not (z <= 6.3e-62):
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)))
	else:
		tmp = (x * 2.0) - (a * (b * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e-37) || !(z <= 6.3e-62))
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(-9.0 * Float64(y * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e-37) || ~((z <= 6.3e-62)))
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)));
	else
		tmp = (x * 2.0) - (a * (b * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e-37], N[Not[LessEqual[z, 6.3e-62]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e-37 or 6.2999999999999997e-62 < z

   1. Initial program 87.5%

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

      1. associate-+l- 87.5%

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

      2. sub-neg 87.5%

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

      3. neg-mul-1 87.5%

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

      4. metadata-eval 87.5%

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

      5. metadata-eval 87.5%

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

      6. cancel-sign-sub-inv 87.5%

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

      7. metadata-eval 87.5%

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

      8. *-lft-identity 87.5%

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

      9. associate-*l* 89.7%

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

      10. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

      1. sub-neg 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-*r* 89.7%

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

      4. associate-*r* 88.2%

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

      5. distribute-rgt-neg-in 88.2%

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

      6. *-commutative 88.2%

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

      7. distribute-rgt-neg-in 88.2%

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

      8. metadata-eval 88.2%

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

   5. Applied egg-rr 88.2%

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

   6. Taylor expanded in y around inf 70.3%

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

      1. add-sqr-sqrt 41.2%

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

      2. sqrt-unprod 47.2%

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

      3. swap-sqr 47.2%

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

      4. metadata-eval 47.2%

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

      5. metadata-eval 47.2%

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

      6. swap-sqr 47.2%

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

      7. *-commutative 47.2%

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

      8. *-commutative 47.2%

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

      9. associate-*r* 47.2%

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

      10. associate-*r* 47.2%

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

      11. associate-*r* 47.9%

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

      12. associate-*r* 47.9%

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

      13. sqrt-unprod 17.0%

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

      14. add-sqr-sqrt 29.1%

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

      15. associate-*r* 29.1%

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

      16. associate-*r* 28.4%

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

      17. metadata-eval 28.4%

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

      18. distribute-rgt-neg-in 28.4%

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

      19. *-commutative 28.4%

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

      20. add-log-exp 23.2%

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

   8. Applied egg-rr 39.6%

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

      1. log-rec 39.6%

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

      2. log-pow 32.7%

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

      3. distribute-rgt-neg-in 32.7%

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

      4. log-pow 32.7%

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

      5. rem-log-exp 76.5%

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

   10. Simplified 76.5%

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

       1. sub-neg 76.5%

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

       2. +-commutative 76.5%

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

       3. distribute-rgt-neg-out 76.5%

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

       4. remove-double-neg 76.5%

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

       5. associate-*r* 76.5%

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

   12. Applied egg-rr 76.5%

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

   if -3e-37 < z < 6.2999999999999997e-62

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*r* 79.9%

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

   6. Simplified 79.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-37} \lor \neg \left(z \leq 6.3 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot 2 + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 8: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-34}:\\ \;\;\;\;x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.32e-34)
   (- (* x 2.0) (* (* y (* z t)) 9.0))
   (if (<= z 3.7e-62)
     (- (* x 2.0) (* a (* b -27.0)))
     (+ (* x 2.0) (* z (* -9.0 (* y t)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.32e-34) {
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0);
	} else if (z <= 3.7e-62) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.32d-34)) then
        tmp = (x * 2.0d0) - ((y * (z * t)) * 9.0d0)
    else if (z <= 3.7d-62) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + (z * ((-9.0d0) * (y * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.32e-34) {
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0);
	} else if (z <= 3.7e-62) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.32e-34:
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0)
	elif z <= 3.7e-62:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.32e-34)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(y * Float64(z * t)) * 9.0));
	elseif (z <= 3.7e-62)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(-9.0 * Float64(y * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.32e-34)
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0);
	elseif (z <= 3.7e-62)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (x * 2.0) + (z * (-9.0 * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.32e-34], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-62], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32e-34

   1. Initial program 84.6%

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

   2. Taylor expanded in a around 0 69.6%

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

   if -1.32e-34 < z < 3.6999999999999998e-62

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*r* 80.1%

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

   6. Simplified 80.1%

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

   if 3.6999999999999998e-62 < z

   1. Initial program 90.4%

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

      1. associate-+l- 90.4%

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

      2. sub-neg 90.4%

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

      3. neg-mul-1 90.4%

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

      4. metadata-eval 90.4%

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

      5. metadata-eval 90.4%

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

      6. cancel-sign-sub-inv 90.4%

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

      7. metadata-eval 90.4%

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

      8. *-lft-identity 90.4%

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

      9. associate-*l* 89.3%

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

      10. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

      1. sub-neg 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 89.3%

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

      4. associate-*r* 90.5%

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

      5. distribute-rgt-neg-in 90.5%

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

      6. *-commutative 90.5%

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

      7. distribute-rgt-neg-in 90.5%

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

      8. metadata-eval 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in y around inf 70.6%

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

      1. add-sqr-sqrt 45.3%

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

      2. sqrt-unprod 48.8%

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

      3. swap-sqr 48.8%

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

      4. metadata-eval 48.8%

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

      5. metadata-eval 48.8%

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

      6. swap-sqr 48.8%

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

      7. *-commutative 48.8%

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

      8. *-commutative 48.8%

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

      9. associate-*r* 48.8%

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

      10. associate-*r* 48.8%

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

      11. associate-*r* 50.1%

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

      12. associate-*r* 50.1%

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

      13. sqrt-unprod 14.6%

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

      14. add-sqr-sqrt 26.2%

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

      15. associate-*r* 26.2%

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

      16. associate-*r* 26.0%

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

      17. metadata-eval 26.0%

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

      18. distribute-rgt-neg-in 26.0%

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

      19. *-commutative 26.0%

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

      20. add-log-exp 18.7%

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

   8. Applied egg-rr 41.4%

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

      1. log-rec 41.4%

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

      2. log-pow 35.7%

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

      3. distribute-rgt-neg-in 35.7%

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

      4. log-pow 35.7%

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

      5. rem-log-exp 77.0%

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

   10. Simplified 77.0%

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

       1. sub-neg 77.0%

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

       2. +-commutative 77.0%

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

       3. distribute-rgt-neg-out 77.0%

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

       4. remove-double-neg 77.0%

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

       5. associate-*r* 77.0%

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

   12. Applied egg-rr 77.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-34}:\\ \;\;\;\;x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(-9 \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \end{array} \end{array} \]

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 -2.35e-35)
   (- (* x 2.0) (* (* y (* z t)) 9.0))
   (if (<= z 4.5e-62)
     (- (* x 2.0) (* a (* b -27.0)))
     (+ (* x 2.0) (* (* y t) (* z -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e-35) {
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0);
	} else if (z <= 4.5e-62) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.35d-35)) then
        tmp = (x * 2.0d0) - ((y * (z * t)) * 9.0d0)
    else if (z <= 4.5d-62) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((y * t) * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e-35) {
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0);
	} else if (z <= 4.5e-62) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.35e-35:
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0)
	elif z <= 4.5e-62:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (x * 2.0) + ((y * t) * (z * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.35e-35)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(y * Float64(z * t)) * 9.0));
	elseif (z <= 4.5e-62)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * t) * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.35e-35)
		tmp = (x * 2.0) - ((y * (z * t)) * 9.0);
	elseif (z <= 4.5e-62)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.35e-35], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-62], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35e-35

   1. Initial program 84.6%

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

   2. Taylor expanded in a around 0 69.6%

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

   if -2.35e-35 < z < 4.50000000000000018e-62

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*r* 80.1%

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

   6. Simplified 80.1%

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

   if 4.50000000000000018e-62 < z

   1. Initial program 90.4%

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

      1. associate-+l- 90.4%

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

      2. sub-neg 90.4%

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

      3. neg-mul-1 90.4%

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

      4. metadata-eval 90.4%

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

      5. metadata-eval 90.4%

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

      6. cancel-sign-sub-inv 90.4%

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

      7. metadata-eval 90.4%

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

      8. *-lft-identity 90.4%

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

      9. associate-*l* 89.3%

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

      10. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

      1. sub-neg 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 89.3%

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

      4. associate-*r* 90.5%

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

      5. distribute-rgt-neg-in 90.5%

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

      6. *-commutative 90.5%

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

      7. distribute-rgt-neg-in 90.5%

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

      8. metadata-eval 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in y around inf 70.6%

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

      1. add-sqr-sqrt 45.3%

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

      2. sqrt-unprod 48.8%

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

      3. swap-sqr 48.8%

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

      4. metadata-eval 48.8%

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

      5. metadata-eval 48.8%

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

      6. swap-sqr 48.8%

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

      7. *-commutative 48.8%

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

      8. *-commutative 48.8%

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

      9. associate-*r* 48.8%

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

      10. associate-*r* 48.8%

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

      11. associate-*r* 50.1%

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

      12. associate-*r* 50.1%

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

      13. sqrt-unprod 14.6%

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

      14. add-sqr-sqrt 26.2%

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

      15. associate-*r* 26.2%

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

      16. associate-*r* 26.0%

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

      17. metadata-eval 26.0%

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

      18. distribute-rgt-neg-in 26.0%

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

      19. *-commutative 26.0%

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

      20. add-log-exp 18.7%

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

   8. Applied egg-rr 41.4%

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

      1. log-rec 41.4%

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

      2. log-pow 35.7%

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

      3. distribute-rgt-neg-in 35.7%

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

      4. log-pow 35.7%

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

      5. rem-log-exp 77.0%

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

   10. Simplified 77.0%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;x \cdot 2 - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \end{array} \]

Alternative 10: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-74}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-61}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \end{array} \end{array} \]

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 -3.9e-74)
   (- (* 27.0 (* a b)) (* (* y (* z t)) 9.0))
   (if (<= z 1.12e-61)
     (- (* x 2.0) (* a (* b -27.0)))
     (+ (* x 2.0) (* (* y t) (* z -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e-74) {
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	} else if (z <= 1.12e-61) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.9d-74)) then
        tmp = (27.0d0 * (a * b)) - ((y * (z * t)) * 9.0d0)
    else if (z <= 1.12d-61) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((y * t) * (z * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e-74) {
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	} else if (z <= 1.12e-61) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.9e-74:
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0)
	elif z <= 1.12e-61:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (x * 2.0) + ((y * t) * (z * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.9e-74)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(Float64(y * Float64(z * t)) * 9.0));
	elseif (z <= 1.12e-61)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * t) * Float64(z * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.9e-74)
		tmp = (27.0 * (a * b)) - ((y * (z * t)) * 9.0);
	elseif (z <= 1.12e-61)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (x * 2.0) + ((y * t) * (z * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.9e-74], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-61], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9000000000000001e-74

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0 60.8%

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

   if -3.9000000000000001e-74 < z < 1.12000000000000001e-61

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*r* 79.8%

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

   6. Simplified 79.8%

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

   if 1.12000000000000001e-61 < z

   1. Initial program 90.3%

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

      1. associate-+l- 90.3%

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

      2. sub-neg 90.3%

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

      3. neg-mul-1 90.3%

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

      4. metadata-eval 90.3%

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

      5. metadata-eval 90.3%

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

      6. cancel-sign-sub-inv 90.3%

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

      7. metadata-eval 90.3%

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

      8. *-lft-identity 90.3%

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

      9. associate-*l* 89.2%

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

      10. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

      1. sub-neg 89.2%

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

      2. *-commutative 89.2%

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

      3. associate-*r* 89.1%

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

      4. associate-*r* 90.4%

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

      5. distribute-rgt-neg-in 90.4%

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

      6. *-commutative 90.4%

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

      7. distribute-rgt-neg-in 90.4%

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

      8. metadata-eval 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in y around inf 70.1%

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

      1. add-sqr-sqrt 45.9%

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

      2. sqrt-unprod 48.1%

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

      3. swap-sqr 48.0%

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

      4. metadata-eval 48.0%

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

      5. metadata-eval 48.0%

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

      6. swap-sqr 48.1%

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

      7. *-commutative 48.1%

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

      8. *-commutative 48.1%

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

      9. associate-*r* 48.1%

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

      10. associate-*r* 48.1%

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

      11. associate-*r* 49.4%

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

      12. associate-*r* 49.4%

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

      13. sqrt-unprod 13.4%

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

      14. add-sqr-sqrt 25.2%

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

      15. associate-*r* 25.2%

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

      16. associate-*r* 25.0%

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

      17. metadata-eval 25.0%

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

      18. distribute-rgt-neg-in 25.0%

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

      19. *-commutative 25.0%

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

      20. add-log-exp 17.6%

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

   8. Applied egg-rr 40.5%

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

      1. log-rec 40.5%

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

      2. log-pow 34.8%

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

      3. distribute-rgt-neg-in 34.8%

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

      4. log-pow 34.8%

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

      5. rem-log-exp 76.7%

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

   10. Simplified 76.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-74}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - \left(y \cdot \left(z \cdot t\right)\right) \cdot 9\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-61}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \end{array} \]

Alternative 11: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 210000000:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot y\right) \cdot -9\right)\\ \end{array} \end{array} \]

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 -3.9e+64)
   (* y (* -9.0 (* z t)))
   (if (<= z 210000000.0)
     (- (* x 2.0) (* (* a b) -27.0))
     (* t (* (* z y) -9.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e+64) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 210000000.0) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = t * ((z * y) * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.9d+64)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= 210000000.0d0) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = t * ((z * y) * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e+64) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 210000000.0) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = t * ((z * y) * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.9e+64:
		tmp = y * (-9.0 * (z * t))
	elif z <= 210000000.0:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = t * ((z * y) * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.9e+64)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= 210000000.0)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(t * Float64(Float64(z * y) * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.9e+64)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= 210000000.0)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = t * ((z * y) * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.9e+64], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 210000000.0], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999998e64

   1. Initial program 79.6%

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

   2. Taylor expanded in y around inf 43.4%

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

      1. *-commutative 43.4%

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

      2. *-commutative 43.4%

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

      3. associate-*l* 43.4%

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

      4. *-commutative 43.4%

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

      5. *-commutative 43.4%

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

   4. Simplified 43.4%

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

   if -3.8999999999999998e64 < z < 2.1e8

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 99.2%

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

      10. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 78.2%

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

   if 2.1e8 < z

   1. Initial program 88.6%

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

   2. Taylor expanded in y around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

      3. associate-*l* 49.9%

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

      4. *-commutative 49.9%

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

      5. *-commutative 49.9%

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

   4. Simplified 49.9%

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

   5. Taylor expanded in y around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. associate-*r* 53.1%

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

      3. associate-*r* 53.1%

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

      4. metadata-eval 53.1%

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

      5. distribute-lft-neg-in 53.1%

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

      6. associate-*l* 53.1%

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

      7. *-commutative 53.1%

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

      8. associate-*l* 53.1%

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

      9. distribute-lft-neg-in 53.1%

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

      10. metadata-eval 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 210000000:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot y\right) \cdot -9\right)\\ \end{array} \]

Alternative 12: 47.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+17} \lor \neg \left(b \leq 0.0004\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 -4.1e+17) (not (<= b 0.0004))) (* a (* 27.0 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 <= -4.1e+17) || !(b <= 0.0004)) {
		tmp = a * (27.0 * 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 <= (-4.1d+17)) .or. (.not. (b <= 0.0004d0))) then
        tmp = a * (27.0d0 * 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 <= -4.1e+17) || !(b <= 0.0004)) {
		tmp = a * (27.0 * 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 <= -4.1e+17) or not (b <= 0.0004):
		tmp = a * (27.0 * 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 <= -4.1e+17) || !(b <= 0.0004))
		tmp = Float64(a * Float64(27.0 * 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 <= -4.1e+17) || ~((b <= 0.0004)))
		tmp = a * (27.0 * 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, -4.1e+17], N[Not[LessEqual[b, 0.0004]], $MachinePrecision]], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.1e17 or 4.00000000000000019e-4 < b

   1. Initial program 92.4%

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

      1. associate-+l- 92.4%

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

      2. sub-neg 92.4%

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

      3. neg-mul-1 92.4%

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

      4. metadata-eval 92.4%

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

      5. metadata-eval 92.4%

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

      6. cancel-sign-sub-inv 92.4%

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

      7. metadata-eval 92.4%

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

      8. *-lft-identity 92.4%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*r* 69.5%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in x around 0 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*l* 50.4%

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

   9. Simplified 50.4%

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

   if -4.1e17 < b < 4.00000000000000019e-4

   1. Initial program 93.2%

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

   2. Taylor expanded in x around inf 50.4%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+17} \lor \neg \left(b \leq 0.0004\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 13: 47.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 0.00115:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

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 -4e+17)
   (* a (* 27.0 b))
   (if (<= b 0.00115) (* 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 <= -4e+17) {
		tmp = a * (27.0 * b);
	} else if (b <= 0.00115) {
		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 <= (-4d+17)) then
        tmp = a * (27.0d0 * b)
    else if (b <= 0.00115d0) 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 <= -4e+17) {
		tmp = a * (27.0 * b);
	} else if (b <= 0.00115) {
		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 <= -4e+17:
		tmp = a * (27.0 * b)
	elif b <= 0.00115:
		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 <= -4e+17)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (b <= 0.00115)
		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 <= -4e+17)
		tmp = a * (27.0 * b);
	elseif (b <= 0.00115)
		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, -4e+17], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00115], N[(x * 2.0), $MachinePrecision], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e17

   1. Initial program 92.8%

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

      1. associate-+l- 92.8%

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

      2. sub-neg 92.8%

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

      3. neg-mul-1 92.8%

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

      4. metadata-eval 92.8%

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

      5. metadata-eval 92.8%

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

      6. cancel-sign-sub-inv 92.8%

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

      7. metadata-eval 92.8%

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

      8. *-lft-identity 92.8%

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

      9. associate-*l* 86.5%

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

      10. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-*r* 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in x around 0 43.5%

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

      1. *-commutative 43.5%

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

      2. associate-*l* 43.5%

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

   9. Simplified 43.5%

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

   if -4e17 < b < 0.00115

   1. Initial program 93.2%

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

   2. Taylor expanded in x around inf 50.4%

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

   if 0.00115 < b

   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. Step-by-step derivation

      1. associate-+l- 91.8%

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

      2. sub-neg 91.8%

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

      3. neg-mul-1 91.8%

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

      4. metadata-eval 91.8%

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

      5. metadata-eval 91.8%

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

      6. cancel-sign-sub-inv 91.8%

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

      7. metadata-eval 91.8%

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

      8. *-lft-identity 91.8%

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

      9. associate-*l* 98.2%

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

      10. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*r* 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in x around 0 58.8%

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

      1. *-commutative 58.8%

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

   9. Simplified 58.8%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;b \leq 0.00115:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 14: 30.7% 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 92.8%

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

2. Taylor expanded in x around inf 35.0%

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

3. Final simplification 35.0%

   \[\leadsto x \cdot 2 \]

Developer target: 94.9% 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 2023196 
(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)))