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

Percentage Accurate: 97.9% → 98.9%

Time: 6.8s

Alternatives: 9

Speedup: 1.0×

• 33.6% 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: 97.9% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate-+l+ 98.8%

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

   2. fma-def 99.6%

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

   3. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 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 98.8%

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

   1. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 3: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+116}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3.8 \cdot 10^{-120}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-322}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-81} \lor \neg \left(a \cdot b \leq 7.5 \cdot 10^{+26}\right) \land a \cdot b \leq 4.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -2e+116)
   (* a b)
   (if (<= (* a b) -3.8e-120)
     (* z t)
     (if (<= (* a b) -1e-322)
       (* x y)
       (if (or (<= (* a b) 8.5e-81)
               (and (not (<= (* a b) 7.5e+26)) (<= (* a b) 4.8e+121)))
         (* z t)
         (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -2e+116) {
		tmp = a * b;
	} else if ((a * b) <= -3.8e-120) {
		tmp = z * t;
	} else if ((a * b) <= -1e-322) {
		tmp = x * y;
	} else if (((a * b) <= 8.5e-81) || (!((a * b) <= 7.5e+26) && ((a * b) <= 4.8e+121))) {
		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) <= (-2d+116)) then
        tmp = a * b
    else if ((a * b) <= (-3.8d-120)) then
        tmp = z * t
    else if ((a * b) <= (-1d-322)) then
        tmp = x * y
    else if (((a * b) <= 8.5d-81) .or. (.not. ((a * b) <= 7.5d+26)) .and. ((a * b) <= 4.8d+121)) 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) <= -2e+116) {
		tmp = a * b;
	} else if ((a * b) <= -3.8e-120) {
		tmp = z * t;
	} else if ((a * b) <= -1e-322) {
		tmp = x * y;
	} else if (((a * b) <= 8.5e-81) || (!((a * b) <= 7.5e+26) && ((a * b) <= 4.8e+121))) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -2e+116:
		tmp = a * b
	elif (a * b) <= -3.8e-120:
		tmp = z * t
	elif (a * b) <= -1e-322:
		tmp = x * y
	elif ((a * b) <= 8.5e-81) or (not ((a * b) <= 7.5e+26) and ((a * b) <= 4.8e+121)):
		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) <= -2e+116)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -3.8e-120)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -1e-322)
		tmp = Float64(x * y);
	elseif ((Float64(a * b) <= 8.5e-81) || (!(Float64(a * b) <= 7.5e+26) && (Float64(a * b) <= 4.8e+121)))
		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) <= -2e+116)
		tmp = a * b;
	elseif ((a * b) <= -3.8e-120)
		tmp = z * t;
	elseif ((a * b) <= -1e-322)
		tmp = x * y;
	elseif (((a * b) <= 8.5e-81) || (~(((a * b) <= 7.5e+26)) && ((a * b) <= 4.8e+121)))
		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], -2e+116], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3.8e-120], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-322], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 8.5e-81], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 7.5e+26]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 4.8e+121]]], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000003e116 or 8.5000000000000001e-81 < (*.f64 a b) < 7.49999999999999941e26 or 4.8e121 < (*.f64 a b)

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 73.8%

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

   if -2.00000000000000003e116 < (*.f64 a b) < -3.7999999999999997e-120 or -9.88131e-323 < (*.f64 a b) < 8.5000000000000001e-81 or 7.49999999999999941e26 < (*.f64 a b) < 4.8e121

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 60.1%

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

   if -3.7999999999999997e-120 < (*.f64 a b) < -9.88131e-323

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+116}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3.8 \cdot 10^{-120}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-322}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-81} \lor \neg \left(a \cdot b \leq 7.5 \cdot 10^{+26}\right) \land a \cdot b \leq 4.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 4: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.7 \cdot 10^{+117}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-78} \lor \neg \left(a \cdot b \leq 4.3 \cdot 10^{+27}\right) \land a \cdot b \leq 1.95 \cdot 10^{+121}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -2.7e+117)
   (* a b)
   (if (or (<= (* a b) 8.6e-78)
           (and (not (<= (* a b) 4.3e+27)) (<= (* a b) 1.95e+121)))
     (* z t)
     (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -2.7e+117) {
		tmp = a * b;
	} else if (((a * b) <= 8.6e-78) || (!((a * b) <= 4.3e+27) && ((a * b) <= 1.95e+121))) {
		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) <= (-2.7d+117)) then
        tmp = a * b
    else if (((a * b) <= 8.6d-78) .or. (.not. ((a * b) <= 4.3d+27)) .and. ((a * b) <= 1.95d+121)) 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) <= -2.7e+117) {
		tmp = a * b;
	} else if (((a * b) <= 8.6e-78) || (!((a * b) <= 4.3e+27) && ((a * b) <= 1.95e+121))) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -2.7e+117:
		tmp = a * b
	elif ((a * b) <= 8.6e-78) or (not ((a * b) <= 4.3e+27) and ((a * b) <= 1.95e+121)):
		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) <= -2.7e+117)
		tmp = Float64(a * b);
	elseif ((Float64(a * b) <= 8.6e-78) || (!(Float64(a * b) <= 4.3e+27) && (Float64(a * b) <= 1.95e+121)))
		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) <= -2.7e+117)
		tmp = a * b;
	elseif (((a * b) <= 8.6e-78) || (~(((a * b) <= 4.3e+27)) && ((a * b) <= 1.95e+121)))
		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], -2.7e+117], N[(a * b), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 8.6e-78], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.3e+27]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 1.95e+121]]], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.7000000000000002e117 or 8.59999999999999987e-78 < (*.f64 a b) < 4.30000000000000008e27 or 1.94999999999999992e121 < (*.f64 a b)

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 73.8%

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

   if -2.7000000000000002e117 < (*.f64 a b) < 8.59999999999999987e-78 or 4.30000000000000008e27 < (*.f64 a b) < 1.94999999999999992e121

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 56.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.7 \cdot 10^{+117}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-78} \lor \neg \left(a \cdot b \leq 4.3 \cdot 10^{+27}\right) \land a \cdot b \leq 1.95 \cdot 10^{+121}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 5: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-185} \lor \neg \left(y \leq 7.6 \cdot 10^{+143}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e-185) (not (<= y 7.6e+143)))
   (+ (* 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 ((y <= -1.4e-185) || !(y <= 7.6e+143)) {
		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 ((y <= (-1.4d-185)) .or. (.not. (y <= 7.6d+143))) 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 ((y <= -1.4e-185) || !(y <= 7.6e+143)) {
		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 (y <= -1.4e-185) or not (y <= 7.6e+143):
		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 ((y <= -1.4e-185) || !(y <= 7.6e+143))
		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 ((y <= -1.4e-185) || ~((y <= 7.6e+143)))
		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[y, -1.4e-185], N[Not[LessEqual[y, 7.6e+143]], $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 y < -1.39999999999999996e-185 or 7.60000000000000001e143 < y

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 71.9%

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

   if -1.39999999999999996e-185 < y < 7.60000000000000001e143

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 89.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-185} \lor \neg \left(y \leq 7.6 \cdot 10^{+143}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+144}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.2e+23) (* x y) (if (<= y 2.6e+144) (+ (* 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 <= -1.2e+23) {
		tmp = x * y;
	} else if (y <= 2.6e+144) {
		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 <= (-1.2d+23)) then
        tmp = x * y
    else if (y <= 2.6d+144) 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 <= -1.2e+23) {
		tmp = x * y;
	} else if (y <= 2.6e+144) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.2e+23:
		tmp = x * y
	elif y <= 2.6e+144:
		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 <= -1.2e+23)
		tmp = Float64(x * y);
	elseif (y <= 2.6e+144)
		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 <= -1.2e+23)
		tmp = x * y;
	elseif (y <= 2.6e+144)
		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, -1.2e+23], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.6e+144], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e23 or 2.5999999999999999e144 < y

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 54.6%

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

   if -1.2e23 < y < 2.5999999999999999e144

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 89.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+144}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-185}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.4e-185)
   (+ (* a b) (* x y))
   (if (<= y 3.5e+126) (+ (* a b) (* z t)) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.4e-185) {
		tmp = (a * b) + (x * y);
	} else if (y <= 3.5e+126) {
		tmp = (a * b) + (z * t);
	} 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 (y <= (-1.4d-185)) then
        tmp = (a * b) + (x * y)
    else if (y <= 3.5d+126) then
        tmp = (a * b) + (z * t)
    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 (y <= -1.4e-185) {
		tmp = (a * b) + (x * y);
	} else if (y <= 3.5e+126) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.4e-185:
		tmp = (a * b) + (x * y)
	elif y <= 3.5e+126:
		tmp = (a * b) + (z * t)
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.4e-185)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (y <= 3.5e+126)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	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 (y <= -1.4e-185)
		tmp = (a * b) + (x * y);
	elseif (y <= 3.5e+126)
		tmp = (a * b) + (z * t);
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.4e-185], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+126], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999996e-185

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 69.9%

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

   if -1.39999999999999996e-185 < y < 3.5000000000000003e126

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 90.3%

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

   if 3.5000000000000003e126 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 87.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-185}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 8: 97.9% 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 98.8%

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

2. Final simplification 98.8%

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

Alternative 9: 35.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Taylor expanded in a around inf 38.4%

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

3. Final simplification 38.4%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023274 
(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)))