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

Percentage Accurate: 97.7% → 98.9%

Time: 6.7s

Alternatives: 10

Speedup: 1.0×

• 32.7% 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: 98.9% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 98.4%

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

   3. fma-define 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. fma-define 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{-180}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{-115}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.1e+77)
   (* x y)
   (if (<= (* x y) 5.8e-180)
     (* z t)
     (if (<= (* x y) 2.6e-115)
       (* a b)
       (if (<= (* x y) 1.35e+129) (* z t) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.1e+77) {
		tmp = x * y;
	} else if ((x * y) <= 5.8e-180) {
		tmp = z * t;
	} else if ((x * y) <= 2.6e-115) {
		tmp = a * b;
	} else if ((x * y) <= 1.35e+129) {
		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) <= (-1.1d+77)) then
        tmp = x * y
    else if ((x * y) <= 5.8d-180) then
        tmp = z * t
    else if ((x * y) <= 2.6d-115) then
        tmp = a * b
    else if ((x * y) <= 1.35d+129) 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) <= -1.1e+77) {
		tmp = x * y;
	} else if ((x * y) <= 5.8e-180) {
		tmp = z * t;
	} else if ((x * y) <= 2.6e-115) {
		tmp = a * b;
	} else if ((x * y) <= 1.35e+129) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.1e+77:
		tmp = x * y
	elif (x * y) <= 5.8e-180:
		tmp = z * t
	elif (x * y) <= 2.6e-115:
		tmp = a * b
	elif (x * y) <= 1.35e+129:
		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) <= -1.1e+77)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 5.8e-180)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.6e-115)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 1.35e+129)
		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) <= -1.1e+77)
		tmp = x * y;
	elseif ((x * y) <= 5.8e-180)
		tmp = z * t;
	elseif ((x * y) <= 2.6e-115)
		tmp = a * b;
	elseif ((x * y) <= 1.35e+129)
		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], -1.1e+77], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.8e-180], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.6e-115], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.35e+129], N[(z * t), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.1e77 or 1.35e129 < (*.f64 x y)

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 77.3%

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

   if -1.1e77 < (*.f64 x y) < 5.79999999999999961e-180 or 2.60000000000000004e-115 < (*.f64 x y) < 1.35e129

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 53.0%

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

   if 5.79999999999999961e-180 < (*.f64 x y) < 2.60000000000000004e-115

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 87.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{-180}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{-115}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+17}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 10^{+37}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* z t) -1e+17)
   (+ (* a b) (* z t))
   (if (<= (* z t) 1e+37) (+ (* a b) (* x y)) (* z (+ t (/ (* x y) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * t) <= -1e+17) {
		tmp = (a * b) + (z * t);
	} else if ((z * t) <= 1e+37) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = z * (t + ((x * y) / z));
	}
	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 * t) <= (-1d+17)) then
        tmp = (a * b) + (z * t)
    else if ((z * t) <= 1d+37) then
        tmp = (a * b) + (x * y)
    else
        tmp = z * (t + ((x * y) / z))
    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 * t) <= -1e+17) {
		tmp = (a * b) + (z * t);
	} else if ((z * t) <= 1e+37) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = z * (t + ((x * y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z * t) <= -1e+17:
		tmp = (a * b) + (z * t)
	elif (z * t) <= 1e+37:
		tmp = (a * b) + (x * y)
	else:
		tmp = z * (t + ((x * y) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * t) <= -1e+17)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(z * t) <= 1e+37)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(z * Float64(t + Float64(Float64(x * y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z * t) <= -1e+17)
		tmp = (a * b) + (z * t);
	elseif ((z * t) <= 1e+37)
		tmp = (a * b) + (x * y);
	else
		tmp = z * (t + ((x * y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+17], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+37], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1e17

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 84.8%

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

   if -1e17 < (*.f64 z t) < 9.99999999999999954e36

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 88.4%

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

   if 9.99999999999999954e36 < (*.f64 z t)

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 98.1%

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

   4. Taylor expanded in a around 0 91.3%

      \[\leadsto \color{blue}{z \cdot \left(t + \frac{x \cdot y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+17}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 10^{+37}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+84} \lor \neg \left(x \cdot y \leq 2.1 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -7e+84) (not (<= (* x y) 2.1e+131)))
   (* x y)
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -7e+84) || !((x * y) <= 2.1e+131)) {
		tmp = x * y;
	} 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) <= (-7d+84)) .or. (.not. ((x * y) <= 2.1d+131))) then
        tmp = x * y
    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) <= -7e+84) || !((x * y) <= 2.1e+131)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -7e+84) or not ((x * y) <= 2.1e+131):
		tmp = x * y
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -7e+84) || !(Float64(x * y) <= 2.1e+131))
		tmp = Float64(x * y);
	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) <= -7e+84) || ~(((x * y) <= 2.1e+131)))
		tmp = x * y;
	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], -7e+84], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.1e+131]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -6.9999999999999998e84 or 2.09999999999999985e131 < (*.f64 x y)

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -6.9999999999999998e84 < (*.f64 x y) < 2.09999999999999985e131

   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 87.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+84} \lor \neg \left(x \cdot y \leq 2.1 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+129}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -4e+75) (not (<= (* x y) 1.35e+129)))
   (+ (* a b) (* x y))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -4e+75) || !((x * y) <= 1.35e+129)) {
		tmp = (a * b) + (x * y);
	} 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) <= (-4d+75)) .or. (.not. ((x * y) <= 1.35d+129))) then
        tmp = (a * b) + (x * y)
    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) <= -4e+75) || !((x * y) <= 1.35e+129)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -4e+75) or not ((x * y) <= 1.35e+129):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -4e+75) || !(Float64(x * y) <= 1.35e+129))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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) <= -4e+75) || ~(((x * y) <= 1.35e+129)))
		tmp = (a * b) + (x * y);
	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], -4e+75], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.35e+129]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.99999999999999971e75 or 1.35e129 < (*.f64 x y)

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0 88.3%

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

   if -3.99999999999999971e75 < (*.f64 x y) < 1.35e129

   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 87.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+75} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+129}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+17}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* z t) -1e+17)
   (+ (* a b) (* z t))
   (if (<= (* z t) 2e+27) (+ (* a b) (* x y)) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z * t) <= -1e+17) {
		tmp = (a * b) + (z * t);
	} else if ((z * t) <= 2e+27) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (x * y) + (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 ((z * t) <= (-1d+17)) then
        tmp = (a * b) + (z * t)
    else if ((z * t) <= 2d+27) then
        tmp = (a * b) + (x * y)
    else
        tmp = (x * y) + (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 ((z * t) <= -1e+17) {
		tmp = (a * b) + (z * t);
	} else if ((z * t) <= 2e+27) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z * t) <= -1e+17:
		tmp = (a * b) + (z * t)
	elif (z * t) <= 2e+27:
		tmp = (a * b) + (x * y)
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(z * t) <= -1e+17)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(z * t) <= 2e+27)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(x * y) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z * t) <= -1e+17)
		tmp = (a * b) + (z * t);
	elseif ((z * t) <= 2e+27)
		tmp = (a * b) + (x * y);
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+17], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+27], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1e17

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 84.8%

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

   if -1e17 < (*.f64 z t) < 2e27

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 88.3%

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

   if 2e27 < (*.f64 z t)

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 89.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+17}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+27}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+231} \lor \neg \left(a \cdot b \leq 2.25 \cdot 10^{+106}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -1.7e+231) (not (<= (* a b) 2.25e+106))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -1.7e+231) || !((a * b) <= 2.25e+106)) {
		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 * b) <= (-1.7d+231)) .or. (.not. ((a * b) <= 2.25d+106))) 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 * b) <= -1.7e+231) || !((a * b) <= 2.25e+106)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -1.7e+231) or not ((a * b) <= 2.25e+106):
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -1.7e+231) || !(Float64(a * b) <= 2.25e+106))
		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 * b) <= -1.7e+231) || ~(((a * b) <= 2.25e+106)))
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.7e+231], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.25e+106]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.7e231 or 2.2499999999999998e106 < (*.f64 a b)

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 78.2%

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

   if -1.7e231 < (*.f64 a b) < 2.2499999999999998e106

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 45.2%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+231} \lor \neg \left(a \cdot b \leq 2.25 \cdot 10^{+106}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 97.6%

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

3. Final simplification 97.6%

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

Alternative 10: 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 97.6%

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

3. Taylor expanded in a around inf 33.8%

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

4. Final simplification 33.8%

   \[\leadsto a \cdot b \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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)))