Linear.V3:$cdot from linear-1.19.1.3, B

Percentage Accurate: 97.7% → 99.4%

Time: 13.0s

Alternatives: 11

Speedup: 0.4×

• 32.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (+ (* x y) (* z t)) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * t)) + (a * 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 * y) + (z * t)) + (a * b)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return ((x * y) + (z * t)) + (a * b)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (+ (* x y) (* z t)) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * y) + (z * t)) + (a * 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 * y) + (z * t)) + (a * b)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return ((x * y) + (z * t)) + (a * b)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + a \cdot \frac{b}{x}\right) + t \cdot \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, 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 b) (+ (* z t) (* x y)))))
   (if (<= t_1 INFINITY) t_1 (* x (+ (+ y (* a (/ b x))) (* t (/ z x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((z * t) + (x * y));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * ((y + (a * (b / x))) + (t * (z / x)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((z * t) + (x * y));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * ((y + (a * (b / x))) + (t * (z / x)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * b) + ((z * t) + (x * y))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * ((y + (a * (b / x))) + (t * (z / x)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y + Float64(a * Float64(b / x))) + Float64(t * Float64(z / x))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + ((z * t) + (x * y));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((y + (a * (b / x))) + (t * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, 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 * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(y + N[(a * N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

      1. fma-define 20.0%

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

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 20.0%

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

      1. associate-+r+ 20.0%

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

      2. associate-/l* 60.0%

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

      3. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b + \left(z \cdot t + x \cdot y\right) \leq \infty:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y + a \cdot \frac{b}{x}\right) + t \cdot \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l+ 98.0%

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

   2. fma-define 98.4%

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

   3. +-commutative 98.4%

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

   4. fma-define 98.8%

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

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, z \cdot t\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. fma-define 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + \frac{z \cdot t}{x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, 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 b) (+ (* z t) (* x y)))))
   (if (<= t_1 INFINITY) t_1 (* x (+ y (/ (* z t) x))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((z * t) + (x * y));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x * (y + ((z * t) / x));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((z * t) + (x * y));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x * (y + ((z * t) / x));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * b) + ((z * t) + (x * y))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x * (y + ((z * t) / x))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y + Float64(Float64(z * t) / x)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + ((z * t) + (x * y));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * (y + ((z * t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, 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 * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(y + N[(N[(z * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

      1. fma-define 20.0%

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

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 20.0%

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

      1. associate-+r+ 20.0%

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

      2. associate-/l* 60.0%

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

      3. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

      1. clear-num 80.0%

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

      2. inv-pow 80.0%

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

   9. Applied egg-rr 80.0%

      \[\leadsto x \cdot \left(\left(y + a \cdot \color{blue}{{\left(\frac{x}{b}\right)}^{-1}}\right) + t \cdot \frac{z}{x}\right) \]
   10. Step-by-step derivation

       1. unpow-1 80.0%

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

   11. Simplified 80.0%

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

   12. Taylor expanded in a around 0 80.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b + \left(z \cdot t + x \cdot y\right) \leq \infty:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + \frac{z \cdot t}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-7}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{-101}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.95 \cdot 10^{+33}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1e-7)
   (* a b)
   (if (<= (* a b) 8e-101)
     (* z t)
     (if (<= (* a b) 1.95e+33) (* x y) (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1e-7) {
		tmp = a * b;
	} else if ((a * b) <= 8e-101) {
		tmp = z * t;
	} else if ((a * b) <= 1.95e+33) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a * b) <= (-1d-7)) then
        tmp = a * b
    else if ((a * b) <= 8d-101) then
        tmp = z * t
    else if ((a * b) <= 1.95d+33) then
        tmp = x * y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1e-7) {
		tmp = a * b;
	} else if ((a * b) <= 8e-101) {
		tmp = z * t;
	} else if ((a * b) <= 1.95e+33) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1e-7:
		tmp = a * b
	elif (a * b) <= 8e-101:
		tmp = z * t
	elif (a * b) <= 1.95e+33:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -1e-7)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 8e-101)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.95e+33)
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a * b) <= -1e-7)
		tmp = a * b;
	elseif ((a * b) <= 8e-101)
		tmp = z * t;
	elseif ((a * b) <= 1.95e+33)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e-7], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8e-101], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.95e+33], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.9999999999999995e-8 or 1.9500000000000001e33 < (*.f64 a b)

   1. Initial program 97.7%

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

      1. fma-define 97.7%

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

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 64.3%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -9.9999999999999995e-8 < (*.f64 a b) < 8.00000000000000041e-101

   1. Initial program 99.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.7%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   6. Taylor expanded in z around inf 64.7%

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

      1. associate-/l* 62.7%

         \[\leadsto z \cdot \left(t + \color{blue}{a \cdot \frac{b}{z}}\right) \]

   8. Simplified 62.7%

      \[\leadsto \color{blue}{z \cdot \left(t + a \cdot \frac{b}{z}\right)} \]

   9. Taylor expanded in t around inf 58.5%

      \[\leadsto z \cdot \color{blue}{t} \]

   if 8.00000000000000041e-101 < (*.f64 a b) < 1.9500000000000001e33

   1. Initial program 95.8%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.5%

      \[\leadsto \color{blue}{x \cdot y} + a \cdot b \]

   4. Taylor expanded in y around inf 94.5%

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

      1. associate-/l* 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in x around inf 70.9%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-7}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{-101}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.95 \cdot 10^{+33}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+111}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 10^{+44}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + a \cdot \frac{b}{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -4e+111)
   (+ (* z t) (* x y))
   (if (<= (* x y) 1e+44) (+ (* z t) (* a b)) (* y (+ x (* a (/ b y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4e+111) {
		tmp = (z * t) + (x * y);
	} else if ((x * y) <= 1e+44) {
		tmp = (z * t) + (a * b);
	} else {
		tmp = y * (x + (a * (b / y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, 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 ((x * y) <= (-4d+111)) then
        tmp = (z * t) + (x * y)
    else if ((x * y) <= 1d+44) then
        tmp = (z * t) + (a * b)
    else
        tmp = y * (x + (a * (b / y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4e+111) {
		tmp = (z * t) + (x * y);
	} else if ((x * y) <= 1e+44) {
		tmp = (z * t) + (a * b);
	} else {
		tmp = y * (x + (a * (b / y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -4e+111:
		tmp = (z * t) + (x * y)
	elif (x * y) <= 1e+44:
		tmp = (z * t) + (a * b)
	else:
		tmp = y * (x + (a * (b / y)))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -4e+111)
		tmp = Float64(Float64(z * t) + Float64(x * y));
	elseif (Float64(x * y) <= 1e+44)
		tmp = Float64(Float64(z * t) + Float64(a * b));
	else
		tmp = Float64(y * Float64(x + Float64(a * Float64(b / y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -4e+111)
		tmp = (z * t) + (x * y);
	elseif ((x * y) <= 1e+44)
		tmp = (z * t) + (a * b);
	else
		tmp = y * (x + (a * (b / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+111], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+44], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(a * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999983e111

   1. Initial program 97.4%

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

      1. fma-define 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.4%

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

      1. associate-+r+ 97.4%

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

      2. associate-/l* 97.3%

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

      3. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

      1. clear-num 97.3%

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

      2. inv-pow 97.3%

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

   9. Applied egg-rr 97.3%

      \[\leadsto x \cdot \left(\left(y + a \cdot \color{blue}{{\left(\frac{x}{b}\right)}^{-1}}\right) + t \cdot \frac{z}{x}\right) \]
   10. Step-by-step derivation

       1. unpow-1 97.3%

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

   11. Simplified 97.3%

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

   12. Taylor expanded in a around 0 95.1%

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

   13. Taylor expanded in x around 0 95.1%

       \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if -3.99999999999999983e111 < (*.f64 x y) < 1.0000000000000001e44

   1. Initial program 99.3%

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

      1. fma-define 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 93.5%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if 1.0000000000000001e44 < (*.f64 x y)

   1. Initial program 95.2%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.1%

      \[\leadsto \color{blue}{x \cdot y} + a \cdot b \]

   4. Taylor expanded in y around inf 87.0%

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

      1. associate-/l* 88.6%

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

   6. Simplified 88.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+111}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 10^{+44}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + a \cdot \frac{b}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+111} \lor \neg \left(x \cdot y \leq 10^{+24}\right):\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -4e+111) (not (<= (* x y) 1e+24)))
   (+ (* z t) (* x y))
   (+ (* z t) (* a b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -4e+111) || !((x * y) <= 1e+24)) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, 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 (((x * y) <= (-4d+111)) .or. (.not. ((x * y) <= 1d+24))) then
        tmp = (z * t) + (x * y)
    else
        tmp = (z * t) + (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -4e+111) || !((x * y) <= 1e+24)) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -4e+111) or not ((x * y) <= 1e+24):
		tmp = (z * t) + (x * y)
	else:
		tmp = (z * t) + (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -4e+111) || !(Float64(x * y) <= 1e+24))
		tmp = Float64(Float64(z * t) + Float64(x * y));
	else
		tmp = Float64(Float64(z * t) + Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -4e+111) || ~(((x * y) <= 1e+24)))
		tmp = (z * t) + (x * y);
	else
		tmp = (z * t) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4e+111], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+24]], $MachinePrecision]], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.99999999999999983e111 or 9.9999999999999998e23 < (*.f64 x y)

   1. Initial program 95.2%

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

      1. fma-define 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 94.4%

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

      1. associate-+r+ 94.4%

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

      2. associate-/l* 94.4%

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

      3. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

      1. clear-num 94.4%

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

      2. inv-pow 94.4%

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

   9. Applied egg-rr 94.4%

      \[\leadsto x \cdot \left(\left(y + a \cdot \color{blue}{{\left(\frac{x}{b}\right)}^{-1}}\right) + t \cdot \frac{z}{x}\right) \]
   10. Step-by-step derivation

       1. unpow-1 94.4%

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

   11. Simplified 94.4%

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

   12. Taylor expanded in a around 0 82.8%

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

   13. Taylor expanded in x around 0 82.7%

       \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if -3.99999999999999983e111 < (*.f64 x y) < 9.9999999999999998e23

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 94.0%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+111} \lor \neg \left(x \cdot y \leq 10^{+24}\right):\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+111}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+42}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -4e+111)
   (+ (* z t) (* x y))
   (if (<= (* x y) 4e+42) (+ (* z t) (* a b)) (+ (* a b) (* x y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4e+111) {
		tmp = (z * t) + (x * y);
	} else if ((x * y) <= 4e+42) {
		tmp = (z * t) + (a * b);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, 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 ((x * y) <= (-4d+111)) then
        tmp = (z * t) + (x * y)
    else if ((x * y) <= 4d+42) then
        tmp = (z * t) + (a * b)
    else
        tmp = (a * b) + (x * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4e+111) {
		tmp = (z * t) + (x * y);
	} else if ((x * y) <= 4e+42) {
		tmp = (z * t) + (a * b);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -4e+111:
		tmp = (z * t) + (x * y)
	elif (x * y) <= 4e+42:
		tmp = (z * t) + (a * b)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -4e+111)
		tmp = Float64(Float64(z * t) + Float64(x * y));
	elseif (Float64(x * y) <= 4e+42)
		tmp = Float64(Float64(z * t) + Float64(a * b));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -4e+111)
		tmp = (z * t) + (x * y);
	elseif ((x * y) <= 4e+42)
		tmp = (z * t) + (a * b);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+111], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+42], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999983e111

   1. Initial program 97.4%

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

      1. fma-define 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.4%

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

      1. associate-+r+ 97.4%

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

      2. associate-/l* 97.3%

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

      3. associate-/l* 97.3%

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

   7. Simplified 97.3%

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

      1. clear-num 97.3%

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

      2. inv-pow 97.3%

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

   9. Applied egg-rr 97.3%

      \[\leadsto x \cdot \left(\left(y + a \cdot \color{blue}{{\left(\frac{x}{b}\right)}^{-1}}\right) + t \cdot \frac{z}{x}\right) \]
   10. Step-by-step derivation

       1. unpow-1 97.3%

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

   11. Simplified 97.3%

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

   12. Taylor expanded in a around 0 95.1%

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

   13. Taylor expanded in x around 0 95.1%

       \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if -3.99999999999999983e111 < (*.f64 x y) < 4.00000000000000018e42

   1. Initial program 99.3%

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

      1. fma-define 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 93.5%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if 4.00000000000000018e42 < (*.f64 x y)

   1. Initial program 95.2%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.3%

      \[\leadsto \color{blue}{x \cdot y} + a \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+111}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+42}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-12} \lor \neg \left(y \leq 8.2 \cdot 10^{+177}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e-12) (not (<= y 8.2e+177))) (* x y) (+ (* z t) (* a b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e-12) || !(y <= 8.2e+177)) {
		tmp = x * y;
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.2d-12)) .or. (.not. (y <= 8.2d+177))) then
        tmp = x * y
    else
        tmp = (z * t) + (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e-12) || !(y <= 8.2e+177)) {
		tmp = x * y;
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e-12) or not (y <= 8.2e+177):
		tmp = x * y
	else:
		tmp = (z * t) + (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e-12) || !(y <= 8.2e+177))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(z * t) + Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e-12) || ~((y <= 8.2e+177)))
		tmp = x * y;
	else
		tmp = (z * t) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e-12], N[Not[LessEqual[y, 8.2e+177]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000002e-12 or 8.20000000000000029e177 < y

   1. Initial program 95.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot y} + a \cdot b \]

   4. Taylor expanded in y around inf 77.7%

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

      1. associate-/l* 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in x around inf 56.2%

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

   if -6.2000000000000002e-12 < y < 8.20000000000000029e177

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.5%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-12} \lor \neg \left(y \leq 8.2 \cdot 10^{+177}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+142} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+34}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -9.5e+142) (not (<= (* a b) 2e+34))) (* a b) (* x y)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -9.5e+142) || !((a * b) <= 2e+34)) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a * b) <= (-9.5d+142)) .or. (.not. ((a * b) <= 2d+34))) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -9.5e+142) || !((a * b) <= 2e+34)) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -9.5e+142) or not ((a * b) <= 2e+34):
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -9.5e+142) || !(Float64(a * b) <= 2e+34))
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a * b) <= -9.5e+142) || ~(((a * b) <= 2e+34)))
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -9.5e+142], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+34]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.50000000000000001e142 or 1.99999999999999989e34 < (*.f64 a b)

   1. Initial program 97.2%

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

      1. fma-define 97.2%

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 70.6%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -9.50000000000000001e142 < (*.f64 a b) < 1.99999999999999989e34

   1. Initial program 98.6%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.6%

      \[\leadsto \color{blue}{x \cdot y} + a \cdot b \]

   4. Taylor expanded in y around inf 58.9%

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

      1. associate-/l* 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in x around inf 45.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+142} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+34}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, 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 * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. fma-define 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 39.5%

   \[\leadsto \color{blue}{a \cdot b} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  (+ (+ (* x y) (* z t)) (* a b)))