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

Percentage Accurate: 97.9% → 99.4%

Time: 7.8s

Alternatives: 9

Speedup: 0.4×

• 32.3% 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: 99.4% accurate, 0.4× speedup

Math

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

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 (* x (+ y (* t (/ z x)))))))

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 = x * (y + (t * (z / x)));
	}
	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 = x * (y + (t * (z / x)));
	}
	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 = x * (y + (t * (z / x)))
	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(x * Float64(y + Float64(t * Float64(z / x))));
	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 = x * (y + (t * (z / x)));
	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[(x * N[(y + N[(t * N[(z / x), $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 a around 0 66.7%

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

   4. Taylor expanded in x around inf 83.3%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b + \left(x \cdot y + z \cdot t\right) \leq \infty:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + t \cdot \frac{z}{x}\right)\\ \end{array} \]
5. 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 99.2%

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

   3. fma-define 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 3: 54.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+170}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.4 \cdot 10^{+131}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -8.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.25 \cdot 10^{-76}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2.1e+170)
   (* x y)
   (if (<= (* x y) -2.4e+131)
     (* z t)
     (if (<= (* x y) -8.1e+80)
       (* x y)
       (if (<= (* x y) -2.8e-41)
         (* z t)
         (if (<= (* x y) -4.25e-76)
           (* a b)
           (if (<= (* x y) -8.2e-179)
             (* z t)
             (if (<= (* x y) -3.2e-289)
               (* a b)
               (if (<= (* x y) 9.5e+23) (* z t) (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -2.1e+170) {
		tmp = x * y;
	} else if ((x * y) <= -2.4e+131) {
		tmp = z * t;
	} else if ((x * y) <= -8.1e+80) {
		tmp = x * y;
	} else if ((x * y) <= -2.8e-41) {
		tmp = z * t;
	} else if ((x * y) <= -4.25e-76) {
		tmp = a * b;
	} else if ((x * y) <= -8.2e-179) {
		tmp = z * t;
	} else if ((x * y) <= -3.2e-289) {
		tmp = a * b;
	} else if ((x * y) <= 9.5e+23) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * y) <= (-2.1d+170)) then
        tmp = x * y
    else if ((x * y) <= (-2.4d+131)) then
        tmp = z * t
    else if ((x * y) <= (-8.1d+80)) then
        tmp = x * y
    else if ((x * y) <= (-2.8d-41)) then
        tmp = z * t
    else if ((x * y) <= (-4.25d-76)) then
        tmp = a * b
    else if ((x * y) <= (-8.2d-179)) then
        tmp = z * t
    else if ((x * y) <= (-3.2d-289)) then
        tmp = a * b
    else if ((x * y) <= 9.5d+23) then
        tmp = z * t
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -2.1e+170) {
		tmp = x * y;
	} else if ((x * y) <= -2.4e+131) {
		tmp = z * t;
	} else if ((x * y) <= -8.1e+80) {
		tmp = x * y;
	} else if ((x * y) <= -2.8e-41) {
		tmp = z * t;
	} else if ((x * y) <= -4.25e-76) {
		tmp = a * b;
	} else if ((x * y) <= -8.2e-179) {
		tmp = z * t;
	} else if ((x * y) <= -3.2e-289) {
		tmp = a * b;
	} else if ((x * y) <= 9.5e+23) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -2.1e+170:
		tmp = x * y
	elif (x * y) <= -2.4e+131:
		tmp = z * t
	elif (x * y) <= -8.1e+80:
		tmp = x * y
	elif (x * y) <= -2.8e-41:
		tmp = z * t
	elif (x * y) <= -4.25e-76:
		tmp = a * b
	elif (x * y) <= -8.2e-179:
		tmp = z * t
	elif (x * y) <= -3.2e-289:
		tmp = a * b
	elif (x * y) <= 9.5e+23:
		tmp = z * t
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+170)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.4e+131)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -8.1e+80)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.8e-41)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -4.25e-76)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -8.2e-179)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -3.2e-289)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 9.5e+23)
		tmp = Float64(z * t);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -2.1e+170)
		tmp = x * y;
	elseif ((x * y) <= -2.4e+131)
		tmp = z * t;
	elseif ((x * y) <= -8.1e+80)
		tmp = x * y;
	elseif ((x * y) <= -2.8e-41)
		tmp = z * t;
	elseif ((x * y) <= -4.25e-76)
		tmp = a * b;
	elseif ((x * y) <= -8.2e-179)
		tmp = z * t;
	elseif ((x * y) <= -3.2e-289)
		tmp = a * b;
	elseif ((x * y) <= 9.5e+23)
		tmp = z * t;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+170], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.4e+131], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.1e+80], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.8e-41], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.25e-76], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.2e-179], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.2e-289], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.5e+23], N[(z * t), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.09999999999999998e170 or -2.3999999999999999e131 < (*.f64 x y) < -8.10000000000000002e80 or 9.50000000000000038e23 < (*.f64 x y)

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 77.7%

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

   if -2.09999999999999998e170 < (*.f64 x y) < -2.3999999999999999e131 or -8.10000000000000002e80 < (*.f64 x y) < -2.8000000000000002e-41 or -4.25000000000000019e-76 < (*.f64 x y) < -8.2e-179 or -3.2000000000000002e-289 < (*.f64 x y) < 9.50000000000000038e23

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 65.8%

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

   if -2.8000000000000002e-41 < (*.f64 x y) < -4.25000000000000019e-76 or -8.2e-179 < (*.f64 x y) < -3.2000000000000002e-289

   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 71.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+170}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.4 \cdot 10^{+131}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -8.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-41}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.25 \cdot 10^{-76}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{-289}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+178} \lor \neg \left(x \cdot y \leq -1.02 \cdot 10^{+129}\right) \land \left(x \cdot y \leq -2.25 \cdot 10^{+108} \lor \neg \left(x \cdot y \leq 4.5 \cdot 10^{+98}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.75e+178)
         (and (not (<= (* x y) -1.02e+129))
              (or (<= (* x y) -2.25e+108) (not (<= (* x y) 4.5e+98)))))
   (* 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) <= -1.75e+178) || (!((x * y) <= -1.02e+129) && (((x * y) <= -2.25e+108) || !((x * y) <= 4.5e+98)))) {
		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) <= (-1.75d+178)) .or. (.not. ((x * y) <= (-1.02d+129))) .and. ((x * y) <= (-2.25d+108)) .or. (.not. ((x * y) <= 4.5d+98))) 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) <= -1.75e+178) || (!((x * y) <= -1.02e+129) && (((x * y) <= -2.25e+108) || !((x * y) <= 4.5e+98)))) {
		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) <= -1.75e+178) or (not ((x * y) <= -1.02e+129) and (((x * y) <= -2.25e+108) or not ((x * y) <= 4.5e+98))):
		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) <= -1.75e+178) || (!(Float64(x * y) <= -1.02e+129) && ((Float64(x * y) <= -2.25e+108) || !(Float64(x * y) <= 4.5e+98))))
		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) <= -1.75e+178) || (~(((x * y) <= -1.02e+129)) && (((x * y) <= -2.25e+108) || ~(((x * y) <= 4.5e+98)))))
		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], -1.75e+178], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -1.02e+129]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -2.25e+108], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.5e+98]], $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) < -1.75e178 or -1.01999999999999996e129 < (*.f64 x y) < -2.25e108 or 4.5000000000000002e98 < (*.f64 x y)

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 85.2%

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

   if -1.75e178 < (*.f64 x y) < -1.01999999999999996e129 or -2.25e108 < (*.f64 x y) < 4.5000000000000002e98

   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 86.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+178} \lor \neg \left(x \cdot y \leq -1.02 \cdot 10^{+129}\right) \land \left(x \cdot y \leq -2.25 \cdot 10^{+108} \lor \neg \left(x \cdot y \leq 4.5 \cdot 10^{+98}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+170} \lor \neg \left(x \cdot y \leq -5.8 \cdot 10^{+130} \lor \neg \left(x \cdot y \leq -1.45 \cdot 10^{+81}\right) \land x \cdot y \leq 2.5 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.6e+170)
         (not
          (or (<= (* x y) -5.8e+130)
              (and (not (<= (* x y) -1.45e+81)) (<= (* x y) 2.5e+26)))))
   (+ (* 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) <= -1.6e+170) || !(((x * y) <= -5.8e+130) || (!((x * y) <= -1.45e+81) && ((x * y) <= 2.5e+26)))) {
		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) <= (-1.6d+170)) .or. (.not. ((x * y) <= (-5.8d+130)) .or. (.not. ((x * y) <= (-1.45d+81))) .and. ((x * y) <= 2.5d+26))) 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) <= -1.6e+170) || !(((x * y) <= -5.8e+130) || (!((x * y) <= -1.45e+81) && ((x * y) <= 2.5e+26)))) {
		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) <= -1.6e+170) or not (((x * y) <= -5.8e+130) or (not ((x * y) <= -1.45e+81) and ((x * y) <= 2.5e+26))):
		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) <= -1.6e+170) || !((Float64(x * y) <= -5.8e+130) || (!(Float64(x * y) <= -1.45e+81) && (Float64(x * y) <= 2.5e+26))))
		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) <= -1.6e+170) || ~((((x * y) <= -5.8e+130) || (~(((x * y) <= -1.45e+81)) && ((x * y) <= 2.5e+26)))))
		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], -1.6e+170], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], -5.8e+130], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -1.45e+81]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 2.5e+26]]]], $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) < -1.59999999999999989e170 or -5.7999999999999998e130 < (*.f64 x y) < -1.45e81 or 2.5e26 < (*.f64 x y)

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 87.2%

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

   if -1.59999999999999989e170 < (*.f64 x y) < -5.7999999999999998e130 or -1.45e81 < (*.f64 x y) < 2.5e26

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 89.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+170} \lor \neg \left(x \cdot y \leq -5.8 \cdot 10^{+130} \lor \neg \left(x \cdot y \leq -1.45 \cdot 10^{+81}\right) \land x \cdot y \leq 2.5 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3.1 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -3.8e+87)
   (+ (* x y) (* a b))
   (if (<= (* a b) 3.1e+56) (+ (* 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) <= -3.8e+87) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= 3.1e+56) {
		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) <= (-3.8d+87)) then
        tmp = (x * y) + (a * b)
    else if ((a * b) <= 3.1d+56) 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) <= -3.8e+87) {
		tmp = (x * y) + (a * b);
	} else if ((a * b) <= 3.1e+56) {
		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) <= -3.8e+87:
		tmp = (x * y) + (a * b)
	elif (a * b) <= 3.1e+56:
		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) <= -3.8e+87)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(a * b) <= 3.1e+56)
		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) <= -3.8e+87)
		tmp = (x * y) + (a * b);
	elseif ((a * b) <= 3.1e+56)
		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], -3.8e+87], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.1e+56], 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) < -3.80000000000000011e87

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 86.6%

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

   if -3.80000000000000011e87 < (*.f64 a b) < 3.10000000000000005e56

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 91.1%

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

   if 3.10000000000000005e56 < (*.f64 a b)

   1. Initial program 92.6%

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

   3. Taylor expanded in x around 0 85.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 3.1 \cdot 10^{+56}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x + \frac{z \cdot t}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 200000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -5e+60)
   (* y (+ x (/ (* z t) y)))
   (if (<= (* x y) 200000.0) (+ (* a b) (* z t)) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -5e+60) {
		tmp = y * (x + ((z * t) / y));
	} else if ((x * y) <= 200000.0) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * y) <= (-5d+60)) then
        tmp = y * (x + ((z * t) / y))
    else if ((x * y) <= 200000.0d0) then
        tmp = (a * b) + (z * t)
    else
        tmp = (x * y) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -5e+60) {
		tmp = y * (x + ((z * t) / y));
	} else if ((x * y) <= 200000.0) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -5e+60:
		tmp = y * (x + ((z * t) / y))
	elif (x * y) <= 200000.0:
		tmp = (a * b) + (z * t)
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -5e+60)
		tmp = Float64(y * Float64(x + Float64(Float64(z * t) / y)));
	elseif (Float64(x * y) <= 200000.0)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(x * y) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -5e+60)
		tmp = y * (x + ((z * t) / y));
	elseif ((x * y) <= 200000.0)
		tmp = (a * b) + (z * t);
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+60], N[(y * N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 200000.0], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999975e60

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 95.0%

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

   4. Taylor expanded in a around 0 85.4%

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

   if -4.99999999999999975e60 < (*.f64 x y) < 2e5

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0 91.6%

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

   if 2e5 < (*.f64 x y)

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 86.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x + \frac{z \cdot t}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 200000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+80} \lor \neg \left(a \cdot b \leq 1.08 \cdot 10^{+66}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -3.8e+80) (not (<= (* a b) 1.08e+66))) (* 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+80) || !((a * b) <= 1.08e+66)) {
		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+80)) .or. (.not. ((a * b) <= 1.08d+66))) 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+80) || !((a * b) <= 1.08e+66)) {
		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+80) or not ((a * b) <= 1.08e+66):
		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+80) || !(Float64(a * b) <= 1.08e+66))
		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+80) || ~(((a * b) <= 1.08e+66)))
		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+80], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.08e+66]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.79999999999999997e80 or 1.08000000000000008e66 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 66.0%

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

   if -3.79999999999999997e80 < (*.f64 a b) < 1.08000000000000008e66

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 51.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+80} \lor \neg \left(a \cdot b \leq 1.08 \cdot 10^{+66}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
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 97.6%

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

3. Taylor expanded in a around inf 27.8%

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

4. Final simplification 27.8%

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

Reproduce

herbie shell --seed 2024079 
(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)))