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

Percentage Accurate: 98.2% → 99.4%

Time: 8.0s

Alternatives: 9

Speedup: 0.4×

• 32.5% 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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

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 = fma(x, y, (z * t)) + (a * b);
	} else {
		tmp = z * (t + (a * (b / z)));
	}
	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(fma(x, y, Float64(z * t)) + Float64(a * b));
	else
		tmp = Float64(z * Float64(t + Float64(a * Float64(b / z))));
	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[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(t + N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision]), $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-define 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 inf 0.0%

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

   4. Taylor expanded in t around inf 0.0%

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

   5. Taylor expanded in z around inf 40.0%

      \[\leadsto \color{blue}{z \cdot \left(t + \frac{a \cdot b}{z}\right)} \]
   6. Step-by-step derivation

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(t + a \cdot \frac{b}{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. fma-define 99.2%

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

   3. fma-define 99.2%

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

3. Simplified 99.2%

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

Alternative 3: 54.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+168}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -7 \cdot 10^{-177}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-220}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -8.8e+168)
   (* x y)
   (if (<= (* x y) -5.5e+69)
     (* z t)
     (if (<= (* x y) -7.5e+38)
       (* x y)
       (if (<= (* x y) -4.5e-48)
         (* z t)
         (if (<= (* x y) -7e-177)
           (* a b)
           (if (<= (* x y) 5e-220)
             (* z t)
             (if (<= (* x y) 1.65e+50) (* a b) (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -8.8e+168) {
		tmp = x * y;
	} else if ((x * y) <= -5.5e+69) {
		tmp = z * t;
	} else if ((x * y) <= -7.5e+38) {
		tmp = x * y;
	} else if ((x * y) <= -4.5e-48) {
		tmp = z * t;
	} else if ((x * y) <= -7e-177) {
		tmp = a * b;
	} else if ((x * y) <= 5e-220) {
		tmp = z * t;
	} else if ((x * y) <= 1.65e+50) {
		tmp = a * b;
	} 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) <= (-8.8d+168)) then
        tmp = x * y
    else if ((x * y) <= (-5.5d+69)) then
        tmp = z * t
    else if ((x * y) <= (-7.5d+38)) then
        tmp = x * y
    else if ((x * y) <= (-4.5d-48)) then
        tmp = z * t
    else if ((x * y) <= (-7d-177)) then
        tmp = a * b
    else if ((x * y) <= 5d-220) then
        tmp = z * t
    else if ((x * y) <= 1.65d+50) then
        tmp = a * b
    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) <= -8.8e+168) {
		tmp = x * y;
	} else if ((x * y) <= -5.5e+69) {
		tmp = z * t;
	} else if ((x * y) <= -7.5e+38) {
		tmp = x * y;
	} else if ((x * y) <= -4.5e-48) {
		tmp = z * t;
	} else if ((x * y) <= -7e-177) {
		tmp = a * b;
	} else if ((x * y) <= 5e-220) {
		tmp = z * t;
	} else if ((x * y) <= 1.65e+50) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -8.8e+168:
		tmp = x * y
	elif (x * y) <= -5.5e+69:
		tmp = z * t
	elif (x * y) <= -7.5e+38:
		tmp = x * y
	elif (x * y) <= -4.5e-48:
		tmp = z * t
	elif (x * y) <= -7e-177:
		tmp = a * b
	elif (x * y) <= 5e-220:
		tmp = z * t
	elif (x * y) <= 1.65e+50:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -8.8e+168)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.5e+69)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -7.5e+38)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4.5e-48)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -7e-177)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 5e-220)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.65e+50)
		tmp = Float64(a * b);
	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) <= -8.8e+168)
		tmp = x * y;
	elseif ((x * y) <= -5.5e+69)
		tmp = z * t;
	elseif ((x * y) <= -7.5e+38)
		tmp = x * y;
	elseif ((x * y) <= -4.5e-48)
		tmp = z * t;
	elseif ((x * y) <= -7e-177)
		tmp = a * b;
	elseif ((x * y) <= 5e-220)
		tmp = z * t;
	elseif ((x * y) <= 1.65e+50)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -8.8e+168], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.5e+69], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -7.5e+38], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.5e-48], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -7e-177], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-220], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.65e+50], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.8000000000000008e168 or -5.50000000000000002e69 < (*.f64 x y) < -7.4999999999999999e38 or 1.65e50 < (*.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.6%

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

   if -8.8000000000000008e168 < (*.f64 x y) < -5.50000000000000002e69 or -7.4999999999999999e38 < (*.f64 x y) < -4.49999999999999988e-48 or -7.0000000000000003e-177 < (*.f64 x y) < 5.0000000000000002e-220

   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 60.1%

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

   if -4.49999999999999988e-48 < (*.f64 x y) < -7.0000000000000003e-177 or 5.0000000000000002e-220 < (*.f64 x y) < 1.65e50

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 56.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.8 \cdot 10^{+168}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -7.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -7 \cdot 10^{-177}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-220}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.9 \cdot 10^{+168} \lor \neg \left(x \cdot y \leq -7.8 \cdot 10^{+62}\right) \land \left(x \cdot y \leq -1.25 \cdot 10^{+44} \lor \neg \left(x \cdot y \leq 2.35 \cdot 10^{+45}\right)\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -5.9e+168)
         (and (not (<= (* x y) -7.8e+62))
              (or (<= (* x y) -1.25e+44) (not (<= (* x y) 2.35e+45)))))
   (+ (* 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) <= -5.9e+168) || (!((x * y) <= -7.8e+62) && (((x * y) <= -1.25e+44) || !((x * y) <= 2.35e+45)))) {
		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) <= (-5.9d+168)) .or. (.not. ((x * y) <= (-7.8d+62))) .and. ((x * y) <= (-1.25d+44)) .or. (.not. ((x * y) <= 2.35d+45))) 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) <= -5.9e+168) || (!((x * y) <= -7.8e+62) && (((x * y) <= -1.25e+44) || !((x * y) <= 2.35e+45)))) {
		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) <= -5.9e+168) or (not ((x * y) <= -7.8e+62) and (((x * y) <= -1.25e+44) or not ((x * y) <= 2.35e+45))):
		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) <= -5.9e+168) || (!(Float64(x * y) <= -7.8e+62) && ((Float64(x * y) <= -1.25e+44) || !(Float64(x * y) <= 2.35e+45))))
		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) <= -5.9e+168) || (~(((x * y) <= -7.8e+62)) && (((x * y) <= -1.25e+44) || ~(((x * y) <= 2.35e+45)))))
		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], -5.9e+168], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -7.8e+62]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -1.25e+44], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.35e+45]], $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) < -5.89999999999999986e168 or -7.8e62 < (*.f64 x y) < -1.2499999999999999e44 or 2.35000000000000001e45 < (*.f64 x y)

   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 0 92.8%

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

   if -5.89999999999999986e168 < (*.f64 x y) < -7.8e62 or -1.2499999999999999e44 < (*.f64 x y) < 2.35000000000000001e45

   1. Initial program 97.5%

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

   3. 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 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.9 \cdot 10^{+168} \lor \neg \left(x \cdot y \leq -7.8 \cdot 10^{+62}\right) \land \left(x \cdot y \leq -1.25 \cdot 10^{+44} \lor \neg \left(x \cdot y \leq 2.35 \cdot 10^{+45}\right)\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% accurate, 0.4× speedup

Math

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

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 (* z (+ t (* a (/ b z)))))))

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 = z * (t + (a * (b / z)));
	}
	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 = z * (t + (a * (b / z)));
	}
	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 = z * (t + (a * (b / z)))
	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(z * Float64(t + Float64(a * Float64(b / z))));
	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 = z * (t + (a * (b / z)));
	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[(z * N[(t + N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision]), $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 inf 0.0%

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

   4. Taylor expanded in t around inf 0.0%

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

   5. Taylor expanded in z around inf 40.0%

      \[\leadsto \color{blue}{z \cdot \left(t + \frac{a \cdot b}{z}\right)} \]
   6. Step-by-step derivation

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(t + a \cdot \frac{b}{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+170} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.65e+170) (not (<= (* x y) 3e+54)))
   (* 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) <= -1.65e+170) || !((x * y) <= 3e+54)) {
		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) <= (-1.65d+170)) .or. (.not. ((x * y) <= 3d+54))) 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) <= -1.65e+170) || !((x * y) <= 3e+54)) {
		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) <= -1.65e+170) or not ((x * y) <= 3e+54):
		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) <= -1.65e+170) || !(Float64(x * y) <= 3e+54))
		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) <= -1.65e+170) || ~(((x * y) <= 3e+54)))
		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], -1.65e+170], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3e+54]], $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) < -1.65000000000000012e170 or 2.9999999999999999e54 < (*.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.8%

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

   if -1.65000000000000012e170 < (*.f64 x y) < 2.9999999999999999e54

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 85.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+170} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{+44}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -5e+15)
   (+ (* x y) (* z t))
   (if (<= (* x y) 1e+44) (+ (* a b) (* z t)) (+ (* x y) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -5e+15) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 1e+44) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (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 ((x * y) <= (-5d+15)) then
        tmp = (x * y) + (z * t)
    else if ((x * y) <= 1d+44) then
        tmp = (a * b) + (z * t)
    else
        tmp = (x * y) + (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 ((x * y) <= -5e+15) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 1e+44) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -5e+15:
		tmp = (x * y) + (z * t)
	elif (x * y) <= 1e+44:
		tmp = (a * b) + (z * t)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -5e+15)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(x * y) <= 1e+44)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -5e+15)
		tmp = (x * y) + (z * t);
	elseif ((x * y) <= 1e+44)
		tmp = (a * b) + (z * t);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+15], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+44], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5e15

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 86.5%

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

   if -5e15 < (*.f64 x y) < 1.0000000000000001e44

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 91.7%

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

   if 1.0000000000000001e44 < (*.f64 x y)

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 88.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{+44}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+73} \lor \neg \left(a \cdot b \leq 3.4 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -3.8e+73) (not (<= (* a b) 3.4e+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) <= -3.8e+73) || !((a * b) <= 3.4e+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) <= (-3.8d+73)) .or. (.not. ((a * b) <= 3.4d+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) <= -3.8e+73) || !((a * b) <= 3.4e+54)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -3.8e+73) or not ((a * b) <= 3.4e+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) <= -3.8e+73) || !(Float64(a * b) <= 3.4e+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) <= -3.8e+73) || ~(((a * b) <= 3.4e+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], -3.8e+73], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.4e+54]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.80000000000000022e73 or 3.4000000000000001e54 < (*.f64 a b)

   1. Initial program 94.9%

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

   3. Taylor expanded in a around inf 66.7%

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

   if -3.80000000000000022e73 < (*.f64 a b) < 3.4000000000000001e54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 44.8%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+73} \lor \neg \left(a \cdot b \leq 3.4 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.5% 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. Add Preprocessing

3. Taylor expanded in a around inf 33.1%

   \[\leadsto \color{blue}{a \cdot b} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024084 
(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)))