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

Percentage Accurate: 97.7% → 98.8%

Time: 7.7s

Alternatives: 10

Speedup: 0.4×

• 34.0% 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: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

   3. Simplified 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 40.0%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   4. Step-by-step derivation

      1. fma-def 70.0%

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

   5. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, b, x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 2: 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 96.1%

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

   1. associate-+l+ 96.1%

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

   2. fma-def 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-def 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) + a \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 40.0%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   4. Step-by-step derivation

      1. fma-def 70.0%

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

   5. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, b, x \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 4: 54.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.42 \cdot 10^{+116}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-270}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-89}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.42e+116)
   (* a b)
   (if (<= (* a b) -8e-16)
     (* x y)
     (if (<= (* a b) -1.5e-122)
       (* z t)
       (if (<= (* a b) 4.4e-270)
         (* x y)
         (if (<= (* a b) 3.9e-89)
           (* z t)
           (if (<= (* a b) 5.2e+35)
             (* x y)
             (if (<= (* a b) 5.4e+110)
               (* z t)
               (if (<= (* a b) 4.8e+120) (* x y) (* a b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.42e+116) {
		tmp = a * b;
	} else if ((a * b) <= -8e-16) {
		tmp = x * y;
	} else if ((a * b) <= -1.5e-122) {
		tmp = z * t;
	} else if ((a * b) <= 4.4e-270) {
		tmp = x * y;
	} else if ((a * b) <= 3.9e-89) {
		tmp = z * t;
	} else if ((a * b) <= 5.2e+35) {
		tmp = x * y;
	} else if ((a * b) <= 5.4e+110) {
		tmp = z * t;
	} else if ((a * b) <= 4.8e+120) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a * b) <= (-1.42d+116)) then
        tmp = a * b
    else if ((a * b) <= (-8d-16)) then
        tmp = x * y
    else if ((a * b) <= (-1.5d-122)) then
        tmp = z * t
    else if ((a * b) <= 4.4d-270) then
        tmp = x * y
    else if ((a * b) <= 3.9d-89) then
        tmp = z * t
    else if ((a * b) <= 5.2d+35) then
        tmp = x * y
    else if ((a * b) <= 5.4d+110) then
        tmp = z * t
    else if ((a * b) <= 4.8d+120) then
        tmp = x * y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.42e+116) {
		tmp = a * b;
	} else if ((a * b) <= -8e-16) {
		tmp = x * y;
	} else if ((a * b) <= -1.5e-122) {
		tmp = z * t;
	} else if ((a * b) <= 4.4e-270) {
		tmp = x * y;
	} else if ((a * b) <= 3.9e-89) {
		tmp = z * t;
	} else if ((a * b) <= 5.2e+35) {
		tmp = x * y;
	} else if ((a * b) <= 5.4e+110) {
		tmp = z * t;
	} else if ((a * b) <= 4.8e+120) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.42e+116:
		tmp = a * b
	elif (a * b) <= -8e-16:
		tmp = x * y
	elif (a * b) <= -1.5e-122:
		tmp = z * t
	elif (a * b) <= 4.4e-270:
		tmp = x * y
	elif (a * b) <= 3.9e-89:
		tmp = z * t
	elif (a * b) <= 5.2e+35:
		tmp = x * y
	elif (a * b) <= 5.4e+110:
		tmp = z * t
	elif (a * b) <= 4.8e+120:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -1.42e+116)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -8e-16)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -1.5e-122)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 4.4e-270)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.9e-89)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.2e+35)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 5.4e+110)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 4.8e+120)
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a * b) <= -1.42e+116)
		tmp = a * b;
	elseif ((a * b) <= -8e-16)
		tmp = x * y;
	elseif ((a * b) <= -1.5e-122)
		tmp = z * t;
	elseif ((a * b) <= 4.4e-270)
		tmp = x * y;
	elseif ((a * b) <= 3.9e-89)
		tmp = z * t;
	elseif ((a * b) <= 5.2e+35)
		tmp = x * y;
	elseif ((a * b) <= 5.4e+110)
		tmp = z * t;
	elseif ((a * b) <= 4.8e+120)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.42e+116], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -8e-16], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.5e-122], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.4e-270], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.9e-89], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.2e+35], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.4e+110], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.8e+120], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.4199999999999999e116 or 4.80000000000000002e120 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 79.2%

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

   if -1.4199999999999999e116 < (*.f64 a b) < -7.9999999999999998e-16 or -1.50000000000000002e-122 < (*.f64 a b) < 4.3999999999999997e-270 or 3.89999999999999978e-89 < (*.f64 a b) < 5.20000000000000013e35 or 5.40000000000000019e110 < (*.f64 a b) < 4.80000000000000002e120

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf 59.6%

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

   if -7.9999999999999998e-16 < (*.f64 a b) < -1.50000000000000002e-122 or 4.3999999999999997e-270 < (*.f64 a b) < 3.89999999999999978e-89 or 5.20000000000000013e35 < (*.f64 a b) < 5.40000000000000019e110

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 63.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.42 \cdot 10^{+116}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-270}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-89}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{+120}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) + a \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 50.4%

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

4. Final simplification 98.0%

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

Alternative 6: 79.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+148} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -2.8e+148) (not (<= (* x y) 2.4e+216)))
   (* 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) <= -2.8e+148) || !((x * y) <= 2.4e+216)) {
		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) <= (-2.8d+148)) .or. (.not. ((x * y) <= 2.4d+216))) 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) <= -2.8e+148) || !((x * y) <= 2.4e+216)) {
		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) <= -2.8e+148) or not ((x * y) <= 2.4e+216):
		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) <= -2.8e+148) || !(Float64(x * y) <= 2.4e+216))
		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) <= -2.8e+148) || ~(((x * y) <= 2.4e+216)))
		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], -2.8e+148], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.4e+216]], $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) < -2.7999999999999998e148 or 2.3999999999999999e216 < (*.f64 x y)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 81.6%

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

   if -2.7999999999999998e148 < (*.f64 x y) < 2.3999999999999999e216

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 82.9%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+148} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.35 \cdot 10^{+64} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -2.35e+64) (not (<= (* x y) 1.25e+57)))
   (+ (* x y) (* a b))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -2.35e+64) || !((x * y) <= 1.25e+57)) {
		tmp = (x * y) + (a * b);
	} 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) <= (-2.35d+64)) .or. (.not. ((x * y) <= 1.25d+57))) then
        tmp = (x * y) + (a * b)
    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) <= -2.35e+64) || !((x * y) <= 1.25e+57)) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -2.35e+64) or not ((x * y) <= 1.25e+57):
		tmp = (x * y) + (a * b)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -2.35e+64) || !(Float64(x * y) <= 1.25e+57))
		tmp = Float64(Float64(x * y) + Float64(a * b));
	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) <= -2.35e+64) || ~(((x * y) <= 1.25e+57)))
		tmp = (x * y) + (a * b);
	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], -2.35e+64], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.25e+57]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.35000000000000015e64 or 1.24999999999999993e57 < (*.f64 x y)

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 82.7%

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

   if -2.35000000000000015e64 < (*.f64 x y) < 1.24999999999999993e57

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 88.8%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.35 \cdot 10^{+64} \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.3 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -2.3e-20)
   (+ (* x y) (* a b))
   (if (<= (* a b) 1.9e+58) (+ (* 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 ((a * b) <= -2.3e-20) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= 1.9e+58) {
		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 ((a * b) <= (-2.3d-20)) then
        tmp = (x * y) + (a * b)
    else if ((a * b) <= 1.9d+58) 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 ((a * b) <= -2.3e-20) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= 1.9e+58) {
		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 (a * b) <= -2.3e-20:
		tmp = (x * y) + (a * b)
	elif (a * b) <= 1.9e+58:
		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(a * b) <= -2.3e-20)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(a * b) <= 1.9e+58)
		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 ((a * b) <= -2.3e-20)
		tmp = (x * y) + (a * b);
	elseif ((a * b) <= 1.9e+58)
		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[LessEqual[N[(a * b), $MachinePrecision], -2.3e-20], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.9e+58], 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 3 regimes

2. if (*.f64 a b) < -2.2999999999999999e-20

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 85.9%

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

   if -2.2999999999999999e-20 < (*.f64 a b) < 1.8999999999999999e58

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 93.5%

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

   if 1.8999999999999999e58 < (*.f64 a b)

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 87.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.3 \cdot 10^{-20}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.8 \cdot 10^{+109} \lor \neg \left(a \cdot b \leq 3 \cdot 10^{+101}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -9.8e+109) (not (<= (* a b) 3e+101))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -9.8e+109) || !((a * b) <= 3e+101)) {
		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) <= (-9.8d+109)) .or. (.not. ((a * b) <= 3d+101))) 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) <= -9.8e+109) || !((a * b) <= 3e+101)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -9.8e+109) or not ((a * b) <= 3e+101):
		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) <= -9.8e+109) || !(Float64(a * b) <= 3e+101))
		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) <= -9.8e+109) || ~(((a * b) <= 3e+101)))
		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], -9.8e+109], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3e+101]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.8000000000000007e109 or 2.99999999999999993e101 < (*.f64 a b)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 76.6%

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

   if -9.8000000000000007e109 < (*.f64 a b) < 2.99999999999999993e101

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 48.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.8 \cdot 10^{+109} \lor \neg \left(a \cdot b \leq 3 \cdot 10^{+101}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.8% 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 96.1%

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

3. Taylor expanded in a around inf 39.4%

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

4. Final simplification 39.4%

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

Reproduce

herbie shell --seed 2024041 
(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)))