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

Percentage Accurate: 97.7% → 97.7%

Time: 1.4s

Alternatives: 7

Speedup: 1.0×

• 32.6% 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: 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]

Derivation

1. Initial program 96.5%

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

Alternative 2: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+198}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.9 \cdot 10^{+62}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-208}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-158}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{+118}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.3e+198)
   (* x y)
   (if (<= (* x y) -4.9e+62)
     (* z t)
     (if (<= (* x y) -2.6e-208)
       (* a b)
       (if (<= (* x y) 7.6e-158)
         (* z t)
         (if (<= (* x y) 7.6e+118) (* a b) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.3e+198) {
		tmp = x * y;
	} else if ((x * y) <= -4.9e+62) {
		tmp = z * t;
	} else if ((x * y) <= -2.6e-208) {
		tmp = a * b;
	} else if ((x * y) <= 7.6e-158) {
		tmp = z * t;
	} else if ((x * y) <= 7.6e+118) {
		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) <= (-1.3d+198)) then
        tmp = x * y
    else if ((x * y) <= (-4.9d+62)) then
        tmp = z * t
    else if ((x * y) <= (-2.6d-208)) then
        tmp = a * b
    else if ((x * y) <= 7.6d-158) then
        tmp = z * t
    else if ((x * y) <= 7.6d+118) 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) <= -1.3e+198) {
		tmp = x * y;
	} else if ((x * y) <= -4.9e+62) {
		tmp = z * t;
	} else if ((x * y) <= -2.6e-208) {
		tmp = a * b;
	} else if ((x * y) <= 7.6e-158) {
		tmp = z * t;
	} else if ((x * y) <= 7.6e+118) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.3e+198:
		tmp = x * y
	elif (x * y) <= -4.9e+62:
		tmp = z * t
	elif (x * y) <= -2.6e-208:
		tmp = a * b
	elif (x * y) <= 7.6e-158:
		tmp = z * t
	elif (x * y) <= 7.6e+118:
		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) <= -1.3e+198)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4.9e+62)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -2.6e-208)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 7.6e-158)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 7.6e+118)
		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) <= -1.3e+198)
		tmp = x * y;
	elseif ((x * y) <= -4.9e+62)
		tmp = z * t;
	elseif ((x * y) <= -2.6e-208)
		tmp = a * b;
	elseif ((x * y) <= 7.6e-158)
		tmp = z * t;
	elseif ((x * y) <= 7.6e+118)
		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], -1.3e+198], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.9e+62], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.6e-208], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.6e-158], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.6e+118], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.2999999999999999e198 or 7.60000000000000033e118 < (*.f64 x y)

   1. Initial program 89.6%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 85.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.8%

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

   if -1.2999999999999999e198 < (*.f64 x y) < -4.8999999999999997e62 or -2.60000000000000017e-208 < (*.f64 x y) < 7.5999999999999998e-158

   1. Initial program 98.8%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 69.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 59.0%

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

   if -4.8999999999999997e62 < (*.f64 x y) < -2.60000000000000017e-208 or 7.5999999999999998e-158 < (*.f64 x y) < 7.60000000000000033e118

   1. Initial program 99.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 44.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 58.5%

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

Alternative 3: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.3 \cdot 10^{+114}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* x y) -8e+78)
     t_1
     (if (<= (* x y) 4.3e+114) (+ (* z t) (* 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 ((x * y) <= -8e+78) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e+114) {
		tmp = (z * t) + (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 ((x * y) <= (-8d+78)) then
        tmp = t_1
    else if ((x * y) <= 4.3d+114) then
        tmp = (z * t) + (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 ((x * y) <= -8e+78) {
		tmp = t_1;
	} else if ((x * y) <= 4.3e+114) {
		tmp = (z * t) + (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 (x * y) <= -8e+78:
		tmp = t_1
	elif (x * y) <= 4.3e+114:
		tmp = (z * t) + (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(x * y) <= -8e+78)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.3e+114)
		tmp = Float64(Float64(z * t) + 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 ((x * y) <= -8e+78)
		tmp = t_1;
	elseif ((x * y) <= 4.3e+114)
		tmp = (z * t) + (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[(x * y), $MachinePrecision], -8e+78], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.3e+114], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -8.00000000000000007e78 or 4.3000000000000001e114 < (*.f64 x y)

   1. Initial program 90.6%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 -8.00000000000000007e78 < (*.f64 x y) < 4.3000000000000001e114

   1. Initial program 99.4%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 88.9%

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

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;z \cdot t \leq -300000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 6.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* z t) -300000000000.0)
     t_1
     (if (<= (* z t) 6.2e+138) (+ (* 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) <= -300000000000.0) {
		tmp = t_1;
	} else if ((z * t) <= 6.2e+138) {
		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) <= (-300000000000.0d0)) then
        tmp = t_1
    else if ((z * t) <= 6.2d+138) 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) <= -300000000000.0) {
		tmp = t_1;
	} else if ((z * t) <= 6.2e+138) {
		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) <= -300000000000.0:
		tmp = t_1
	elif (z * t) <= 6.2e+138:
		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) <= -300000000000.0)
		tmp = t_1;
	elseif (Float64(z * t) <= 6.2e+138)
		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) <= -300000000000.0)
		tmp = t_1;
	elseif ((z * t) <= 6.2e+138)
		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], -300000000000.0], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 6.2e+138], 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) < -3e11 or 6.1999999999999995e138 < (*.f64 z t)

   1. Initial program 93.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 82.5%

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

   if -3e11 < (*.f64 z t) < 6.1999999999999995e138

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.2%

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

Alternative 5: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.5 \cdot 10^{+256}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+142}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -5.5e+256)
   (* a b)
   (if (<= (* a b) 4.8e+142) (+ (* 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) <= -5.5e+256) {
		tmp = a * b;
	} else if ((a * b) <= 4.8e+142) {
		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) <= (-5.5d+256)) then
        tmp = a * b
    else if ((a * b) <= 4.8d+142) 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) <= -5.5e+256) {
		tmp = a * b;
	} else if ((a * b) <= 4.8e+142) {
		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) <= -5.5e+256:
		tmp = a * b
	elif (a * b) <= 4.8e+142:
		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) <= -5.5e+256)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 4.8e+142)
		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) <= -5.5e+256)
		tmp = a * b;
	elseif ((a * b) <= 4.8e+142)
		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], -5.5e+256], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.8e+142], 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) < -5.4999999999999998e256 or 4.7999999999999998e142 < (*.f64 a b)

   1. Initial program 90.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 23.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 84.2%

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

   if -5.4999999999999998e256 < (*.f64 a b) < 4.7999999999999998e142

   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 77.2%

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

Alternative 6: 53.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{+118}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2.05e+63)
   (* x y)
   (if (<= (* x y) 7.6e+118) (* a b) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -2.05e+63) {
		tmp = x * y;
	} else if ((x * y) <= 7.6e+118) {
		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) <= (-2.05d+63)) then
        tmp = x * y
    else if ((x * y) <= 7.6d+118) 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) <= -2.05e+63) {
		tmp = x * y;
	} else if ((x * y) <= 7.6e+118) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -2.05e+63:
		tmp = x * y
	elif (x * y) <= 7.6e+118:
		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) <= -2.05e+63)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 7.6e+118)
		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) <= -2.05e+63)
		tmp = x * y;
	elseif ((x * y) <= 7.6e+118)
		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], -2.05e+63], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.6e+118], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.04999999999999996e63 or 7.60000000000000033e118 < (*.f64 x y)

   1. Initial program 90.8%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 87.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.4%

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

   if -2.04999999999999996e63 < (*.f64 x y) < 7.60000000000000033e118

   1. Initial program 99.4%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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 50.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 53.2%

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

Alternative 7: 35.3% 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 96.5%

   \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
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 63.3%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 39.0%

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

Reproduce

herbie shell --seed 2024313 
(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)))