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

Percentage Accurate: 98.0% → 99.0%

Time: 3.9s

Alternatives: 9

Speedup: 1.0×

• 33.2% 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: 98.0% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate-+l+ 98.8%

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

   2. fma-def 98.8%

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

   3. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 98.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 54.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+121}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -5.8 \cdot 10^{-184}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -4.5 \cdot 10^{-202}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.4 \cdot 10^{-115}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-71}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.15e+121)
   (* a b)
   (if (<= (* a b) -7.2e-13)
     (* z t)
     (if (<= (* a b) -5.8e-184)
       (* x y)
       (if (<= (* a b) -4.5e-202)
         (* z t)
         (if (<= (* a b) 7.4e-115)
           (* x y)
           (if (<= (* a b) 7.2e-71)
             (* z t)
             (if (<= (* a b) 6.2e+61) (* x y) (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.15e+121) {
		tmp = a * b;
	} else if ((a * b) <= -7.2e-13) {
		tmp = z * t;
	} else if ((a * b) <= -5.8e-184) {
		tmp = x * y;
	} else if ((a * b) <= -4.5e-202) {
		tmp = z * t;
	} else if ((a * b) <= 7.4e-115) {
		tmp = x * y;
	} else if ((a * b) <= 7.2e-71) {
		tmp = z * t;
	} else if ((a * b) <= 6.2e+61) {
		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) <= (-1.15d+121)) then
        tmp = a * b
    else if ((a * b) <= (-7.2d-13)) then
        tmp = z * t
    else if ((a * b) <= (-5.8d-184)) then
        tmp = x * y
    else if ((a * b) <= (-4.5d-202)) then
        tmp = z * t
    else if ((a * b) <= 7.4d-115) then
        tmp = x * y
    else if ((a * b) <= 7.2d-71) then
        tmp = z * t
    else if ((a * b) <= 6.2d+61) 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) <= -1.15e+121) {
		tmp = a * b;
	} else if ((a * b) <= -7.2e-13) {
		tmp = z * t;
	} else if ((a * b) <= -5.8e-184) {
		tmp = x * y;
	} else if ((a * b) <= -4.5e-202) {
		tmp = z * t;
	} else if ((a * b) <= 7.4e-115) {
		tmp = x * y;
	} else if ((a * b) <= 7.2e-71) {
		tmp = z * t;
	} else if ((a * b) <= 6.2e+61) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.15e+121:
		tmp = a * b
	elif (a * b) <= -7.2e-13:
		tmp = z * t
	elif (a * b) <= -5.8e-184:
		tmp = x * y
	elif (a * b) <= -4.5e-202:
		tmp = z * t
	elif (a * b) <= 7.4e-115:
		tmp = x * y
	elif (a * b) <= 7.2e-71:
		tmp = z * t
	elif (a * b) <= 6.2e+61:
		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) <= -1.15e+121)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -7.2e-13)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -5.8e-184)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -4.5e-202)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 7.4e-115)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 7.2e-71)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 6.2e+61)
		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) <= -1.15e+121)
		tmp = a * b;
	elseif ((a * b) <= -7.2e-13)
		tmp = z * t;
	elseif ((a * b) <= -5.8e-184)
		tmp = x * y;
	elseif ((a * b) <= -4.5e-202)
		tmp = z * t;
	elseif ((a * b) <= 7.4e-115)
		tmp = x * y;
	elseif ((a * b) <= 7.2e-71)
		tmp = z * t;
	elseif ((a * b) <= 6.2e+61)
		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], -1.15e+121], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -7.2e-13], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5.8e-184], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.5e-202], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.4e-115], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.2e-71], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.2e+61], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.1499999999999999e121 or 6.1999999999999998e61 < (*.f64 a b)

   1. Initial program 96.2%

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

   2. Taylor expanded in a around inf 76.3%

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

   if -1.1499999999999999e121 < (*.f64 a b) < -7.1999999999999996e-13 or -5.80000000000000028e-184 < (*.f64 a b) < -4.50000000000000039e-202 or 7.4e-115 < (*.f64 a b) < 7.2e-71

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 65.1%

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

   if -7.1999999999999996e-13 < (*.f64 a b) < -5.80000000000000028e-184 or -4.50000000000000039e-202 < (*.f64 a b) < 7.4e-115 or 7.2e-71 < (*.f64 a b) < 6.1999999999999998e61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 62.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+121}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -5.8 \cdot 10^{-184}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -4.5 \cdot 10^{-202}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.4 \cdot 10^{-115}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-71}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{+61}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 4: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+243}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+220} \lor \neg \left(x \leq -2.35 \cdot 10^{+155}\right) \land \left(x \leq -1.9 \cdot 10^{+138} \lor \neg \left(x \leq -6.4 \cdot 10^{+128}\right) \land x \leq 4.3 \cdot 10^{-49}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.8e+243)
   (* x y)
   (if (or (<= x -7.8e+220)
           (and (not (<= x -2.35e+155))
                (or (<= x -1.9e+138)
                    (and (not (<= x -6.4e+128)) (<= x 4.3e-49)))))
     (+ (* a b) (* z t))
     (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+243) {
		tmp = x * y;
	} else if ((x <= -7.8e+220) || (!(x <= -2.35e+155) && ((x <= -1.9e+138) || (!(x <= -6.4e+128) && (x <= 4.3e-49))))) {
		tmp = (a * b) + (z * t);
	} 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 <= (-1.8d+243)) then
        tmp = x * y
    else if ((x <= (-7.8d+220)) .or. (.not. (x <= (-2.35d+155))) .and. (x <= (-1.9d+138)) .or. (.not. (x <= (-6.4d+128))) .and. (x <= 4.3d-49)) then
        tmp = (a * b) + (z * t)
    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 <= -1.8e+243) {
		tmp = x * y;
	} else if ((x <= -7.8e+220) || (!(x <= -2.35e+155) && ((x <= -1.9e+138) || (!(x <= -6.4e+128) && (x <= 4.3e-49))))) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.8e+243:
		tmp = x * y
	elif (x <= -7.8e+220) or (not (x <= -2.35e+155) and ((x <= -1.9e+138) or (not (x <= -6.4e+128) and (x <= 4.3e-49)))):
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.8e+243)
		tmp = Float64(x * y);
	elseif ((x <= -7.8e+220) || (!(x <= -2.35e+155) && ((x <= -1.9e+138) || (!(x <= -6.4e+128) && (x <= 4.3e-49)))))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	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 <= -1.8e+243)
		tmp = x * y;
	elseif ((x <= -7.8e+220) || (~((x <= -2.35e+155)) && ((x <= -1.9e+138) || (~((x <= -6.4e+128)) && (x <= 4.3e-49)))))
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.8e+243], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, -7.8e+220], And[N[Not[LessEqual[x, -2.35e+155]], $MachinePrecision], Or[LessEqual[x, -1.9e+138], And[N[Not[LessEqual[x, -6.4e+128]], $MachinePrecision], LessEqual[x, 4.3e-49]]]]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999998e243 or -7.80000000000000032e220 < x < -2.35000000000000009e155 or -1.90000000000000006e138 < x < -6.39999999999999971e128 or 4.30000000000000016e-49 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 61.5%

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

   if -1.7999999999999998e243 < x < -7.80000000000000032e220 or -2.35000000000000009e155 < x < -1.90000000000000006e138 or -6.39999999999999971e128 < x < 4.30000000000000016e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+243}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+220} \lor \neg \left(x \leq -2.35 \cdot 10^{+155}\right) \land \left(x \leq -1.9 \cdot 10^{+138} \lor \neg \left(x \leq -6.4 \cdot 10^{+128}\right) \land x \leq 4.3 \cdot 10^{-49}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.65 \cdot 10^{+50} \lor \neg \left(a \cdot b \leq 3.7 \cdot 10^{+61}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -2.65e+50) (not (<= (* a b) 3.7e+61)))
   (+ (* a b) (* z t))
   (+ (* z t) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -2.65e+50) || !((a * b) <= 3.7e+61)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (z * t) + (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 (((a * b) <= (-2.65d+50)) .or. (.not. ((a * b) <= 3.7d+61))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (z * t) + (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 (((a * b) <= -2.65e+50) || !((a * b) <= 3.7e+61)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (z * t) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -2.65e+50) or not ((a * b) <= 3.7e+61):
		tmp = (a * b) + (z * t)
	else:
		tmp = (z * t) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -2.65e+50) || !(Float64(a * b) <= 3.7e+61))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(z * t) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a * b) <= -2.65e+50) || ~(((a * b) <= 3.7e+61)))
		tmp = (a * b) + (z * t);
	else
		tmp = (z * t) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2.65e+50], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.7e+61]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.6500000000000001e50 or 3.70000000000000003e61 < (*.f64 a b)

   1. Initial program 96.6%

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

   2. Taylor expanded in x around 0 88.9%

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

   if -2.6500000000000001e50 < (*.f64 a b) < 3.70000000000000003e61

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 95.5%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.65 \cdot 10^{+50} \lor \neg \left(a \cdot b \leq 3.7 \cdot 10^{+61}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \]

Alternative 6: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+31} \lor \neg \left(z \leq 3.4 \cdot 10^{-88}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.55e+31) (not (<= z 3.4e-88)))
   (+ (* a b) (* z t))
   (+ (* a b) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.55e+31) || !(z <= 3.4e-88)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (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 ((z <= (-1.55d+31)) .or. (.not. (z <= 3.4d-88))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (a * b) + (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 ((z <= -1.55e+31) || !(z <= 3.4e-88)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.55e+31) or not (z <= 3.4e-88):
		tmp = (a * b) + (z * t)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.55e+31) || !(z <= 3.4e-88))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.55e+31) || ~((z <= 3.4e-88)))
		tmp = (a * b) + (z * t);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.55e+31], N[Not[LessEqual[z, 3.4e-88]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e31 or 3.39999999999999975e-88 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0 74.2%

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

   if -1.5500000000000001e31 < z < 3.39999999999999975e-88

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.5%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+31} \lor \neg \left(z \leq 3.4 \cdot 10^{-88}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 7: 54.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.15 \cdot 10^{+67}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.2e+122)
   (* a b)
   (if (<= (* a b) 2.15e+67) (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.2e+122) {
		tmp = a * b;
	} else if ((a * b) <= 2.15e+67) {
		tmp = 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) <= (-1.2d+122)) then
        tmp = a * b
    else if ((a * b) <= 2.15d+67) then
        tmp = 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) <= -1.2e+122) {
		tmp = a * b;
	} else if ((a * b) <= 2.15e+67) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.2e+122:
		tmp = a * b
	elif (a * b) <= 2.15e+67:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -1.2e+122)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 2.15e+67)
		tmp = 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) <= -1.2e+122)
		tmp = a * b;
	elseif ((a * b) <= 2.15e+67)
		tmp = 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], -1.2e+122], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.15e+67], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.2000000000000001e122 or 2.1500000000000001e67 < (*.f64 a b)

   1. Initial program 96.1%

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

   2. Taylor expanded in a around inf 78.1%

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

   if -1.2000000000000001e122 < (*.f64 a b) < 2.1500000000000001e67

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 42.5%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.15 \cdot 10^{+67}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((z * t) + (x * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 9: 35.0% 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 98.8%

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

2. Taylor expanded in a around inf 29.1%

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

3. Final simplification 29.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023230 
(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)))