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

Percentage Accurate: 97.4% → 97.4%

Time: 1.4s

Alternatives: 7

Speedup: 1.0×

• 33.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 97.4% 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: 97.4% 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]

Derivation

1. Initial program 98.4%

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

Alternative 2: 54.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.8 \cdot 10^{-180}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.3 \cdot 10^{+48}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -5.5e+53)
   (* x y)
   (if (<= (* x y) -4.8e-180)
     (* a b)
     (if (<= (* x y) 1.2e-35)
       (* z t)
       (if (<= (* x y) 3.3e+48) (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -5.5e+53) {
		tmp = x * y;
	} else if ((x * y) <= -4.8e-180) {
		tmp = a * b;
	} else if ((x * y) <= 1.2e-35) {
		tmp = z * t;
	} else if ((x * y) <= 3.3e+48) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	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 ((x * y) <= (-5.5d+53)) then
        tmp = x * y
    else if ((x * y) <= (-4.8d-180)) then
        tmp = a * b
    else if ((x * y) <= 1.2d-35) then
        tmp = z * t
    else if ((x * y) <= 3.3d+48) then
        tmp = a * b
    else
        tmp = x * y
    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 ((x * y) <= -5.5e+53) {
		tmp = x * y;
	} else if ((x * y) <= -4.8e-180) {
		tmp = a * b;
	} else if ((x * y) <= 1.2e-35) {
		tmp = z * t;
	} else if ((x * y) <= 3.3e+48) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -5.5e+53:
		tmp = x * y
	elif (x * y) <= -4.8e-180:
		tmp = a * b
	elif (x * y) <= 1.2e-35:
		tmp = z * t
	elif (x * y) <= 3.3e+48:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -5.5e+53)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4.8e-180)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 1.2e-35)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 3.3e+48)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -5.5e+53)
		tmp = x * y;
	elseif ((x * y) <= -4.8e-180)
		tmp = a * b;
	elseif ((x * y) <= 1.2e-35)
		tmp = z * t;
	elseif ((x * y) <= 3.3e+48)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.5e+53], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.8e-180], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.2e-35], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.3e+48], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.49999999999999975e53 or 3.30000000000000023e48 < (*.f64 x y)

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 66.6%

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

   if -5.49999999999999975e53 < (*.f64 x y) < -4.79999999999999959e-180 or 1.2000000000000001e-35 < (*.f64 x y) < 3.30000000000000023e48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 57.0%

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

   if -4.79999999999999959e-180 < (*.f64 x y) < 1.2000000000000001e-35

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 59.8%

      \[\leadsto z \cdot \color{blue}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;z \cdot t \leq -3 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -5.2 \cdot 10^{-32}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* z t) -3e+62)
     t_1
     (if (<= (* z t) -5.2e-32)
       (+ (* z t) (* a b))
       (if (<= (* z t) 1.4e+108) (+ (* x y) (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((z * t) <= -3e+62) {
		tmp = t_1;
	} else if ((z * t) <= -5.2e-32) {
		tmp = (z * t) + (a * b);
	} else if ((z * t) <= 1.4e+108) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((z * t) <= (-3d+62)) then
        tmp = t_1
    else if ((z * t) <= (-5.2d-32)) then
        tmp = (z * t) + (a * b)
    else if ((z * t) <= 1.4d+108) then
        tmp = (x * y) + (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((z * t) <= -3e+62) {
		tmp = t_1;
	} else if ((z * t) <= -5.2e-32) {
		tmp = (z * t) + (a * b);
	} else if ((z * t) <= 1.4e+108) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (z * t) <= -3e+62:
		tmp = t_1
	elif (z * t) <= -5.2e-32:
		tmp = (z * t) + (a * b)
	elif (z * t) <= 1.4e+108:
		tmp = (x * y) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -3e+62)
		tmp = t_1;
	elseif (Float64(z * t) <= -5.2e-32)
		tmp = Float64(Float64(z * t) + Float64(a * b));
	elseif (Float64(z * t) <= 1.4e+108)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((z * t) <= -3e+62)
		tmp = t_1;
	elseif ((z * t) <= -5.2e-32)
		tmp = (z * t) + (a * b);
	elseif ((z * t) <= 1.4e+108)
		tmp = (x * y) + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -3e+62], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -5.2e-32], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1.4e+108], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -3e62 or 1.3999999999999999e108 < (*.f64 z t)

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.8%

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

   if -3e62 < (*.f64 z t) < -5.1999999999999995e-32

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.5%

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

   if -5.1999999999999995e-32 < (*.f64 z t) < 1.3999999999999999e108

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.3%

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

Alternative 4: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;z \cdot t \leq -8.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* z t) -8.2e+44)
     t_1
     (if (<= (* z t) 1.4e+108) (+ (* x y) (* a b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((z * t) <= -8.2e+44) {
		tmp = t_1;
	} else if ((z * t) <= 1.4e+108) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((z * t) <= (-8.2d+44)) then
        tmp = t_1
    else if ((z * t) <= 1.4d+108) then
        tmp = (x * y) + (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((z * t) <= -8.2e+44) {
		tmp = t_1;
	} else if ((z * t) <= 1.4e+108) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (z * t) <= -8.2e+44:
		tmp = t_1
	elif (z * t) <= 1.4e+108:
		tmp = (x * y) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -8.2e+44)
		tmp = t_1;
	elseif (Float64(z * t) <= 1.4e+108)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((z * t) <= -8.2e+44)
		tmp = t_1;
	elseif ((z * t) <= 1.4e+108)
		tmp = (x * y) + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -8.2e+44], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1.4e+108], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -8.1999999999999993e44 or 1.3999999999999999e108 < (*.f64 z t)

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 87.4%

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

   if -8.1999999999999993e44 < (*.f64 z t) < 1.3999999999999999e108

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.7%

      \[\leadsto \color{blue}{x \cdot y} + a \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.9 \cdot 10^{+185}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 6.8 \cdot 10^{+171}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.9e+185)
   (* a b)
   (if (<= (* a b) 6.8e+171) (+ (* x y) (* z t)) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.9e+185) {
		tmp = a * b;
	} else if ((a * b) <= 6.8e+171) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = a * 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 ((a * b) <= (-1.9d+185)) then
        tmp = a * b
    else if ((a * b) <= 6.8d+171) then
        tmp = (x * y) + (z * t)
    else
        tmp = a * 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 ((a * b) <= -1.9e+185) {
		tmp = a * b;
	} else if ((a * b) <= 6.8e+171) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.9e+185:
		tmp = a * b
	elif (a * b) <= 6.8e+171:
		tmp = (x * y) + (z * t)
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -1.9e+185)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 6.8e+171)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a * b) <= -1.9e+185)
		tmp = a * b;
	elseif ((a * b) <= 6.8e+171)
		tmp = (x * y) + (z * t);
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.9e+185], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.8e+171], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.8999999999999999e185 or 6.8000000000000003e171 < (*.f64 a b)

   1. Initial program 93.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 23.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 85.9%

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

   if -1.8999999999999999e185 < (*.f64 a b) < 6.8000000000000003e171

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.3%

      \[\leadsto \color{blue}{x \cdot y + z \cdot t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 53.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.8 \cdot 10^{+104}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -8.8e+104)
   (* a b)
   (if (<= (* a b) 1.15e-22) (* x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8.8e+104) {
		tmp = a * b;
	} else if ((a * b) <= 1.15e-22) {
		tmp = x * y;
	} else {
		tmp = a * 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 ((a * b) <= (-8.8d+104)) then
        tmp = a * b
    else if ((a * b) <= 1.15d-22) then
        tmp = x * y
    else
        tmp = a * 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 ((a * b) <= -8.8e+104) {
		tmp = a * b;
	} else if ((a * b) <= 1.15e-22) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -8.8e+104:
		tmp = a * b
	elif (a * b) <= 1.15e-22:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -8.8e+104)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.15e-22)
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a * b) <= -8.8e+104)
		tmp = a * b;
	elseif ((a * b) <= 1.15e-22)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -8.8e+104], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.15e-22], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8.80000000000000002e104 or 1.1499999999999999e-22 < (*.f64 a b)

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 64.7%

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

   if -8.80000000000000002e104 < (*.f64 a b) < 1.1499999999999999e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 50.5%

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

Alternative 7: 35.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 69.7%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 34.1%

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  :pre (TRUE)
  (+ (+ (* x y) (* z t)) (* a b)))