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

Percentage Accurate: 95.6% → 98.6%

Time: 14.6s

Alternatives: 14

Speedup: 0.9×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% 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: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+150}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 1e+150)
   (+ (- (* x 2.0) (* (* 9.0 (* y z)) t)) (* (* a 27.0) b))
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 1e+150) {
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + ((a * 27.0) * b);
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 1e+150)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(9.0 * Float64(y * z)) * t)) + Float64(Float64(a * 27.0) * b));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 1e+150], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 9.99999999999999981e149

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   if 9.99999999999999981e149 < (*.f64 (*.f64 y 9) z)

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-*l* 88.0%

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

      3. fma-def 88.0%

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

      4. associate-*l* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+150}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+150}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= (* (* y 9.0) z) 1e+150)
     (+ (- (* x 2.0) (* (* 9.0 (* y z)) t)) t_1)
     (+ t_1 (- (* x 2.0) (* y (* t (* 9.0 z))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (((y * 9.0) * z) <= 1e+150) {
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + t_1;
	} else {
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (((y * 9.0d0) * z) <= 1d+150) then
        tmp = ((x * 2.0d0) - ((9.0d0 * (y * z)) * t)) + t_1
    else
        tmp = t_1 + ((x * 2.0d0) - (y * (t * (9.0d0 * z))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (((y * 9.0) * z) <= 1e+150) {
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + t_1;
	} else {
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if ((y * 9.0) * z) <= 1e+150:
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + t_1
	else:
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 1e+150)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(9.0 * Float64(y * z)) * t)) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (((y * 9.0) * z) <= 1e+150)
		tmp = ((x * 2.0) - ((9.0 * (y * z)) * t)) + t_1;
	else
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 1e+150], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 9.99999999999999981e149

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   if 9.99999999999999981e149 < (*.f64 (*.f64 y 9) z)

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-*r* 97.4%

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

      3. associate-*l* 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+150}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot \left(y \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 3: 47.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := \left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* (* y (* z t)) -9.0)))
   (if (<= z -5.7e-30)
     t_2
     (if (<= z -4.4e-74)
       (* a (* 27.0 b))
       (if (<= z -1.2e-294)
         (* x 2.0)
         (if (<= z 1.4e-289)
           t_1
           (if (<= z 8.8e-244)
             (* x 2.0)
             (if (<= z 1.1e-158) t_1 (if (<= z 1.8e+27) (* x 2.0) t_2)))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = (y * (z * t)) * -9.0;
	double tmp;
	if (z <= -5.7e-30) {
		tmp = t_2;
	} else if (z <= -4.4e-74) {
		tmp = a * (27.0 * b);
	} else if (z <= -1.2e-294) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-289) {
		tmp = t_1;
	} else if (z <= 8.8e-244) {
		tmp = x * 2.0;
	} else if (z <= 1.1e-158) {
		tmp = t_1;
	} else if (z <= 1.8e+27) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (y * (z * t)) * (-9.0d0)
    if (z <= (-5.7d-30)) then
        tmp = t_2
    else if (z <= (-4.4d-74)) then
        tmp = a * (27.0d0 * b)
    else if (z <= (-1.2d-294)) then
        tmp = x * 2.0d0
    else if (z <= 1.4d-289) then
        tmp = t_1
    else if (z <= 8.8d-244) then
        tmp = x * 2.0d0
    else if (z <= 1.1d-158) then
        tmp = t_1
    else if (z <= 1.8d+27) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = (y * (z * t)) * -9.0;
	double tmp;
	if (z <= -5.7e-30) {
		tmp = t_2;
	} else if (z <= -4.4e-74) {
		tmp = a * (27.0 * b);
	} else if (z <= -1.2e-294) {
		tmp = x * 2.0;
	} else if (z <= 1.4e-289) {
		tmp = t_1;
	} else if (z <= 8.8e-244) {
		tmp = x * 2.0;
	} else if (z <= 1.1e-158) {
		tmp = t_1;
	} else if (z <= 1.8e+27) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = (y * (z * t)) * -9.0
	tmp = 0
	if z <= -5.7e-30:
		tmp = t_2
	elif z <= -4.4e-74:
		tmp = a * (27.0 * b)
	elif z <= -1.2e-294:
		tmp = x * 2.0
	elif z <= 1.4e-289:
		tmp = t_1
	elif z <= 8.8e-244:
		tmp = x * 2.0
	elif z <= 1.1e-158:
		tmp = t_1
	elif z <= 1.8e+27:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(Float64(y * Float64(z * t)) * -9.0)
	tmp = 0.0
	if (z <= -5.7e-30)
		tmp = t_2;
	elseif (z <= -4.4e-74)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (z <= -1.2e-294)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.4e-289)
		tmp = t_1;
	elseif (z <= 8.8e-244)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.1e-158)
		tmp = t_1;
	elseif (z <= 1.8e+27)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = (y * (z * t)) * -9.0;
	tmp = 0.0;
	if (z <= -5.7e-30)
		tmp = t_2;
	elseif (z <= -4.4e-74)
		tmp = a * (27.0 * b);
	elseif (z <= -1.2e-294)
		tmp = x * 2.0;
	elseif (z <= 1.4e-289)
		tmp = t_1;
	elseif (z <= 8.8e-244)
		tmp = x * 2.0;
	elseif (z <= 1.1e-158)
		tmp = t_1;
	elseif (z <= 1.8e+27)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]}, If[LessEqual[z, -5.7e-30], t$95$2, If[LessEqual[z, -4.4e-74], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-294], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.4e-289], t$95$1, If[LessEqual[z, 8.8e-244], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.1e-158], t$95$1, If[LessEqual[z, 1.8e+27], N[(x * 2.0), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.69999999999999977e-30 or 1.79999999999999991e27 < z

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 92.4%

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

      1. *-commutative 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in y around inf 51.7%

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

   if -5.69999999999999977e-30 < z < -4.40000000000000021e-74

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-*l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*r* 91.0%

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

   9. Simplified 91.0%

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

   10. Taylor expanded in x around 0 60.6%

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

       1. *-commutative 60.6%

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

       2. associate-*r* 60.6%

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

   12. Simplified 60.6%

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

   if -4.40000000000000021e-74 < z < -1.19999999999999999e-294 or 1.39999999999999993e-289 < z < 8.79999999999999939e-244 or 1.1000000000000001e-158 < z < 1.79999999999999991e27

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. fma-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. neg-sub0 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. fma-def 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-rgt-neg-in 99.9%

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

      12. *-commutative 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 47.5%

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

   if -1.19999999999999999e-294 < z < 1.39999999999999993e-289 or 8.79999999999999939e-244 < z < 1.1000000000000001e-158

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in a around inf 43.2%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-30}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-289}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \end{array} \]

Alternative 4: 47.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* y (* (* z t) -9.0))))
   (if (<= z -1.4e-29)
     t_2
     (if (<= z -2.8e-74)
       (* a (* 27.0 b))
       (if (<= z -1.8e-294)
         (* x 2.0)
         (if (<= z 3.65e-289)
           t_1
           (if (<= z 8.5e-244)
             (* x 2.0)
             (if (<= z 2.5e-152) t_1 (if (<= z 1.8e+27) (* x 2.0) t_2)))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = y * ((z * t) * -9.0);
	double tmp;
	if (z <= -1.4e-29) {
		tmp = t_2;
	} else if (z <= -2.8e-74) {
		tmp = a * (27.0 * b);
	} else if (z <= -1.8e-294) {
		tmp = x * 2.0;
	} else if (z <= 3.65e-289) {
		tmp = t_1;
	} else if (z <= 8.5e-244) {
		tmp = x * 2.0;
	} else if (z <= 2.5e-152) {
		tmp = t_1;
	} else if (z <= 1.8e+27) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = y * ((z * t) * (-9.0d0))
    if (z <= (-1.4d-29)) then
        tmp = t_2
    else if (z <= (-2.8d-74)) then
        tmp = a * (27.0d0 * b)
    else if (z <= (-1.8d-294)) then
        tmp = x * 2.0d0
    else if (z <= 3.65d-289) then
        tmp = t_1
    else if (z <= 8.5d-244) then
        tmp = x * 2.0d0
    else if (z <= 2.5d-152) then
        tmp = t_1
    else if (z <= 1.8d+27) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = y * ((z * t) * -9.0);
	double tmp;
	if (z <= -1.4e-29) {
		tmp = t_2;
	} else if (z <= -2.8e-74) {
		tmp = a * (27.0 * b);
	} else if (z <= -1.8e-294) {
		tmp = x * 2.0;
	} else if (z <= 3.65e-289) {
		tmp = t_1;
	} else if (z <= 8.5e-244) {
		tmp = x * 2.0;
	} else if (z <= 2.5e-152) {
		tmp = t_1;
	} else if (z <= 1.8e+27) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = y * ((z * t) * -9.0)
	tmp = 0
	if z <= -1.4e-29:
		tmp = t_2
	elif z <= -2.8e-74:
		tmp = a * (27.0 * b)
	elif z <= -1.8e-294:
		tmp = x * 2.0
	elif z <= 3.65e-289:
		tmp = t_1
	elif z <= 8.5e-244:
		tmp = x * 2.0
	elif z <= 2.5e-152:
		tmp = t_1
	elif z <= 1.8e+27:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(y * Float64(Float64(z * t) * -9.0))
	tmp = 0.0
	if (z <= -1.4e-29)
		tmp = t_2;
	elseif (z <= -2.8e-74)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (z <= -1.8e-294)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.65e-289)
		tmp = t_1;
	elseif (z <= 8.5e-244)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.5e-152)
		tmp = t_1;
	elseif (z <= 1.8e+27)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = y * ((z * t) * -9.0);
	tmp = 0.0;
	if (z <= -1.4e-29)
		tmp = t_2;
	elseif (z <= -2.8e-74)
		tmp = a * (27.0 * b);
	elseif (z <= -1.8e-294)
		tmp = x * 2.0;
	elseif (z <= 3.65e-289)
		tmp = t_1;
	elseif (z <= 8.5e-244)
		tmp = x * 2.0;
	elseif (z <= 2.5e-152)
		tmp = t_1;
	elseif (z <= 1.8e+27)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-29], t$95$2, If[LessEqual[z, -2.8e-74], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-294], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.65e-289], t$95$1, If[LessEqual[z, 8.5e-244], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.5e-152], t$95$1, If[LessEqual[z, 1.8e+27], N[(x * 2.0), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e-29 or 1.79999999999999991e27 < z

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 92.4%

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

      1. *-commutative 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-*l* 51.7%

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

      4. *-commutative 51.7%

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

   7. Simplified 51.7%

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

   if -1.4000000000000001e-29 < z < -2.79999999999999988e-74

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-*l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*r* 91.0%

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

   9. Simplified 91.0%

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

   10. Taylor expanded in x around 0 60.6%

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

       1. *-commutative 60.6%

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

       2. associate-*r* 60.6%

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

   12. Simplified 60.6%

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

   if -2.79999999999999988e-74 < z < -1.8000000000000001e-294 or 3.64999999999999978e-289 < z < 8.4999999999999999e-244 or 2.4999999999999998e-152 < z < 1.79999999999999991e27

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. fma-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. neg-sub0 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. fma-def 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-rgt-neg-in 99.9%

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

      12. *-commutative 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 47.5%

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

   if -1.8000000000000001e-294 < z < 3.64999999999999978e-289 or 8.4999999999999999e-244 < z < 2.4999999999999998e-152

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in a around inf 43.2%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-289}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-244}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-152}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \end{array} \]

Alternative 5: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-294}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-243}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -6e-29)
     (* y (* (* z t) -9.0))
     (if (<= z -1.15e-76)
       (* a (* 27.0 b))
       (if (<= z -1.5e-294)
         (* x 2.0)
         (if (<= z 6.5e-294)
           t_1
           (if (<= z 1.1e-243)
             (* x 2.0)
             (if (<= z 1e-149)
               t_1
               (if (<= z 1.6e+29) (* x 2.0) (* (* y z) (* t -9.0)))))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -6e-29) {
		tmp = y * ((z * t) * -9.0);
	} else if (z <= -1.15e-76) {
		tmp = a * (27.0 * b);
	} else if (z <= -1.5e-294) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-294) {
		tmp = t_1;
	} else if (z <= 1.1e-243) {
		tmp = x * 2.0;
	} else if (z <= 1e-149) {
		tmp = t_1;
	} else if (z <= 1.6e+29) {
		tmp = x * 2.0;
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (z <= (-6d-29)) then
        tmp = y * ((z * t) * (-9.0d0))
    else if (z <= (-1.15d-76)) then
        tmp = a * (27.0d0 * b)
    else if (z <= (-1.5d-294)) then
        tmp = x * 2.0d0
    else if (z <= 6.5d-294) then
        tmp = t_1
    else if (z <= 1.1d-243) then
        tmp = x * 2.0d0
    else if (z <= 1d-149) then
        tmp = t_1
    else if (z <= 1.6d+29) then
        tmp = x * 2.0d0
    else
        tmp = (y * z) * (t * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -6e-29) {
		tmp = y * ((z * t) * -9.0);
	} else if (z <= -1.15e-76) {
		tmp = a * (27.0 * b);
	} else if (z <= -1.5e-294) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-294) {
		tmp = t_1;
	} else if (z <= 1.1e-243) {
		tmp = x * 2.0;
	} else if (z <= 1e-149) {
		tmp = t_1;
	} else if (z <= 1.6e+29) {
		tmp = x * 2.0;
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if z <= -6e-29:
		tmp = y * ((z * t) * -9.0)
	elif z <= -1.15e-76:
		tmp = a * (27.0 * b)
	elif z <= -1.5e-294:
		tmp = x * 2.0
	elif z <= 6.5e-294:
		tmp = t_1
	elif z <= 1.1e-243:
		tmp = x * 2.0
	elif z <= 1e-149:
		tmp = t_1
	elif z <= 1.6e+29:
		tmp = x * 2.0
	else:
		tmp = (y * z) * (t * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -6e-29)
		tmp = Float64(y * Float64(Float64(z * t) * -9.0));
	elseif (z <= -1.15e-76)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (z <= -1.5e-294)
		tmp = Float64(x * 2.0);
	elseif (z <= 6.5e-294)
		tmp = t_1;
	elseif (z <= 1.1e-243)
		tmp = Float64(x * 2.0);
	elseif (z <= 1e-149)
		tmp = t_1;
	elseif (z <= 1.6e+29)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -6e-29)
		tmp = y * ((z * t) * -9.0);
	elseif (z <= -1.15e-76)
		tmp = a * (27.0 * b);
	elseif (z <= -1.5e-294)
		tmp = x * 2.0;
	elseif (z <= 6.5e-294)
		tmp = t_1;
	elseif (z <= 1.1e-243)
		tmp = x * 2.0;
	elseif (z <= 1e-149)
		tmp = t_1;
	elseif (z <= 1.6e+29)
		tmp = x * 2.0;
	else
		tmp = (y * z) * (t * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-29], N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-76], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-294], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6.5e-294], t$95$1, If[LessEqual[z, 1.1e-243], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1e-149], t$95$1, If[LessEqual[z, 1.6e+29], N[(x * 2.0), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.0000000000000005e-29

   1. Initial program 89.4%

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

   2. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in y around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. *-commutative 50.6%

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

      3. associate-*l* 50.6%

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

      4. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   if -6.0000000000000005e-29 < z < -1.15000000000000003e-76

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

      1. associate-+l- 99.7%

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

      2. associate-*l* 99.7%

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

      3. associate-*l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*r* 91.0%

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

   9. Simplified 91.0%

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

   10. Taylor expanded in x around 0 60.6%

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

       1. *-commutative 60.6%

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

       2. associate-*r* 60.6%

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

   12. Simplified 60.6%

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

   if -1.15000000000000003e-76 < z < -1.4999999999999999e-294 or 6.4999999999999995e-294 < z < 1.1e-243 or 9.99999999999999979e-150 < z < 1.59999999999999993e29

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. fma-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. neg-sub0 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. fma-def 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. distribute-rgt-neg-in 99.9%

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

      12. *-commutative 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 47.0%

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

   if -1.4999999999999999e-294 < z < 6.4999999999999995e-294 or 1.1e-243 < z < 9.99999999999999979e-150

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in a around inf 41.7%

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

   if 1.59999999999999993e29 < z

   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. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate-*l* 95.4%

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

      3. associate-*l* 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 60.9%

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

      4. associate-*l* 60.9%

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

   9. Simplified 60.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-294}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-294}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-243}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 10^{-149}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 6: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;z \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= z -2e-21)
     (+ t_1 (- (* x 2.0) (* y (* t (* 9.0 z)))))
     (+ t_1 (- (* x 2.0) (* (* (* y 9.0) z) t))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (z <= -2e-21) {
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))));
	} else {
		tmp = t_1 + ((x * 2.0) - (((y * 9.0) * z) * t));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    if (z <= (-2d-21)) then
        tmp = t_1 + ((x * 2.0d0) - (y * (t * (9.0d0 * z))))
    else
        tmp = t_1 + ((x * 2.0d0) - (((y * 9.0d0) * z) * t))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double tmp;
	if (z <= -2e-21) {
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))));
	} else {
		tmp = t_1 + ((x * 2.0) - (((y * 9.0) * z) * t));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	tmp = 0
	if z <= -2e-21:
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))))
	else:
		tmp = t_1 + ((x * 2.0) - (((y * 9.0) * z) * t))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (z <= -2e-21)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z)))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	tmp = 0.0;
	if (z <= -2e-21)
		tmp = t_1 + ((x * 2.0) - (y * (t * (9.0 * z))));
	else
		tmp = t_1 + ((x * 2.0) - (((y * 9.0) * z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[z, -2e-21], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999982e-21

   1. Initial program 89.4%

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

   2. Taylor expanded in y around 0 95.1%

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

      1. *-commutative 95.1%

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

      2. associate-*r* 95.1%

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

      3. associate-*l* 95.1%

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

   4. Simplified 95.1%

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

   if -1.99999999999999982e-21 < z

   1. Initial program 98.3%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array} \]

Alternative 7: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;x \cdot 2 - 9 \cdot t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + t_1 \cdot -9\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (* z t))))
   (if (<= z -1.4e-29)
     (- (* x 2.0) (* 9.0 t_1))
     (if (<= z 1.4e+18)
       (- (* x 2.0) (* (* a b) -27.0))
       (+ (* a (* 27.0 b)) (* t_1 -9.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (z * t);
	double tmp;
	if (z <= -1.4e-29) {
		tmp = (x * 2.0) - (9.0 * t_1);
	} else if (z <= 1.4e+18) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (a * (27.0 * b)) + (t_1 * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z * t)
    if (z <= (-1.4d-29)) then
        tmp = (x * 2.0d0) - (9.0d0 * t_1)
    else if (z <= 1.4d+18) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (a * (27.0d0 * b)) + (t_1 * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (z * t);
	double tmp;
	if (z <= -1.4e-29) {
		tmp = (x * 2.0) - (9.0 * t_1);
	} else if (z <= 1.4e+18) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (a * (27.0 * b)) + (t_1 * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = y * (z * t)
	tmp = 0
	if z <= -1.4e-29:
		tmp = (x * 2.0) - (9.0 * t_1)
	elif z <= 1.4e+18:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (a * (27.0 * b)) + (t_1 * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(z * t))
	tmp = 0.0
	if (z <= -1.4e-29)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * t_1));
	elseif (z <= 1.4e+18)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(t_1 * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (z * t);
	tmp = 0.0;
	if (z <= -1.4e-29)
		tmp = (x * 2.0) - (9.0 * t_1);
	elseif (z <= 1.4e+18)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (a * (27.0 * b)) + (t_1 * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-29], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+18], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * -9.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e-29

   1. Initial program 89.4%

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

   2. Taylor expanded in a around 0 71.1%

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

   if -1.4000000000000001e-29 < z < 1.4e18

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 96.8%

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

      10. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 82.3%

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

      1. *-commutative 82.3%

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

   6. Simplified 82.3%

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

   if 1.4e18 < z

   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. Taylor expanded in x around 0 72.0%

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

      1. cancel-sign-sub-inv 72.0%

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

      2. associate-*r* 72.0%

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

      3. *-commutative 72.0%

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

      4. associate-*l* 72.0%

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

      5. metadata-eval 72.0%

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

      6. *-commutative 72.0%

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

   4. Applied egg-rr 72.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(y \cdot \left(z \cdot t\right)\right) \cdot -9\\ \end{array} \]

Alternative 8: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

2. Taylor expanded in y around 0 94.0%

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

   1. *-commutative 94.0%

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

   2. associate-*r* 94.0%

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

   3. associate-*l* 94.0%

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

4. Simplified 94.0%

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

5. Final simplification 94.0%

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

Alternative 9: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -740000000:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -740000000.0)
   (* y (* (* z t) -9.0))
   (if (<= z 2.7e+29) (- (* x 2.0) (* a (* b -27.0))) (* (* y z) (* t -9.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -740000000.0) {
		tmp = y * ((z * t) * -9.0);
	} else if (z <= 2.7e+29) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-740000000.0d0)) then
        tmp = y * ((z * t) * (-9.0d0))
    else if (z <= 2.7d+29) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (y * z) * (t * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -740000000.0) {
		tmp = y * ((z * t) * -9.0);
	} else if (z <= 2.7e+29) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -740000000.0:
		tmp = y * ((z * t) * -9.0)
	elif z <= 2.7e+29:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (y * z) * (t * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -740000000.0)
		tmp = Float64(y * Float64(Float64(z * t) * -9.0));
	elseif (z <= 2.7e+29)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -740000000.0)
		tmp = y * ((z * t) * -9.0);
	elseif (z <= 2.7e+29)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (y * z) * (t * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -740000000.0], N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+29], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4e8

   1. Initial program 88.5%

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

   2. Taylor expanded in y around 0 88.5%

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

      1. *-commutative 88.5%

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

   4. Simplified 88.5%

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

   5. Taylor expanded in y around inf 48.1%

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

      1. *-commutative 48.1%

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

      2. *-commutative 48.1%

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

      3. associate-*l* 48.1%

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

      4. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   if -7.4e8 < z < 2.7e29

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate-*l* 99.0%

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

      3. associate-*l* 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*r* 79.7%

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

   9. Simplified 79.7%

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

   if 2.7e29 < z

   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. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate-*l* 95.4%

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

      3. associate-*l* 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 60.9%

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

      4. associate-*l* 60.9%

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

   9. Simplified 60.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -740000000:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 10: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -310000000000:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -310000000000.0)
   (* y (* (* z t) -9.0))
   (if (<= z 1.65e+29)
     (- (* x 2.0) (* (* a b) -27.0))
     (* (* y z) (* t -9.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -310000000000.0) {
		tmp = y * ((z * t) * -9.0);
	} else if (z <= 1.65e+29) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-310000000000.0d0)) then
        tmp = y * ((z * t) * (-9.0d0))
    else if (z <= 1.65d+29) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (y * z) * (t * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -310000000000.0) {
		tmp = y * ((z * t) * -9.0);
	} else if (z <= 1.65e+29) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -310000000000.0:
		tmp = y * ((z * t) * -9.0)
	elif z <= 1.65e+29:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (y * z) * (t * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -310000000000.0)
		tmp = Float64(y * Float64(Float64(z * t) * -9.0));
	elseif (z <= 1.65e+29)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -310000000000.0)
		tmp = y * ((z * t) * -9.0);
	elseif (z <= 1.65e+29)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (y * z) * (t * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -310000000000.0], N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+29], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e11

   1. Initial program 88.3%

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

   2. Taylor expanded in y around 0 88.3%

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

      1. *-commutative 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in y around inf 47.2%

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

      1. *-commutative 47.2%

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

      2. *-commutative 47.2%

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

      3. associate-*l* 47.2%

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

      4. *-commutative 47.2%

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

   7. Simplified 47.2%

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

   if -3.1e11 < z < 1.64999999999999992e29

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 97.0%

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

      10. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 79.2%

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

      1. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   if 1.64999999999999992e29 < z

   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. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate-*l* 95.4%

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

      3. associate-*l* 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 60.9%

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

      4. associate-*l* 60.9%

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

   9. Simplified 60.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -310000000000:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 11: 78.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-29}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.65e-29)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= z 5.6e+28) (- (* x 2.0) (* (* a b) -27.0)) (* (* y z) (* t -9.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e-29) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 5.6e+28) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.65d-29)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (z <= 5.6d+28) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (y * z) * (t * (-9.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e-29) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 5.6e+28) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (y * z) * (t * -9.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.65e-29:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif z <= 5.6e+28:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (y * z) * (t * -9.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e-29)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 5.6e+28)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(y * z) * Float64(t * -9.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.65e-29)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (z <= 5.6e+28)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (y * z) * (t * -9.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e-29], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+28], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000014e-29

   1. Initial program 89.4%

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

   2. Taylor expanded in a around 0 71.1%

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

   if -1.65000000000000014e-29 < z < 5.6000000000000003e28

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 96.8%

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

      10. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. *-commutative 81.9%

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

   6. Simplified 81.9%

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

   if 5.6000000000000003e28 < z

   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. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

      1. associate-+l- 95.4%

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

      2. associate-*l* 95.4%

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

      3. associate-*l* 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. *-commutative 52.8%

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

      3. associate-*r* 60.9%

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

      4. associate-*l* 60.9%

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

   9. Simplified 60.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-29}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 12: 47.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{-27} \lor \neg \left(b \leq 7.6 \cdot 10^{+24}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.6e-27) (not (<= b 7.6e+24))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.6e-27) || !(b <= 7.6e+24)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.6d-27)) .or. (.not. (b <= 7.6d+24))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.6e-27) || !(b <= 7.6e+24)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.6e-27) or not (b <= 7.6e+24):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.6e-27) || !(b <= 7.6e+24))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.6e-27) || ~((b <= 7.6e+24)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.6e-27], N[Not[LessEqual[b, 7.6e+24]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.60000000000000017e-27 or 7.6000000000000003e24 < b

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in a around inf 48.4%

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

   if -2.60000000000000017e-27 < b < 7.6000000000000003e24

   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. associate-+l- 96.9%

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

      2. fma-neg 96.9%

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

      3. neg-sub0 96.9%

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

      4. associate-+l- 96.9%

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

      5. neg-sub0 96.9%

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

      6. *-commutative 96.9%

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

      7. distribute-rgt-neg-in 96.9%

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

      8. fma-def 96.9%

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

      9. *-commutative 96.9%

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

      10. associate-*r* 96.9%

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

      11. distribute-rgt-neg-in 96.9%

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

      12. *-commutative 96.9%

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

      13. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 44.0%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{-27} \lor \neg \left(b \leq 7.6 \cdot 10^{+24}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 13: 47.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-24}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e-24)
   (* 27.0 (* a b))
   (if (<= b 3.05e+29) (* x 2.0) (* a (* 27.0 b)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-24) {
		tmp = 27.0 * (a * b);
	} else if (b <= 3.05e+29) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d-24)) then
        tmp = 27.0d0 * (a * b)
    else if (b <= 3.05d+29) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-24) {
		tmp = 27.0 * (a * b);
	} else if (b <= 3.05e+29) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e-24:
		tmp = 27.0 * (a * b)
	elif b <= 3.05e+29:
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e-24)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (b <= 3.05e+29)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e-24)
		tmp = 27.0 * (a * b);
	elseif (b <= 3.05e+29)
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e-24], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.05e+29], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.9999999999999998e-24

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. *-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in a around inf 48.2%

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

   if -4.9999999999999998e-24 < b < 3.0499999999999999e29

   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. associate-+l- 96.9%

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

      2. fma-neg 96.9%

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

      3. neg-sub0 96.9%

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

      4. associate-+l- 96.9%

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

      5. neg-sub0 96.9%

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

      6. *-commutative 96.9%

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

      7. distribute-rgt-neg-in 96.9%

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

      8. fma-def 96.9%

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

      9. *-commutative 96.9%

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

      10. associate-*r* 96.9%

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

      11. distribute-rgt-neg-in 96.9%

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

      12. *-commutative 96.9%

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

      13. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 44.0%

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

   if 3.0499999999999999e29 < b

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 94.6%

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

      1. *-commutative 94.6%

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

   4. Simplified 94.6%

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

      1. associate-+l- 94.6%

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

      2. associate-*l* 92.8%

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

      3. associate-*l* 91.1%

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

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-*r* 70.1%

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

   9. Simplified 70.1%

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

   10. Taylor expanded in x around 0 48.8%

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

       1. *-commutative 48.8%

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

       2. associate-*r* 48.9%

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

   12. Simplified 48.9%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-24}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{+29}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 14: 30.5% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. associate-+l- 96.1%

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

   2. fma-neg 96.1%

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

   3. neg-sub0 96.1%

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

   4. associate-+l- 96.1%

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

   5. neg-sub0 96.1%

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

   6. *-commutative 96.1%

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

   7. distribute-rgt-neg-in 96.1%

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

   8. fma-def 96.1%

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

   9. *-commutative 96.1%

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

   10. associate-*r* 96.1%

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

   11. distribute-rgt-neg-in 96.1%

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

   12. *-commutative 96.1%

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

   13. metadata-eval 96.1%

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

3. Simplified 96.1%

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

4. Taylor expanded in x around inf 34.2%

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

5. Final simplification 34.2%

   \[\leadsto x \cdot 2 \]

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 2023185 
(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)))