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

Percentage Accurate: 97.7% → 99.0%

Time: 5.0s

Alternatives: 10

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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * y) + (z * t)) + (a * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% 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 97.3%

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

   1. associate-+l+ 97.3%

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

   2. fma-def 98.0%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. +-commutative 97.3%

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

   2. fma-def 98.0%

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

   3. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 98.2% 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 97.3%

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

   1. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 4: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-111}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-84}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2.2e+86)
   (* x y)
   (if (<= (* x y) -1.7e-111)
     (* z t)
     (if (<= (* x y) 7.6e-84)
       (* a b)
       (if (<= (* x y) 3.9e+36) (* z t) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -2.2e+86) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e-111) {
		tmp = z * t;
	} else if ((x * y) <= 7.6e-84) {
		tmp = a * b;
	} else if ((x * y) <= 3.9e+36) {
		tmp = 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 * y) <= (-2.2d+86)) then
        tmp = x * y
    else if ((x * y) <= (-1.7d-111)) then
        tmp = z * t
    else if ((x * y) <= 7.6d-84) then
        tmp = a * b
    else if ((x * y) <= 3.9d+36) then
        tmp = 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 * y) <= -2.2e+86) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e-111) {
		tmp = z * t;
	} else if ((x * y) <= 7.6e-84) {
		tmp = a * b;
	} else if ((x * y) <= 3.9e+36) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -2.2e+86:
		tmp = x * y
	elif (x * y) <= -1.7e-111:
		tmp = z * t
	elif (x * y) <= 7.6e-84:
		tmp = a * b
	elif (x * y) <= 3.9e+36:
		tmp = z * t
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -2.2e+86)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.7e-111)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 7.6e-84)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 3.9e+36)
		tmp = 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 * y) <= -2.2e+86)
		tmp = x * y;
	elseif ((x * y) <= -1.7e-111)
		tmp = z * t;
	elseif ((x * y) <= 7.6e-84)
		tmp = a * b;
	elseif ((x * y) <= 3.9e+36)
		tmp = z * t;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.2e+86], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.7e-111], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.6e-84], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.9e+36], N[(z * t), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.20000000000000003e86 or 3.90000000000000021e36 < (*.f64 x y)

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 72.2%

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

   if -2.20000000000000003e86 < (*.f64 x y) < -1.69999999999999998e-111 or 7.59999999999999971e-84 < (*.f64 x y) < 3.90000000000000021e36

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 61.5%

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

   if -1.69999999999999998e-111 < (*.f64 x y) < 7.59999999999999971e-84

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 58.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-111}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-84}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+52} \lor \neg \left(x \cdot y \leq 1.7 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.2e+52) (not (<= (* x y) 1.7e+91)))
   (+ (* x y) (* z t))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -3.2e+52) || !((x * y) <= 1.7e+91)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (a * b) + (z * t);
	}
	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) <= (-3.2d+52)) .or. (.not. ((x * y) <= 1.7d+91))) then
        tmp = (x * y) + (z * t)
    else
        tmp = (a * b) + (z * t)
    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) <= -3.2e+52) || !((x * y) <= 1.7e+91)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -3.2e+52) or not ((x * y) <= 1.7e+91):
		tmp = (x * y) + (z * t)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -3.2e+52) || !(Float64(x * y) <= 1.7e+91))
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -3.2e+52) || ~(((x * y) <= 1.7e+91)))
		tmp = (x * y) + (z * t);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.2e+52], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.7e+91]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.2e52 or 1.7e91 < (*.f64 x y)

   1. Initial program 93.1%

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

   2. Taylor expanded in a around 0 87.4%

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

   if -3.2e52 < (*.f64 x y) < 1.7e91

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+52} \lor \neg \left(x \cdot y \leq 1.7 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -5.2e+89)
   (* x y)
   (if (<= (* x y) 6.6e+156) (+ (* 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 * y) <= -5.2e+89) {
		tmp = x * y;
	} else if ((x * y) <= 6.6e+156) {
		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 * y) <= (-5.2d+89)) then
        tmp = x * y
    else if ((x * y) <= 6.6d+156) 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 * y) <= -5.2e+89) {
		tmp = x * y;
	} else if ((x * y) <= 6.6e+156) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -5.2e+89:
		tmp = x * y
	elif (x * y) <= 6.6e+156:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -5.2e+89)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 6.6e+156)
		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 * y) <= -5.2e+89)
		tmp = x * y;
	elseif ((x * y) <= 6.6e+156)
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.2e+89], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.6e+156], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.2000000000000001e89 or 6.5999999999999997e156 < (*.f64 x y)

   1. Initial program 93.7%

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

   2. Taylor expanded in x around inf 81.4%

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

   if -5.2000000000000001e89 < (*.f64 x y) < 6.5999999999999997e156

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 85.5%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -5.2e+53)
   (+ (* a b) (* x y))
   (if (<= (* x y) 5e+156) (+ (* 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 * y) <= -5.2e+53) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 5e+156) {
		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 * y) <= (-5.2d+53)) then
        tmp = (a * b) + (x * y)
    else if ((x * y) <= 5d+156) 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 * y) <= -5.2e+53) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 5e+156) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -5.2e+53:
		tmp = (a * b) + (x * y)
	elif (x * y) <= 5e+156:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -5.2e+53)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(x * y) <= 5e+156)
		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 * y) <= -5.2e+53)
		tmp = (a * b) + (x * y);
	elseif ((x * y) <= 5e+156)
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.2e+53], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+156], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.19999999999999996e53

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0 81.0%

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

   if -5.19999999999999996e53 < (*.f64 x y) < 4.99999999999999992e156

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.6%

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

   if 4.99999999999999992e156 < (*.f64 x y)

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf 90.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Final simplification 97.3%

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

Alternative 9: 47.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+59} \lor \neg \left(a \leq 3.4 \cdot 10^{-145}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.2e+59) (not (<= a 3.4e-145))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.2e+59) || !(a <= 3.4e-145)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	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 <= (-6.2d+59)) .or. (.not. (a <= 3.4d-145))) then
        tmp = a * b
    else
        tmp = z * t
    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 <= -6.2e+59) || !(a <= 3.4e-145)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.2e+59) or not (a <= 3.4e-145):
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.2e+59) || !(a <= 3.4e-145))
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.2e+59) || ~((a <= 3.4e-145)))
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.2e+59], N[Not[LessEqual[a, 3.4e-145]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.20000000000000029e59 or 3.3999999999999999e-145 < a

   1. Initial program 95.8%

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

   2. Taylor expanded in a around inf 50.2%

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

   if -6.20000000000000029e59 < a < 3.3999999999999999e-145

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 44.2%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+59} \lor \neg \left(a \leq 3.4 \cdot 10^{-145}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 10: 35.8% 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 97.3%

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

2. Taylor expanded in a around inf 34.1%

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

3. Final simplification 34.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023293 
(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)))