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

Percentage Accurate: 95.5% → 98.2%

Time: 16.3s

Alternatives: 13

Speedup: 1.0×

• 27.8% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;z \leq -5 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(z, y \cdot \left(t \cdot -9\right), t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= z -5e-36)
     (fma x 2.0 (fma z (* y (* t -9.0)) t_1))
     (+ t_1 (- (* x 2.0) (* t (* z (* y 9.0))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (z <= -5e-36) {
		tmp = fma(x, 2.0, fma(z, (y * (t * -9.0)), t_1));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (z * (y * 9.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (z <= -5e-36)
		tmp = fma(x, 2.0, fma(z, Float64(y * Float64(t * -9.0)), t_1));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[z, -5e-36], N[(x * 2.0 + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000004e-36

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-+r- 90.5%

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

      3. cancel-sign-sub-inv 90.5%

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

      4. *-commutative 90.5%

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

      5. distribute-rgt-neg-out 90.5%

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

      6. associate-*r* 95.7%

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

      7. *-commutative 95.7%

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

      8. distribute-rgt-neg-in 95.7%

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

      9. associate-+r+ 95.7%

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

      10. sub-neg 95.7%

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

      11. +-commutative 95.7%

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

      12. associate-+l- 95.7%

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

      13. fma-neg 95.7%

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

      14. associate-*l* 89.3%

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

      15. fma-neg 92.1%

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

      16. *-commutative 92.1%

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

      17. fma-neg 89.3%

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

   3. Simplified 98.5%

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

   if -5.00000000000000004e-36 < z

   1. Initial program 97.2%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(z, y \cdot \left(t \cdot -9\right), \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-54}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2e-54)
   (+ (- (* x 2.0) (* (* y 9.0) (* z t))) (* a (* 27.0 b)))
   (+ (* (* a 27.0) b) (- (* x 2.0) (* t (* z (* y 9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e-54) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (z * (y * 9.0))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t 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 <= 2d-54) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (z * t))) + (a * (27.0d0 * b))
    else
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (t * (z * (y * 9.0d0))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e-54) {
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (z * (y * 9.0))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2e-54:
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b))
	else:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (z * (y * 9.0))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2e-54)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(z * t))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(y * 9.0)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2e-54)
		tmp = ((x * 2.0) - ((y * 9.0) * (z * t))) + (a * (27.0 * b));
	else
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2e-54], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.0000000000000001e-54

   1. Initial program 94.3%

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

      1. sub-neg 94.3%

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

      2. distribute-lft-neg-in 94.3%

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

      3. associate-*l* 94.9%

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

      4. *-commutative 94.9%

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

      5. *-commutative 94.9%

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

      6. cancel-sign-sub-inv 94.9%

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

      7. *-commutative 94.9%

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

      8. *-commutative 94.9%

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

      9. associate-*l* 94.3%

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

      10. associate-*l* 94.4%

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

      11. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   if 2.0000000000000001e-54 < z

   1. Initial program 97.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-54}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(z \cdot \left(y \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 3: 47.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* -9.0 (* z y)))) (t_2 (* 27.0 (* a b))))
   (if (<= x -5.5e+102)
     (* x 2.0)
     (if (<= x -8e-158)
       t_2
       (if (<= x -5.5e-242)
         t_1
         (if (<= x 1.02e-229)
           t_2
           (if (<= x 3.5e-153) t_1 (if (<= x 2.4e-36) t_2 (* x 2.0)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (-9.0 * (z * y));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -5.5e+102) {
		tmp = x * 2.0;
	} else if (x <= -8e-158) {
		tmp = t_2;
	} else if (x <= -5.5e-242) {
		tmp = t_1;
	} else if (x <= 1.02e-229) {
		tmp = t_2;
	} else if (x <= 3.5e-153) {
		tmp = t_1;
	} else if (x <= 2.4e-36) {
		tmp = t_2;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((-9.0d0) * (z * y))
    t_2 = 27.0d0 * (a * b)
    if (x <= (-5.5d+102)) then
        tmp = x * 2.0d0
    else if (x <= (-8d-158)) then
        tmp = t_2
    else if (x <= (-5.5d-242)) then
        tmp = t_1
    else if (x <= 1.02d-229) then
        tmp = t_2
    else if (x <= 3.5d-153) then
        tmp = t_1
    else if (x <= 2.4d-36) then
        tmp = t_2
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (-9.0 * (z * y));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (x <= -5.5e+102) {
		tmp = x * 2.0;
	} else if (x <= -8e-158) {
		tmp = t_2;
	} else if (x <= -5.5e-242) {
		tmp = t_1;
	} else if (x <= 1.02e-229) {
		tmp = t_2;
	} else if (x <= 3.5e-153) {
		tmp = t_1;
	} else if (x <= 2.4e-36) {
		tmp = t_2;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = t * (-9.0 * (z * y))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if x <= -5.5e+102:
		tmp = x * 2.0
	elif x <= -8e-158:
		tmp = t_2
	elif x <= -5.5e-242:
		tmp = t_1
	elif x <= 1.02e-229:
		tmp = t_2
	elif x <= 3.5e-153:
		tmp = t_1
	elif x <= 2.4e-36:
		tmp = t_2
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-9.0 * Float64(z * y)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -5.5e+102)
		tmp = Float64(x * 2.0);
	elseif (x <= -8e-158)
		tmp = t_2;
	elseif (x <= -5.5e-242)
		tmp = t_1;
	elseif (x <= 1.02e-229)
		tmp = t_2;
	elseif (x <= 3.5e-153)
		tmp = t_1;
	elseif (x <= 2.4e-36)
		tmp = t_2;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (-9.0 * (z * y));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -5.5e+102)
		tmp = x * 2.0;
	elseif (x <= -8e-158)
		tmp = t_2;
	elseif (x <= -5.5e-242)
		tmp = t_1;
	elseif (x <= 1.02e-229)
		tmp = t_2;
	elseif (x <= 3.5e-153)
		tmp = t_1;
	elseif (x <= 2.4e-36)
		tmp = t_2;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+102], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -8e-158], t$95$2, If[LessEqual[x, -5.5e-242], t$95$1, If[LessEqual[x, 1.02e-229], t$95$2, If[LessEqual[x, 3.5e-153], t$95$1, If[LessEqual[x, 2.4e-36], t$95$2, N[(x * 2.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.49999999999999981e102 or 2.4e-36 < x

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. distribute-lft-neg-in 95.6%

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

      3. associate-*l* 95.6%

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

      4. *-commutative 95.6%

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

      5. *-commutative 95.6%

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

      6. cancel-sign-sub-inv 95.6%

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

      7. *-commutative 95.6%

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

      8. *-commutative 95.6%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 94.8%

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

      11. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 57.7%

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

   if -5.49999999999999981e102 < x < -8.00000000000000052e-158 or -5.4999999999999998e-242 < x < 1.02e-229 or 3.49999999999999981e-153 < x < 2.4e-36

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. associate-*l* 95.1%

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

      4. *-commutative 95.1%

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

      5. *-commutative 95.1%

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

      6. cancel-sign-sub-inv 95.1%

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

      7. *-commutative 95.1%

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

      8. *-commutative 95.1%

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

      9. associate-*l* 94.2%

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

      10. associate-*l* 92.5%

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

      11. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 58.6%

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

   if -8.00000000000000052e-158 < x < -5.4999999999999998e-242 or 1.02e-229 < x < 3.49999999999999981e-153

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. distribute-lft-neg-in 97.4%

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

      3. associate-*l* 97.2%

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

      4. *-commutative 97.2%

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

      5. *-commutative 97.2%

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

      6. cancel-sign-sub-inv 97.2%

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

      7. *-commutative 97.2%

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

      8. *-commutative 97.2%

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

      9. associate-*l* 97.4%

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

      10. associate-*l* 97.2%

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

      11. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. associate-*r* 58.1%

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

      3. associate-*r* 58.2%

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

      4. associate-*l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in y around 0 63.0%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

      3. associate-*r* 63.0%

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

      4. associate-*l* 62.9%

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

      5. *-commutative 62.9%

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

      6. associate-*l* 62.9%

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

   9. Simplified 62.9%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-229}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-36}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 4: 47.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+91}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= x -1.15e+91)
     (* x 2.0)
     (if (<= x -1.2e-156)
       t_1
       (if (<= x -1.45e-242)
         (* t (* y (* z -9.0)))
         (if (<= x 4.6e-229)
           t_1
           (if (<= x 5.8e-151)
             (* t (* -9.0 (* z y)))
             (if (<= x 2.4e-36) t_1 (* x 2.0)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -1.15e+91) {
		tmp = x * 2.0;
	} else if (x <= -1.2e-156) {
		tmp = t_1;
	} else if (x <= -1.45e-242) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 4.6e-229) {
		tmp = t_1;
	} else if (x <= 5.8e-151) {
		tmp = t * (-9.0 * (z * y));
	} else if (x <= 2.4e-36) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (x <= (-1.15d+91)) then
        tmp = x * 2.0d0
    else if (x <= (-1.2d-156)) then
        tmp = t_1
    else if (x <= (-1.45d-242)) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 4.6d-229) then
        tmp = t_1
    else if (x <= 5.8d-151) then
        tmp = t * ((-9.0d0) * (z * y))
    else if (x <= 2.4d-36) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -1.15e+91) {
		tmp = x * 2.0;
	} else if (x <= -1.2e-156) {
		tmp = t_1;
	} else if (x <= -1.45e-242) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 4.6e-229) {
		tmp = t_1;
	} else if (x <= 5.8e-151) {
		tmp = t * (-9.0 * (z * y));
	} else if (x <= 2.4e-36) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if x <= -1.15e+91:
		tmp = x * 2.0
	elif x <= -1.2e-156:
		tmp = t_1
	elif x <= -1.45e-242:
		tmp = t * (y * (z * -9.0))
	elif x <= 4.6e-229:
		tmp = t_1
	elif x <= 5.8e-151:
		tmp = t * (-9.0 * (z * y))
	elif x <= 2.4e-36:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -1.15e+91)
		tmp = Float64(x * 2.0);
	elseif (x <= -1.2e-156)
		tmp = t_1;
	elseif (x <= -1.45e-242)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 4.6e-229)
		tmp = t_1;
	elseif (x <= 5.8e-151)
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	elseif (x <= 2.4e-36)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -1.15e+91)
		tmp = x * 2.0;
	elseif (x <= -1.2e-156)
		tmp = t_1;
	elseif (x <= -1.45e-242)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 4.6e-229)
		tmp = t_1;
	elseif (x <= 5.8e-151)
		tmp = t * (-9.0 * (z * y));
	elseif (x <= 2.4e-36)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+91], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -1.2e-156], t$95$1, If[LessEqual[x, -1.45e-242], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-229], t$95$1, If[LessEqual[x, 5.8e-151], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-36], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.14999999999999996e91 or 2.4e-36 < x

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. distribute-lft-neg-in 95.6%

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

      3. associate-*l* 95.6%

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

      4. *-commutative 95.6%

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

      5. *-commutative 95.6%

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

      6. cancel-sign-sub-inv 95.6%

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

      7. *-commutative 95.6%

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

      8. *-commutative 95.6%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 94.8%

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

      11. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 57.7%

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

   if -1.14999999999999996e91 < x < -1.2e-156 or -1.45e-242 < x < 4.59999999999999992e-229 or 5.80000000000000025e-151 < x < 2.4e-36

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. associate-*l* 95.1%

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

      4. *-commutative 95.1%

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

      5. *-commutative 95.1%

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

      6. cancel-sign-sub-inv 95.1%

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

      7. *-commutative 95.1%

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

      8. *-commutative 95.1%

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

      9. associate-*l* 94.2%

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

      10. associate-*l* 92.5%

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

      11. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 58.6%

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

   if -1.2e-156 < x < -1.45e-242

   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. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.6%

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

      4. *-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. cancel-sign-sub-inv 99.6%

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

      7. *-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.6%

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

      11. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 58.7%

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

      3. associate-*r* 58.7%

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

      4. *-commutative 58.7%

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

      5. associate-*l* 67.6%

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

   6. Simplified 67.6%

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

   if 4.59999999999999992e-229 < x < 5.80000000000000025e-151

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. distribute-lft-neg-in 94.6%

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

      3. associate-*l* 94.5%

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

      4. *-commutative 94.5%

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

      5. *-commutative 94.5%

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

      6. cancel-sign-sub-inv 94.5%

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

      7. *-commutative 94.5%

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

      8. *-commutative 94.5%

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

      9. associate-*l* 94.6%

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

      10. associate-*l* 94.3%

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

      11. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-*r* 57.4%

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

      3. associate-*r* 57.6%

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

      4. associate-*l* 57.5%

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

   6. Simplified 57.5%

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

   7. Taylor expanded in y around 0 57.4%

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

      1. associate-*r* 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-*r* 57.5%

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

      4. associate-*l* 57.4%

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

      5. *-commutative 57.4%

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

      6. associate-*l* 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+91}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-156}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-229}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-36}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 5: 47.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -7.4 \cdot 10^{+102}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= x -7.4e+102)
     (* x 2.0)
     (if (<= x -8.5e-156)
       t_1
       (if (<= x -3.8e-242)
         (* t (* y (* z -9.0)))
         (if (<= x 7.4e-230)
           t_1
           (if (<= x 4.1e-151)
             (* t (* z (* y -9.0)))
             (if (<= x 2.2e-36) t_1 (* x 2.0)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -7.4e+102) {
		tmp = x * 2.0;
	} else if (x <= -8.5e-156) {
		tmp = t_1;
	} else if (x <= -3.8e-242) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 7.4e-230) {
		tmp = t_1;
	} else if (x <= 4.1e-151) {
		tmp = t * (z * (y * -9.0));
	} else if (x <= 2.2e-36) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (x <= (-7.4d+102)) then
        tmp = x * 2.0d0
    else if (x <= (-8.5d-156)) then
        tmp = t_1
    else if (x <= (-3.8d-242)) then
        tmp = t * (y * (z * (-9.0d0)))
    else if (x <= 7.4d-230) then
        tmp = t_1
    else if (x <= 4.1d-151) then
        tmp = t * (z * (y * (-9.0d0)))
    else if (x <= 2.2d-36) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (x <= -7.4e+102) {
		tmp = x * 2.0;
	} else if (x <= -8.5e-156) {
		tmp = t_1;
	} else if (x <= -3.8e-242) {
		tmp = t * (y * (z * -9.0));
	} else if (x <= 7.4e-230) {
		tmp = t_1;
	} else if (x <= 4.1e-151) {
		tmp = t * (z * (y * -9.0));
	} else if (x <= 2.2e-36) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if x <= -7.4e+102:
		tmp = x * 2.0
	elif x <= -8.5e-156:
		tmp = t_1
	elif x <= -3.8e-242:
		tmp = t * (y * (z * -9.0))
	elif x <= 7.4e-230:
		tmp = t_1
	elif x <= 4.1e-151:
		tmp = t * (z * (y * -9.0))
	elif x <= 2.2e-36:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (x <= -7.4e+102)
		tmp = Float64(x * 2.0);
	elseif (x <= -8.5e-156)
		tmp = t_1;
	elseif (x <= -3.8e-242)
		tmp = Float64(t * Float64(y * Float64(z * -9.0)));
	elseif (x <= 7.4e-230)
		tmp = t_1;
	elseif (x <= 4.1e-151)
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	elseif (x <= 2.2e-36)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (x <= -7.4e+102)
		tmp = x * 2.0;
	elseif (x <= -8.5e-156)
		tmp = t_1;
	elseif (x <= -3.8e-242)
		tmp = t * (y * (z * -9.0));
	elseif (x <= 7.4e-230)
		tmp = t_1;
	elseif (x <= 4.1e-151)
		tmp = t * (z * (y * -9.0));
	elseif (x <= 2.2e-36)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.4e+102], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -8.5e-156], t$95$1, If[LessEqual[x, -3.8e-242], N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-230], t$95$1, If[LessEqual[x, 4.1e-151], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-36], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.40000000000000045e102 or 2.1999999999999999e-36 < x

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. distribute-lft-neg-in 95.6%

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

      3. associate-*l* 95.6%

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

      4. *-commutative 95.6%

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

      5. *-commutative 95.6%

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

      6. cancel-sign-sub-inv 95.6%

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

      7. *-commutative 95.6%

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

      8. *-commutative 95.6%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 94.8%

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

      11. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 57.7%

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

   if -7.40000000000000045e102 < x < -8.5e-156 or -3.8000000000000002e-242 < x < 7.39999999999999963e-230 or 4.1000000000000001e-151 < x < 2.1999999999999999e-36

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. associate-*l* 95.1%

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

      4. *-commutative 95.1%

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

      5. *-commutative 95.1%

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

      6. cancel-sign-sub-inv 95.1%

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

      7. *-commutative 95.1%

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

      8. *-commutative 95.1%

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

      9. associate-*l* 94.2%

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

      10. associate-*l* 92.5%

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

      11. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 58.6%

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

   if -8.5e-156 < x < -3.8000000000000002e-242

   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. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.6%

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

      4. *-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. cancel-sign-sub-inv 99.6%

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

      7. *-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.6%

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

      11. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 58.7%

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

      3. associate-*r* 58.7%

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

      4. *-commutative 58.7%

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

      5. associate-*l* 67.6%

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

   6. Simplified 67.6%

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

   if 7.39999999999999963e-230 < x < 4.1000000000000001e-151

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. distribute-lft-neg-in 94.6%

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

      3. associate-*l* 94.5%

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

      4. *-commutative 94.5%

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

      5. *-commutative 94.5%

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

      6. cancel-sign-sub-inv 94.5%

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

      7. *-commutative 94.5%

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

      8. *-commutative 94.5%

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

      9. associate-*l* 94.6%

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

      10. associate-*l* 94.3%

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

      11. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-*r* 57.4%

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

      3. associate-*r* 57.6%

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

      4. *-commutative 57.6%

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

      5. associate-*l* 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in y around 0 57.4%

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

      1. associate-*r* 57.5%

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

   9. Simplified 57.5%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+102}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-156}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-230}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-36}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 6: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_3 := x \cdot 2 - t_2\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;t_1 - t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot 2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b)))
        (t_2 (* 9.0 (* y (* z t))))
        (t_3 (- (* x 2.0) t_2)))
   (if (<= x -5.2e+115)
     t_3
     (if (<= x 3.8e+26)
       (- t_1 t_2)
       (if (<= x 9.5e+129) (+ (* x 2.0) t_1) t_3)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (y * (z * t));
	double t_3 = (x * 2.0) - t_2;
	double tmp;
	if (x <= -5.2e+115) {
		tmp = t_3;
	} else if (x <= 3.8e+26) {
		tmp = t_1 - t_2;
	} else if (x <= 9.5e+129) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = 9.0d0 * (y * (z * t))
    t_3 = (x * 2.0d0) - t_2
    if (x <= (-5.2d+115)) then
        tmp = t_3
    else if (x <= 3.8d+26) then
        tmp = t_1 - t_2
    else if (x <= 9.5d+129) then
        tmp = (x * 2.0d0) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = 9.0 * (y * (z * t));
	double t_3 = (x * 2.0) - t_2;
	double tmp;
	if (x <= -5.2e+115) {
		tmp = t_3;
	} else if (x <= 3.8e+26) {
		tmp = t_1 - t_2;
	} else if (x <= 9.5e+129) {
		tmp = (x * 2.0) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = 9.0 * (y * (z * t))
	t_3 = (x * 2.0) - t_2
	tmp = 0
	if x <= -5.2e+115:
		tmp = t_3
	elif x <= 3.8e+26:
		tmp = t_1 - t_2
	elif x <= 9.5e+129:
		tmp = (x * 2.0) + t_1
	else:
		tmp = t_3
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(9.0 * Float64(y * Float64(z * t)))
	t_3 = Float64(Float64(x * 2.0) - t_2)
	tmp = 0.0
	if (x <= -5.2e+115)
		tmp = t_3;
	elseif (x <= 3.8e+26)
		tmp = Float64(t_1 - t_2);
	elseif (x <= 9.5e+129)
		tmp = Float64(Float64(x * 2.0) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = 9.0 * (y * (z * t));
	t_3 = (x * 2.0) - t_2;
	tmp = 0.0;
	if (x <= -5.2e+115)
		tmp = t_3;
	elseif (x <= 3.8e+26)
		tmp = t_1 - t_2;
	elseif (x <= 9.5e+129)
		tmp = (x * 2.0) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 2.0), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[x, -5.2e+115], t$95$3, If[LessEqual[x, 3.8e+26], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[x, 9.5e+129], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2000000000000001e115 or 9.5000000000000004e129 < x

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. distribute-lft-neg-in 95.4%

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

      3. associate-*l* 95.4%

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

      4. *-commutative 95.4%

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

      5. *-commutative 95.4%

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

      6. cancel-sign-sub-inv 95.4%

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

      7. *-commutative 95.4%

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

      8. *-commutative 95.4%

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

      9. associate-*l* 95.4%

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

      10. associate-*l* 93.2%

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

      11. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in a around 0 85.6%

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

   if -5.2000000000000001e115 < x < 3.8000000000000002e26

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. distribute-lft-neg-in 95.4%

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

      3. associate-*l* 96.0%

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

      4. *-commutative 96.0%

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

      5. *-commutative 96.0%

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

      6. cancel-sign-sub-inv 96.0%

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

      7. *-commutative 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-*l* 95.4%

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

      10. associate-*l* 94.2%

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

      11. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 84.6%

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

   if 3.8000000000000002e26 < x < 9.5000000000000004e129

   1. Initial program 93.1%

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

      1. sub-neg 93.1%

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

      2. distribute-lft-neg-in 93.1%

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

      3. associate-*l* 93.1%

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

      4. *-commutative 93.1%

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

      5. *-commutative 93.1%

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

      6. cancel-sign-sub-inv 93.1%

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

      7. *-commutative 93.1%

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

      8. *-commutative 93.1%

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

      9. associate-*l* 93.1%

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

      10. associate-*l* 99.8%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 93.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+115}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.85e-85)
   (+ (* x 2.0) (* 27.0 (* a b)))
   (if (<= b 2.7e+14)
     (- (* x 2.0) (* 9.0 (* y (* z t))))
     (+ (* a (* 27.0 b)) (* y (* z (* t -9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.85e-85) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (b <= 2.7e+14) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (a * (27.0 * b)) + (y * (z * (t * -9.0)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.85d-85)) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else if (b <= 2.7d+14) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = (a * (27.0d0 * b)) + (y * (z * (t * (-9.0d0))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.85e-85) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (b <= 2.7e+14) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (a * (27.0 * b)) + (y * (z * (t * -9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.85e-85:
		tmp = (x * 2.0) + (27.0 * (a * b))
	elif b <= 2.7e+14:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = (a * (27.0 * b)) + (y * (z * (t * -9.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.85e-85)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	elseif (b <= 2.7e+14)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(y * Float64(z * Float64(t * -9.0))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.85e-85)
		tmp = (x * 2.0) + (27.0 * (a * b));
	elseif (b <= 2.7e+14)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = (a * (27.0 * 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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.85e-85], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+14], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.84999999999999992e-85

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. distribute-lft-neg-in 91.6%

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

      3. associate-*l* 91.6%

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

      4. *-commutative 91.6%

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

      5. *-commutative 91.6%

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

      6. cancel-sign-sub-inv 91.6%

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

      7. *-commutative 91.6%

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

      8. *-commutative 91.6%

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

      9. associate-*l* 91.6%

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

      10. associate-*l* 93.7%

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

      11. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 73.4%

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

   if -1.84999999999999992e-85 < b < 2.7e14

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. distribute-lft-neg-in 97.1%

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

      3. associate-*l* 98.0%

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

      4. *-commutative 98.0%

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

      5. *-commutative 98.0%

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

      6. cancel-sign-sub-inv 98.0%

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

      7. *-commutative 98.0%

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

      8. *-commutative 98.0%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 92.8%

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

      11. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around 0 79.9%

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

   if 2.7e14 < b

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*l* 97.8%

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

      4. *-commutative 97.8%

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

      5. *-commutative 97.8%

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

      6. cancel-sign-sub-inv 97.8%

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

      7. *-commutative 97.8%

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

      8. *-commutative 97.8%

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

      9. associate-*l* 97.9%

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

      10. associate-*l* 97.9%

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

      11. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around 0 82.0%

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

      1. sub-neg 82.0%

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

      2. *-commutative 82.0%

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

      3. associate-*r* 82.0%

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

      4. *-commutative 82.0%

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

      5. distribute-rgt-neg-in 82.0%

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

      6. associate-*r* 83.8%

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

      7. metadata-eval 83.8%

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

      8. associate-*r* 83.8%

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

      9. associate-*l* 82.0%

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

      10. *-commutative 82.0%

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

      11. associate-*r* 82.1%

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

   6. Applied egg-rr 82.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \end{array} \]

Alternative 8: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

assert(y < z && z < t);
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

NOTE: y, z, and t 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) - ((y * 9.0d0) * (z * t))) + (a * (27.0d0 * b))
end function

Java

assert y < z && z < t;
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

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. sub-neg 95.3%

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

   2. distribute-lft-neg-in 95.3%

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

   3. associate-*l* 95.6%

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

   4. *-commutative 95.6%

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

   5. *-commutative 95.6%

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

   6. cancel-sign-sub-inv 95.6%

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

   7. *-commutative 95.6%

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

   8. *-commutative 95.6%

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

   9. associate-*l* 95.3%

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

   10. associate-*l* 94.2%

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

   11. associate-*l* 94.6%

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

3. Simplified 94.6%

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

4. Final simplification 94.6%

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

Alternative 9: 46.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= a -1e+27)
     t_1
     (if (<= a -4.8e-170)
       (* x 2.0)
       (if (<= a 1.15e-188)
         (* -9.0 (* y (* z t)))
         (if (<= a 9.5e-115) (* x 2.0) t_1))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (a <= -1e+27) {
		tmp = t_1;
	} else if (a <= -4.8e-170) {
		tmp = x * 2.0;
	} else if (a <= 1.15e-188) {
		tmp = -9.0 * (y * (z * t));
	} else if (a <= 9.5e-115) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (a <= (-1d+27)) then
        tmp = t_1
    else if (a <= (-4.8d-170)) then
        tmp = x * 2.0d0
    else if (a <= 1.15d-188) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (a <= 9.5d-115) then
        tmp = x * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (a <= -1e+27) {
		tmp = t_1;
	} else if (a <= -4.8e-170) {
		tmp = x * 2.0;
	} else if (a <= 1.15e-188) {
		tmp = -9.0 * (y * (z * t));
	} else if (a <= 9.5e-115) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if a <= -1e+27:
		tmp = t_1
	elif a <= -4.8e-170:
		tmp = x * 2.0
	elif a <= 1.15e-188:
		tmp = -9.0 * (y * (z * t))
	elif a <= 9.5e-115:
		tmp = x * 2.0
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (a <= -1e+27)
		tmp = t_1;
	elseif (a <= -4.8e-170)
		tmp = Float64(x * 2.0);
	elseif (a <= 1.15e-188)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (a <= 9.5e-115)
		tmp = Float64(x * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (a <= -1e+27)
		tmp = t_1;
	elseif (a <= -4.8e-170)
		tmp = x * 2.0;
	elseif (a <= 1.15e-188)
		tmp = -9.0 * (y * (z * t));
	elseif (a <= 9.5e-115)
		tmp = x * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+27], t$95$1, If[LessEqual[a, -4.8e-170], N[(x * 2.0), $MachinePrecision], If[LessEqual[a, 1.15e-188], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-115], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e27 or 9.4999999999999996e-115 < a

   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. sub-neg 94.0%

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

      2. distribute-lft-neg-in 94.0%

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

      3. associate-*l* 94.6%

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

      4. *-commutative 94.6%

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

      5. *-commutative 94.6%

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

      6. cancel-sign-sub-inv 94.6%

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

      7. *-commutative 94.6%

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

      8. *-commutative 94.6%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 95.3%

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

      11. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around inf 54.5%

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

   if -1e27 < a < -4.7999999999999999e-170 or 1.15e-188 < a < 9.4999999999999996e-115

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-lft-neg-in 98.1%

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

      3. associate-*l* 98.1%

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

      4. *-commutative 98.1%

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

      5. *-commutative 98.1%

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

      6. cancel-sign-sub-inv 98.1%

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

      7. *-commutative 98.1%

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

      8. *-commutative 98.1%

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

      9. associate-*l* 98.1%

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

      10. associate-*l* 90.2%

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

      11. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around inf 46.2%

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

   if -4.7999999999999999e-170 < a < 1.15e-188

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. distribute-lft-neg-in 95.7%

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

      3. associate-*l* 95.8%

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

      4. *-commutative 95.8%

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

      5. *-commutative 95.8%

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

      6. cancel-sign-sub-inv 95.8%

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

      7. *-commutative 95.8%

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

      8. *-commutative 95.8%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 95.7%

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

      11. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 55.2%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+27}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 10: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{+133}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 3.7e+133)
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.7e+133) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 3.7d+133) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 3.7e+133) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 3.7e+133:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 3.7e+133)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 3.7e+133)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 3.7e+133], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.70000000000000023e133

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. distribute-lft-neg-in 95.0%

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

      3. associate-*l* 95.4%

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

      4. *-commutative 95.4%

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

      5. *-commutative 95.4%

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

      6. cancel-sign-sub-inv 95.4%

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

      7. *-commutative 95.4%

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

      8. *-commutative 95.4%

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

      9. associate-*l* 95.0%

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

      10. associate-*l* 95.0%

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

      11. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around 0 69.6%

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

   if 3.70000000000000023e133 < t

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. distribute-lft-neg-in 96.9%

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

      3. associate-*l* 97.0%

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

      4. *-commutative 97.0%

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

      5. *-commutative 97.0%

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

      6. cancel-sign-sub-inv 97.0%

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

      7. *-commutative 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*l* 96.9%

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

      10. associate-*l* 88.8%

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

      11. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in a around 0 77.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.7 \cdot 10^{+133}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 70.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.32 \cdot 10^{+166}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.32e+166) (+ (* x 2.0) (* 27.0 (* a b))) (* t (* z (* y -9.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.32e+166) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.32d+166) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t * (z * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.32e+166) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (z * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.32e+166:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t * (z * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.32e+166)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.32e+166)
		tmp = (x * 2.0) + (27.0 * (a * b));
	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.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.32e+166], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.3199999999999999e166

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. distribute-lft-neg-in 95.0%

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

      3. associate-*l* 95.5%

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

      4. *-commutative 95.5%

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

      5. *-commutative 95.5%

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

      6. cancel-sign-sub-inv 95.5%

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

      7. *-commutative 95.5%

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

      8. *-commutative 95.5%

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

      9. associate-*l* 95.0%

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

      10. associate-*l* 94.2%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 69.4%

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

   if 1.3199999999999999e166 < t

   1. Initial program 96.8%

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

      1. sub-neg 96.8%

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

      2. distribute-lft-neg-in 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. *-commutative 96.8%

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

      6. cancel-sign-sub-inv 96.8%

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

      7. *-commutative 96.8%

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

      8. *-commutative 96.8%

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

      9. associate-*l* 96.8%

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

      10. associate-*l* 93.9%

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

      11. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-*r* 55.2%

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

      3. associate-*r* 55.3%

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

      4. *-commutative 55.3%

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

      5. associate-*l* 57.7%

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

   6. Simplified 57.7%

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

   7. Taylor expanded in y around 0 57.6%

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

      1. associate-*r* 57.7%

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

   9. Simplified 57.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.32 \cdot 10^{+166}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 12: 46.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+27} \lor \neg \left(a \leq 4.6 \cdot 10^{-141}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1e+27) (not (<= a 4.6e-141))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+27) || !(a <= 4.6e-141)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1d+27)) .or. (.not. (a <= 4.6d-141))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+27) || !(a <= 4.6e-141)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1e+27) or not (a <= 4.6e-141):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1e+27) || !(a <= 4.6e-141))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1e+27) || ~((a <= 4.6e-141)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1e+27], N[Not[LessEqual[a, 4.6e-141]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1e27 or 4.5999999999999999e-141 < a

   1. Initial program 94.2%

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

      1. sub-neg 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. associate-*l* 94.7%

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

      4. *-commutative 94.7%

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

      5. *-commutative 94.7%

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

      6. cancel-sign-sub-inv 94.7%

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

      7. *-commutative 94.7%

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

      8. *-commutative 94.7%

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

      9. associate-*l* 94.2%

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

      10. associate-*l* 95.4%

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

      11. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in a around inf 53.5%

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

   if -1e27 < a < 4.5999999999999999e-141

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. distribute-lft-neg-in 97.0%

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

      3. associate-*l* 97.0%

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

      4. *-commutative 97.0%

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

      5. *-commutative 97.0%

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

      6. cancel-sign-sub-inv 97.0%

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

      7. *-commutative 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*l* 97.0%

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

      10. associate-*l* 92.4%

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

      11. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 44.3%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+27} \lor \neg \left(a \leq 4.6 \cdot 10^{-141}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 13: 31.0% accurate, 5.7× speedup

Math

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

FPCore

NOTE: y, z, and t 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);
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.
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;
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])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

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

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
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.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 95.3%

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

   1. sub-neg 95.3%

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

   2. distribute-lft-neg-in 95.3%

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

   3. associate-*l* 95.6%

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

   4. *-commutative 95.6%

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

   5. *-commutative 95.6%

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

   6. cancel-sign-sub-inv 95.6%

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

   7. *-commutative 95.6%

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

   8. *-commutative 95.6%

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

   9. associate-*l* 95.3%

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

   10. associate-*l* 94.2%

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

   11. associate-*l* 94.6%

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

3. Simplified 94.6%

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

4. Taylor expanded in x around inf 31.4%

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

5. Final simplification 31.4%

   \[\leadsto x \cdot 2 \]

Developer target: 95.1% 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 2023279 
(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)))