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

Percentage Accurate: 97.9% → 99.3%

Time: 7.5s

Alternatives: 8

Speedup: 0.4×

• 33.3% 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: 99.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(x + N[(a * N[(b / y), $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 0 44.4%

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

   4. Taylor expanded in y around inf 77.8%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{a \cdot b}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.0% 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 96.5%

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

   1. associate-+l+ 96.5%

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

   2. fma-define 97.6%

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

   3. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 77.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.3 \cdot 10^{+290} \lor \neg \left(x \cdot y \leq -3 \cdot 10^{+53}\right) \land \left(x \cdot y \leq -39000000 \lor \neg \left(x \cdot y \leq 7 \cdot 10^{+207}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.3e+290)
         (and (not (<= (* x y) -3e+53))
              (or (<= (* x y) -39000000.0) (not (<= (* x y) 7e+207)))))
   (* 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) <= -3.3e+290) || (!((x * y) <= -3e+53) && (((x * y) <= -39000000.0) || !((x * y) <= 7e+207)))) {
		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) <= (-3.3d+290)) .or. (.not. ((x * y) <= (-3d+53))) .and. ((x * y) <= (-39000000.0d0)) .or. (.not. ((x * y) <= 7d+207))) 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) <= -3.3e+290) || (!((x * y) <= -3e+53) && (((x * y) <= -39000000.0) || !((x * y) <= 7e+207)))) {
		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) <= -3.3e+290) or (not ((x * y) <= -3e+53) and (((x * y) <= -39000000.0) or not ((x * y) <= 7e+207))):
		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) <= -3.3e+290) || (!(Float64(x * y) <= -3e+53) && ((Float64(x * y) <= -39000000.0) || !(Float64(x * y) <= 7e+207))))
		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) <= -3.3e+290) || (~(((x * y) <= -3e+53)) && (((x * y) <= -39000000.0) || ~(((x * y) <= 7e+207)))))
		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], -3.3e+290], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -3e+53]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -39000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7e+207]], $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) < -3.2999999999999999e290 or -2.99999999999999998e53 < (*.f64 x y) < -3.9e7 or 7.00000000000000056e207 < (*.f64 x y)

   1. Initial program 88.7%

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

   3. Taylor expanded in x around inf 88.9%

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

   if -3.2999999999999999e290 < (*.f64 x y) < -2.99999999999999998e53 or -3.9e7 < (*.f64 x y) < 7.00000000000000056e207

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 83.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.3 \cdot 10^{+290} \lor \neg \left(x \cdot y \leq -3 \cdot 10^{+53}\right) \land \left(x \cdot y \leq -39000000 \lor \neg \left(x \cdot y \leq 7 \cdot 10^{+207}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{-13} \lor \neg \left(x \cdot y \leq 5.8 \cdot 10^{+61}\right) \land \left(x \cdot y \leq 2.4 \cdot 10^{+104} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+170}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -8.2e-13)
         (and (not (<= (* x y) 5.8e+61))
              (or (<= (* x y) 2.4e+104) (not (<= (* x y) 4e+170)))))
   (+ (* 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) <= -8.2e-13) || (!((x * y) <= 5.8e+61) && (((x * y) <= 2.4e+104) || !((x * y) <= 4e+170)))) {
		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) <= (-8.2d-13)) .or. (.not. ((x * y) <= 5.8d+61)) .and. ((x * y) <= 2.4d+104) .or. (.not. ((x * y) <= 4d+170))) 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) <= -8.2e-13) || (!((x * y) <= 5.8e+61) && (((x * y) <= 2.4e+104) || !((x * y) <= 4e+170)))) {
		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) <= -8.2e-13) or (not ((x * y) <= 5.8e+61) and (((x * y) <= 2.4e+104) or not ((x * y) <= 4e+170))):
		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) <= -8.2e-13) || (!(Float64(x * y) <= 5.8e+61) && ((Float64(x * y) <= 2.4e+104) || !(Float64(x * y) <= 4e+170))))
		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) <= -8.2e-13) || (~(((x * y) <= 5.8e+61)) && (((x * y) <= 2.4e+104) || ~(((x * y) <= 4e+170)))))
		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], -8.2e-13], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.8e+61]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 2.4e+104], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4e+170]], $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) < -8.2000000000000004e-13 or 5.8000000000000001e61 < (*.f64 x y) < 2.4e104 or 4.00000000000000014e170 < (*.f64 x y)

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 82.7%

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

   if -8.2000000000000004e-13 < (*.f64 x y) < 5.8000000000000001e61 or 2.4e104 < (*.f64 x y) < 4.00000000000000014e170

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{-13} \lor \neg \left(x \cdot y \leq 5.8 \cdot 10^{+61}\right) \land \left(x \cdot y \leq 2.4 \cdot 10^{+104} \lor \neg \left(x \cdot y \leq 4 \cdot 10^{+170}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+237} \lor \neg \left(a \cdot b \leq -2.9 \cdot 10^{+227}\right) \land \left(a \cdot b \leq -5.8 \cdot 10^{-28} \lor \neg \left(a \cdot b \leq 4.4 \cdot 10^{+22}\right)\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -2e+237)
         (and (not (<= (* a b) -2.9e+227))
              (or (<= (* a b) -5.8e-28) (not (<= (* a b) 4.4e+22)))))
   (* a b)
   (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -2e+237) || (!((a * b) <= -2.9e+227) && (((a * b) <= -5.8e-28) || !((a * b) <= 4.4e+22)))) {
		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) <= (-2d+237)) .or. (.not. ((a * b) <= (-2.9d+227))) .and. ((a * b) <= (-5.8d-28)) .or. (.not. ((a * b) <= 4.4d+22))) 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) <= -2e+237) || (!((a * b) <= -2.9e+227) && (((a * b) <= -5.8e-28) || !((a * b) <= 4.4e+22)))) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -2e+237) or (not ((a * b) <= -2.9e+227) and (((a * b) <= -5.8e-28) or not ((a * b) <= 4.4e+22))):
		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) <= -2e+237) || (!(Float64(a * b) <= -2.9e+227) && ((Float64(a * b) <= -5.8e-28) || !(Float64(a * b) <= 4.4e+22))))
		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) <= -2e+237) || (~(((a * b) <= -2.9e+227)) && (((a * b) <= -5.8e-28) || ~(((a * b) <= 4.4e+22)))))
		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], -2e+237], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], -2.9e+227]], $MachinePrecision], Or[LessEqual[N[(a * b), $MachinePrecision], -5.8e-28], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.4e+22]], $MachinePrecision]]]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.99999999999999988e237 or -2.8999999999999998e227 < (*.f64 a b) < -5.80000000000000026e-28 or 4.4e22 < (*.f64 a b)

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf 62.5%

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

   if -1.99999999999999988e237 < (*.f64 a b) < -2.8999999999999998e227 or -5.80000000000000026e-28 < (*.f64 a b) < 4.4e22

   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 52.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+237} \lor \neg \left(a \cdot b \leq -2.9 \cdot 10^{+227}\right) \land \left(a \cdot b \leq -5.8 \cdot 10^{-28} \lor \neg \left(a \cdot b \leq 4.4 \cdot 10^{+22}\right)\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.7 \cdot 10^{+169}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.35 \cdot 10^{+57}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-8} \lor \neg \left(x \cdot y \leq 1.6 \cdot 10^{+171}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -3.7e+169)
   (* x y)
   (if (<= (* x y) -2.35e+57)
     (* a b)
     (if (or (<= (* x y) -4.1e-8) (not (<= (* x y) 1.6e+171)))
       (* x y)
       (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -3.7e+169) {
		tmp = x * y;
	} else if ((x * y) <= -2.35e+57) {
		tmp = a * b;
	} else if (((x * y) <= -4.1e-8) || !((x * y) <= 1.6e+171)) {
		tmp = x * y;
	} 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 ((x * y) <= (-3.7d+169)) then
        tmp = x * y
    else if ((x * y) <= (-2.35d+57)) then
        tmp = a * b
    else if (((x * y) <= (-4.1d-8)) .or. (.not. ((x * y) <= 1.6d+171))) then
        tmp = x * y
    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 ((x * y) <= -3.7e+169) {
		tmp = x * y;
	} else if ((x * y) <= -2.35e+57) {
		tmp = a * b;
	} else if (((x * y) <= -4.1e-8) || !((x * y) <= 1.6e+171)) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -3.7e+169:
		tmp = x * y
	elif (x * y) <= -2.35e+57:
		tmp = a * b
	elif ((x * y) <= -4.1e-8) or not ((x * y) <= 1.6e+171):
		tmp = x * y
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -3.7e+169)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.35e+57)
		tmp = Float64(a * b);
	elseif ((Float64(x * y) <= -4.1e-8) || !(Float64(x * y) <= 1.6e+171))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -3.7e+169)
		tmp = x * y;
	elseif ((x * y) <= -2.35e+57)
		tmp = a * b;
	elseif (((x * y) <= -4.1e-8) || ~(((x * y) <= 1.6e+171)))
		tmp = x * y;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.7e+169], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.35e+57], N[(a * b), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.1e-8], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.6e+171]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.70000000000000001e169 or -2.3500000000000001e57 < (*.f64 x y) < -4.10000000000000032e-8 or 1.60000000000000006e171 < (*.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around inf 78.1%

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

   if -3.70000000000000001e169 < (*.f64 x y) < -2.3500000000000001e57

   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 inf 46.2%

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

   if -4.10000000000000032e-8 < (*.f64 x y) < 1.60000000000000006e171

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 50.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.7 \cdot 10^{+169}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.35 \cdot 10^{+57}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-8} \lor \neg \left(x \cdot y \leq 1.6 \cdot 10^{+171}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+22}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 10^{+131}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* a b) -3.5e-26)
     t_1
     (if (<= (* a b) 2e+22)
       (+ (* x y) (* z t))
       (if (<= (* a b) 1e+131) (+ (* a b) (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -3.5e-26) {
		tmp = t_1;
	} else if ((a * b) <= 2e+22) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 1e+131) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((a * b) <= (-3.5d-26)) then
        tmp = t_1
    else if ((a * b) <= 2d+22) then
        tmp = (x * y) + (z * t)
    else if ((a * b) <= 1d+131) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -3.5e-26) {
		tmp = t_1;
	} else if ((a * b) <= 2e+22) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 1e+131) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (a * b) <= -3.5e-26:
		tmp = t_1
	elif (a * b) <= 2e+22:
		tmp = (x * y) + (z * t)
	elif (a * b) <= 1e+131:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -3.5e-26)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e+22)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(a * b) <= 1e+131)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -3.5e-26)
		tmp = t_1;
	elseif ((a * b) <= 2e+22)
		tmp = (x * y) + (z * t);
	elseif ((a * b) <= 1e+131)
		tmp = (a * b) + (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.5e-26], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e+22], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+131], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.49999999999999985e-26 or 9.9999999999999991e130 < (*.f64 a b)

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 83.8%

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

   if -3.49999999999999985e-26 < (*.f64 a b) < 2e22

   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 93.6%

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

   if 2e22 < (*.f64 a b) < 9.9999999999999991e130

   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 0 81.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{-26}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+22}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 10^{+131}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.4% 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 96.5%

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

3. Taylor expanded in a around inf 34.5%

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

4. Final simplification 34.5%

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

Reproduce

herbie shell --seed 2024076 
(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)))