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

Percentage Accurate: 97.7% → 98.9%

Time: 6.3s

Alternatives: 8

Speedup: 0.4×

• 33.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.4× speedup

Math

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

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

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 = a * (b + ((z * t) / a));
	}
	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 = a * (b + ((z * t) / a));
	}
	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 = a * (b + ((z * t) / a))
	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(a * Float64(b + Float64(Float64(z * t) / a)));
	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 = a * (b + ((z * t) / a));
	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[(a * N[(b + N[(N[(z * t), $MachinePrecision] / a), $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 inf 60.0%

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

   4. Taylor expanded in x around 0 80.0%

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

4. Final simplification 99.6%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. associate-+l+ 98.0%

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

   3. fma-define 98.4%

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

   4. +-commutative 98.4%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

Alternative 3: 51.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.5 \cdot 10^{+187}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.9 \cdot 10^{-54}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -7.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{-271}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -8.5e+187)
   (* a b)
   (if (<= (* a b) -1.9e-54)
     (* z t)
     (if (<= (* a b) -7.2e-236)
       (* x y)
       (if (<= (* a b) 1.55e-271)
         (* z t)
         (if (<= (* a b) 3.7e-81)
           (* x y)
           (if (<= (* a b) 3.5e+32) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8.5e+187) {
		tmp = a * b;
	} else if ((a * b) <= -1.9e-54) {
		tmp = z * t;
	} else if ((a * b) <= -7.2e-236) {
		tmp = x * y;
	} else if ((a * b) <= 1.55e-271) {
		tmp = z * t;
	} else if ((a * b) <= 3.7e-81) {
		tmp = x * y;
	} else if ((a * b) <= 3.5e+32) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a * b) <= (-8.5d+187)) then
        tmp = a * b
    else if ((a * b) <= (-1.9d-54)) then
        tmp = z * t
    else if ((a * b) <= (-7.2d-236)) then
        tmp = x * y
    else if ((a * b) <= 1.55d-271) then
        tmp = z * t
    else if ((a * b) <= 3.7d-81) then
        tmp = x * y
    else if ((a * b) <= 3.5d+32) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8.5e+187) {
		tmp = a * b;
	} else if ((a * b) <= -1.9e-54) {
		tmp = z * t;
	} else if ((a * b) <= -7.2e-236) {
		tmp = x * y;
	} else if ((a * b) <= 1.55e-271) {
		tmp = z * t;
	} else if ((a * b) <= 3.7e-81) {
		tmp = x * y;
	} else if ((a * b) <= 3.5e+32) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -8.5e+187:
		tmp = a * b
	elif (a * b) <= -1.9e-54:
		tmp = z * t
	elif (a * b) <= -7.2e-236:
		tmp = x * y
	elif (a * b) <= 1.55e-271:
		tmp = z * t
	elif (a * b) <= 3.7e-81:
		tmp = x * y
	elif (a * b) <= 3.5e+32:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -8.5e+187)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.9e-54)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -7.2e-236)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.55e-271)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 3.7e-81)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.5e+32)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a * b) <= -8.5e+187)
		tmp = a * b;
	elseif ((a * b) <= -1.9e-54)
		tmp = z * t;
	elseif ((a * b) <= -7.2e-236)
		tmp = x * y;
	elseif ((a * b) <= 1.55e-271)
		tmp = z * t;
	elseif ((a * b) <= 3.7e-81)
		tmp = x * y;
	elseif ((a * b) <= 3.5e+32)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -8.5e+187], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.9e-54], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -7.2e-236], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.55e-271], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.7e-81], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.5e+32], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.49999999999999989e187 or 3.5000000000000001e32 < (*.f64 a b)

   1. Initial program 95.5%

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

   3. Taylor expanded in a around inf 75.9%

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

   if -8.49999999999999989e187 < (*.f64 a b) < -1.9000000000000001e-54 or -7.20000000000000015e-236 < (*.f64 a b) < 1.54999999999999995e-271 or 3.69999999999999986e-81 < (*.f64 a b) < 3.5000000000000001e32

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 54.6%

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

   if -1.9000000000000001e-54 < (*.f64 a b) < -7.20000000000000015e-236 or 1.54999999999999995e-271 < (*.f64 a b) < 3.69999999999999986e-81

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 60.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.5 \cdot 10^{+187}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.9 \cdot 10^{-54}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -7.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{-271}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.1 \cdot 10^{+230} \lor \neg \left(x \cdot y \leq -1.85 \cdot 10^{+92}\right) \land \left(x \cdot y \leq -6 \cdot 10^{+73} \lor \neg \left(x \cdot y \leq 2.8 \cdot 10^{+233}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -5.1e+230)
         (and (not (<= (* x y) -1.85e+92))
              (or (<= (* x y) -6e+73) (not (<= (* x y) 2.8e+233)))))
   (* 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) <= -5.1e+230) || (!((x * y) <= -1.85e+92) && (((x * y) <= -6e+73) || !((x * y) <= 2.8e+233)))) {
		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) <= (-5.1d+230)) .or. (.not. ((x * y) <= (-1.85d+92))) .and. ((x * y) <= (-6d+73)) .or. (.not. ((x * y) <= 2.8d+233))) 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) <= -5.1e+230) || (!((x * y) <= -1.85e+92) && (((x * y) <= -6e+73) || !((x * y) <= 2.8e+233)))) {
		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) <= -5.1e+230) or (not ((x * y) <= -1.85e+92) and (((x * y) <= -6e+73) or not ((x * y) <= 2.8e+233))):
		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) <= -5.1e+230) || (!(Float64(x * y) <= -1.85e+92) && ((Float64(x * y) <= -6e+73) || !(Float64(x * y) <= 2.8e+233))))
		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) <= -5.1e+230) || (~(((x * y) <= -1.85e+92)) && (((x * y) <= -6e+73) || ~(((x * y) <= 2.8e+233)))))
		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], -5.1e+230], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -1.85e+92]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -6e+73], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.8e+233]], $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) < -5.1e230 or -1.84999999999999999e92 < (*.f64 x y) < -6.00000000000000021e73 or 2.8000000000000001e233 < (*.f64 x y)

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 89.3%

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

   if -5.1e230 < (*.f64 x y) < -1.84999999999999999e92 or -6.00000000000000021e73 < (*.f64 x y) < 2.8000000000000001e233

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 81.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.1 \cdot 10^{+230} \lor \neg \left(x \cdot y \leq -1.85 \cdot 10^{+92}\right) \land \left(x \cdot y \leq -6 \cdot 10^{+73} \lor \neg \left(x \cdot y \leq 2.8 \cdot 10^{+233}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+100} \lor \neg \left(a \cdot b \leq 10^{+18}\right):\\ \;\;\;\;a \cdot \left(b + \frac{z \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -1e+100) (not (<= (* a b) 1e+18)))
   (* a (+ b (/ (* z t) a)))
   (+ (* x y) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -1e+100) || !((a * b) <= 1e+18)) {
		tmp = a * (b + ((z * t) / a));
	} 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 (((a * b) <= (-1d+100)) .or. (.not. ((a * b) <= 1d+18))) then
        tmp = a * (b + ((z * t) / a))
    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 (((a * b) <= -1e+100) || !((a * b) <= 1e+18)) {
		tmp = a * (b + ((z * t) / a));
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -1e+100) or not ((a * b) <= 1e+18):
		tmp = a * (b + ((z * t) / a))
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -1e+100) || !(Float64(a * b) <= 1e+18))
		tmp = Float64(a * Float64(b + Float64(Float64(z * t) / a)));
	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 (((a * b) <= -1e+100) || ~(((a * b) <= 1e+18)))
		tmp = a * (b + ((z * t) / a));
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+100], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+18]], $MachinePrecision]], N[(a * N[(b + N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.00000000000000002e100 or 1e18 < (*.f64 a b)

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 98.1%

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

   4. Taylor expanded in x around 0 87.8%

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

   if -1.00000000000000002e100 < (*.f64 a b) < 1e18

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0 87.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+100} \lor \neg \left(a \cdot b \leq 10^{+18}\right):\\ \;\;\;\;a \cdot \left(b + \frac{z \cdot t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -0.0005 \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+109}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* z t) -0.0005) (not (<= (* z t) 2e+109)))
   (+ (* 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 (((z * t) <= -0.0005) || !((z * t) <= 2e+109)) {
		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 (((z * t) <= (-0.0005d0)) .or. (.not. ((z * t) <= 2d+109))) 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 (((z * t) <= -0.0005) || !((z * t) <= 2e+109)) {
		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 ((z * t) <= -0.0005) or not ((z * t) <= 2e+109):
		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(z * t) <= -0.0005) || !(Float64(z * t) <= 2e+109))
		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 (((z * t) <= -0.0005) || ~(((z * t) <= 2e+109)))
		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[Or[LessEqual[N[(z * t), $MachinePrecision], -0.0005], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+109]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 z t) < -5.0000000000000001e-4 or 1.99999999999999996e109 < (*.f64 z t)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 87.7%

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

   if -5.0000000000000001e-4 < (*.f64 z t) < 1.99999999999999996e109

   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 0 88.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -0.0005 \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+109}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.4 \cdot 10^{+185} \lor \neg \left(a \cdot b \leq 3.3 \cdot 10^{+38}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -7.4e+185) (not (<= (* a b) 3.3e+38))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -7.4e+185) || !((a * b) <= 3.3e+38)) {
		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) <= (-7.4d+185)) .or. (.not. ((a * b) <= 3.3d+38))) 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) <= -7.4e+185) || !((a * b) <= 3.3e+38)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -7.4e+185) or not ((a * b) <= 3.3e+38):
		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) <= -7.4e+185) || !(Float64(a * b) <= 3.3e+38))
		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) <= -7.4e+185) || ~(((a * b) <= 3.3e+38)))
		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], -7.4e+185], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.3e+38]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.3999999999999995e185 or 3.2999999999999999e38 < (*.f64 a b)

   1. Initial program 95.5%

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

   3. Taylor expanded in a around inf 75.9%

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

   if -7.3999999999999995e185 < (*.f64 a b) < 3.2999999999999999e38

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 47.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.4 \cdot 10^{+185} \lor \neg \left(a \cdot b \leq 3.3 \cdot 10^{+38}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.6% 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 35.1%

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

Reproduce

herbie shell --seed 2024095 
(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)))