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

Percentage Accurate: 97.7% → 98.9%

Time: 4.8s

Alternatives: 8

Speedup: 1.0×

• 32.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l+ 98.0%

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

   2. fma-def 98.4%

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

   3. +-commutative 98.4%

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

   4. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 98.2% 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 98.0%

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

   1. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-101}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -9.5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{-184}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.1 \cdot 10^{-149}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -8.2e+99)
   (* a b)
   (if (<= (* a b) -2.3e-101)
     (* z t)
     (if (<= (* a b) -9.5e-157)
       (* x y)
       (if (<= (* a b) 1.3e-184)
         (* z t)
         (if (<= (* a b) 3.1e-149)
           (* x y)
           (if (<= (* a b) 2.8e+54) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8.2e+99) {
		tmp = a * b;
	} else if ((a * b) <= -2.3e-101) {
		tmp = z * t;
	} else if ((a * b) <= -9.5e-157) {
		tmp = x * y;
	} else if ((a * b) <= 1.3e-184) {
		tmp = z * t;
	} else if ((a * b) <= 3.1e-149) {
		tmp = x * y;
	} else if ((a * b) <= 2.8e+54) {
		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) <= (-8.2d+99)) then
        tmp = a * b
    else if ((a * b) <= (-2.3d-101)) then
        tmp = z * t
    else if ((a * b) <= (-9.5d-157)) then
        tmp = x * y
    else if ((a * b) <= 1.3d-184) then
        tmp = z * t
    else if ((a * b) <= 3.1d-149) then
        tmp = x * y
    else if ((a * b) <= 2.8d+54) 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) <= -8.2e+99) {
		tmp = a * b;
	} else if ((a * b) <= -2.3e-101) {
		tmp = z * t;
	} else if ((a * b) <= -9.5e-157) {
		tmp = x * y;
	} else if ((a * b) <= 1.3e-184) {
		tmp = z * t;
	} else if ((a * b) <= 3.1e-149) {
		tmp = x * y;
	} else if ((a * b) <= 2.8e+54) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -8.2e+99:
		tmp = a * b
	elif (a * b) <= -2.3e-101:
		tmp = z * t
	elif (a * b) <= -9.5e-157:
		tmp = x * y
	elif (a * b) <= 1.3e-184:
		tmp = z * t
	elif (a * b) <= 3.1e-149:
		tmp = x * y
	elif (a * b) <= 2.8e+54:
		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) <= -8.2e+99)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.3e-101)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -9.5e-157)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.3e-184)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 3.1e-149)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.8e+54)
		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) <= -8.2e+99)
		tmp = a * b;
	elseif ((a * b) <= -2.3e-101)
		tmp = z * t;
	elseif ((a * b) <= -9.5e-157)
		tmp = x * y;
	elseif ((a * b) <= 1.3e-184)
		tmp = z * t;
	elseif ((a * b) <= 3.1e-149)
		tmp = x * y;
	elseif ((a * b) <= 2.8e+54)
		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], -8.2e+99], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.3e-101], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -9.5e-157], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.3e-184], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.1e-149], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.8e+54], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.19999999999999959e99 or 2.80000000000000015e54 < (*.f64 a b)

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf 69.3%

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

   if -8.19999999999999959e99 < (*.f64 a b) < -2.2999999999999999e-101 or -9.50000000000000019e-157 < (*.f64 a b) < 1.29999999999999989e-184 or 3.09999999999999987e-149 < (*.f64 a b) < 2.80000000000000015e54

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 69.2%

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

   3. Taylor expanded in t around inf 56.3%

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

   if -2.2999999999999999e-101 < (*.f64 a b) < -9.50000000000000019e-157 or 1.29999999999999989e-184 < (*.f64 a b) < 3.09999999999999987e-149

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 73.7%

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

   3. Taylor expanded in x around inf 72.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-101}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -9.5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{-184}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.1 \cdot 10^{-149}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 4: 80.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+183} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -2.05e+183) (not (<= (* x y) 2.4e+147)))
   (* 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) <= -2.05e+183) || !((x * y) <= 2.4e+147)) {
		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) <= (-2.05d+183)) .or. (.not. ((x * y) <= 2.4d+147))) 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) <= -2.05e+183) || !((x * y) <= 2.4e+147)) {
		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) <= -2.05e+183) or not ((x * y) <= 2.4e+147):
		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) <= -2.05e+183) || !(Float64(x * y) <= 2.4e+147))
		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) <= -2.05e+183) || ~(((x * y) <= 2.4e+147)))
		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], -2.05e+183], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.4e+147]], $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) < -2.05000000000000007e183 or 2.40000000000000002e147 < (*.f64 x y)

   1. Initial program 93.0%

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

   2. Taylor expanded in x around inf 82.5%

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

   3. Taylor expanded in x around inf 78.9%

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

   if -2.05000000000000007e183 < (*.f64 x y) < 2.40000000000000002e147

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 85.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+183} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 5: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+111} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+89}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -8e+111) (not (<= (* x y) 2.9e+89)))
   (+ (* 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) <= -8e+111) || !((x * y) <= 2.9e+89)) {
		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) <= (-8d+111)) .or. (.not. ((x * y) <= 2.9d+89))) 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) <= -8e+111) || !((x * y) <= 2.9e+89)) {
		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) <= -8e+111) or not ((x * y) <= 2.9e+89):
		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) <= -8e+111) || !(Float64(x * y) <= 2.9e+89))
		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) <= -8e+111) || ~(((x * y) <= 2.9e+89)))
		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], -8e+111], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+89]], $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) < -7.99999999999999965e111 or 2.90000000000000025e89 < (*.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 79.2%

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

   if -7.99999999999999965e111 < (*.f64 x y) < 2.90000000000000025e89

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 88.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8 \cdot 10^{+111} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+89}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 53.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+100} \lor \neg \left(a \cdot b \leq 3.6 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -1.1e+100) (not (<= (* a b) 3.6e+54))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -1.1e+100) || !((a * b) <= 3.6e+54)) {
		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) <= (-1.1d+100)) .or. (.not. ((a * b) <= 3.6d+54))) 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) <= -1.1e+100) || !((a * b) <= 3.6e+54)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -1.1e+100) or not ((a * b) <= 3.6e+54):
		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) <= -1.1e+100) || !(Float64(a * b) <= 3.6e+54))
		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) <= -1.1e+100) || ~(((a * b) <= 3.6e+54)))
		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], -1.1e+100], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.6e+54]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.1e100 or 3.6000000000000001e54 < (*.f64 a b)

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf 69.3%

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

   if -1.1e100 < (*.f64 a b) < 3.6000000000000001e54

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 63.9%

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

   3. Taylor expanded in t around inf 52.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+100} \lor \neg \left(a \cdot b \leq 3.6 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 7: 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 98.0%

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

2. Final simplification 98.0%

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

Alternative 8: 36.0% 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 98.0%

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

2. Taylor expanded in a around inf 34.0%

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

3. Final simplification 34.0%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023298 
(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)))