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

Percentage Accurate: 97.7% → 98.5%

Time: 3.3s

Alternatives: 7

Speedup: 0.5×

• 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: 98.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))))
   (if (<= t_1 INFINITY) t_1 (* x y))))

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + ((x * y) + (z * t));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

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

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

   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. Taylor expanded in x around inf 57.1%

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

   3. Taylor expanded in y around inf 71.5%

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

4. Final simplification 99.2%

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

Alternative 2: 98.8% 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 97.2%

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

   1. associate-+l+ 97.2%

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

   2. fma-def 97.6%

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

   3. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 48.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-110}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-141}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-218}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.7e+36)
   (* x y)
   (if (<= x -1.55e-53)
     (* a b)
     (if (<= x -2.2e-110)
       (* z t)
       (if (<= x -1.95e-141)
         (* a b)
         (if (<= x -8.5e-218) (* z t) (if (<= x 3.7e+15) (* a b) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.7e+36) {
		tmp = x * y;
	} else if (x <= -1.55e-53) {
		tmp = a * b;
	} else if (x <= -2.2e-110) {
		tmp = z * t;
	} else if (x <= -1.95e-141) {
		tmp = a * b;
	} else if (x <= -8.5e-218) {
		tmp = z * t;
	} else if (x <= 3.7e+15) {
		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 <= (-4.7d+36)) then
        tmp = x * y
    else if (x <= (-1.55d-53)) then
        tmp = a * b
    else if (x <= (-2.2d-110)) then
        tmp = z * t
    else if (x <= (-1.95d-141)) then
        tmp = a * b
    else if (x <= (-8.5d-218)) then
        tmp = z * t
    else if (x <= 3.7d+15) 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 <= -4.7e+36) {
		tmp = x * y;
	} else if (x <= -1.55e-53) {
		tmp = a * b;
	} else if (x <= -2.2e-110) {
		tmp = z * t;
	} else if (x <= -1.95e-141) {
		tmp = a * b;
	} else if (x <= -8.5e-218) {
		tmp = z * t;
	} else if (x <= 3.7e+15) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.7e+36:
		tmp = x * y
	elif x <= -1.55e-53:
		tmp = a * b
	elif x <= -2.2e-110:
		tmp = z * t
	elif x <= -1.95e-141:
		tmp = a * b
	elif x <= -8.5e-218:
		tmp = z * t
	elif x <= 3.7e+15:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.7e+36)
		tmp = Float64(x * y);
	elseif (x <= -1.55e-53)
		tmp = Float64(a * b);
	elseif (x <= -2.2e-110)
		tmp = Float64(z * t);
	elseif (x <= -1.95e-141)
		tmp = Float64(a * b);
	elseif (x <= -8.5e-218)
		tmp = Float64(z * t);
	elseif (x <= 3.7e+15)
		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 <= -4.7e+36)
		tmp = x * y;
	elseif (x <= -1.55e-53)
		tmp = a * b;
	elseif (x <= -2.2e-110)
		tmp = z * t;
	elseif (x <= -1.95e-141)
		tmp = a * b;
	elseif (x <= -8.5e-218)
		tmp = z * t;
	elseif (x <= 3.7e+15)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.7e+36], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.55e-53], N[(a * b), $MachinePrecision], If[LessEqual[x, -2.2e-110], N[(z * t), $MachinePrecision], If[LessEqual[x, -1.95e-141], N[(a * b), $MachinePrecision], If[LessEqual[x, -8.5e-218], N[(z * t), $MachinePrecision], If[LessEqual[x, 3.7e+15], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.69999999999999989e36 or 3.7e15 < x

   1. Initial program 94.6%

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

   2. Taylor expanded in x around inf 73.7%

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

   3. Taylor expanded in y around inf 64.1%

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

   if -4.69999999999999989e36 < x < -1.55000000000000008e-53 or -2.1999999999999999e-110 < x < -1.9499999999999999e-141 or -8.5000000000000004e-218 < x < 3.7e15

   1. Initial program 99.1%

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

   2. Taylor expanded in a around inf 55.8%

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

   if -1.55000000000000008e-53 < x < -2.1999999999999999e-110 or -1.9499999999999999e-141 < x < -8.5000000000000004e-218

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.6%

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

   3. Taylor expanded in t around inf 66.1%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-110}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-141}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-218}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.85e+31) (* a b) (if (<= (* a b) 4.4e-35) (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.85e+31) {
		tmp = a * b;
	} else if ((a * b) <= 4.4e-35) {
		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) <= (-1.85d+31)) then
        tmp = a * b
    else if ((a * b) <= 4.4d-35) 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) <= -1.85e+31) {
		tmp = a * b;
	} else if ((a * b) <= 4.4e-35) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.85e+31:
		tmp = a * b
	elif (a * b) <= 4.4e-35:
		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) <= -1.85e+31)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 4.4e-35)
		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) <= -1.85e+31)
		tmp = a * b;
	elseif ((a * b) <= 4.4e-35)
		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], -1.85e+31], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.4e-35], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.8499999999999999e31 or 4.39999999999999987e-35 < (*.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 59.8%

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

   if -1.8499999999999999e31 < (*.f64 a b) < 4.39999999999999987e-35

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 53.6%

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

   3. Taylor expanded in t around inf 47.5%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 5: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.6e-54) (* x y) (if (<= y 5.2e+97) (+ (* a b) (* z t)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.6e-54) {
		tmp = x * y;
	} else if (y <= 5.2e+97) {
		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 (y <= (-6.6d-54)) then
        tmp = x * y
    else if (y <= 5.2d+97) 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 (y <= -6.6e-54) {
		tmp = x * y;
	} else if (y <= 5.2e+97) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.6e-54:
		tmp = x * y
	elif y <= 5.2e+97:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.6e-54)
		tmp = Float64(x * y);
	elseif (y <= 5.2e+97)
		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 (y <= -6.6e-54)
		tmp = x * y;
	elseif (y <= 5.2e+97)
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.6e-54], N[(x * y), $MachinePrecision], If[LessEqual[y, 5.2e+97], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.59999999999999986e-54 or 5.2e97 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 78.3%

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

   3. Taylor expanded in y around inf 58.2%

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

   if -6.59999999999999986e-54 < y < 5.2e97

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 71.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+96}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.6e-54)
   (* x y)
   (if (<= y 7.2e+96) (+ (* 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 (y <= -6.6e-54) {
		tmp = x * y;
	} else if (y <= 7.2e+96) {
		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 (y <= (-6.6d-54)) then
        tmp = x * y
    else if (y <= 7.2d+96) 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 (y <= -6.6e-54) {
		tmp = x * y;
	} else if (y <= 7.2e+96) {
		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 y <= -6.6e-54:
		tmp = x * y
	elif y <= 7.2e+96:
		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 (y <= -6.6e-54)
		tmp = Float64(x * y);
	elseif (y <= 7.2e+96)
		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 (y <= -6.6e-54)
		tmp = x * y;
	elseif (y <= 7.2e+96)
		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[LessEqual[y, -6.6e-54], N[(x * y), $MachinePrecision], If[LessEqual[y, 7.2e+96], 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 3 regimes

2. if y < -6.59999999999999986e-54

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 78.2%

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

   3. Taylor expanded in y around inf 61.9%

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

   if -6.59999999999999986e-54 < y < 7.20000000000000026e96

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.4%

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

   if 7.20000000000000026e96 < y

   1. Initial program 90.9%

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

   2. Taylor expanded in x around inf 78.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+96}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

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 97.2%

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

2. Taylor expanded in a around inf 34.7%

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

3. Final simplification 34.7%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023195 
(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)))