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

Percentage Accurate: 98.0% → 98.7%

Time: 6.3s

Alternatives: 8

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: 98.0% 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: 98.7% accurate, 0.4× speedup

Math

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

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))))

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;
	}
	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;
	}
	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
	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 * 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 = x * 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[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 40.0%

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

   4. Taylor expanded in x around inf 80.0%

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

4. Final simplification 99.6%

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

Alternative 2: 98.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(a * b + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * t), $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. associate-+l+ 98.0%

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

   2. fma-def 98.4%

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

   3. +-commutative 98.4%

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

   4. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 98.0%

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

   2. +-commutative 98.0%

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

   3. fma-udef 98.0%

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

   4. associate-+r+ 98.0%

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

   5. +-commutative 98.0%

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

   6. associate-+r+ 98.0%

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

   7. fma-def 98.8%

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

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

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

Alternative 3: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-250}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.1 \cdot 10^{-288}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{-112}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -4.8e-31)
   (* x y)
   (if (<= (* x y) -2.9e-250)
     (* z t)
     (if (<= (* x y) 5.1e-288)
       (* a b)
       (if (<= (* x y) 1.65e-112)
         (* z t)
         (if (<= (* x y) 1.6e+50) (* a b) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4.8e-31) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e-250) {
		tmp = z * t;
	} else if ((x * y) <= 5.1e-288) {
		tmp = a * b;
	} else if ((x * y) <= 1.65e-112) {
		tmp = z * t;
	} else if ((x * y) <= 1.6e+50) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * y) <= (-4.8d-31)) then
        tmp = x * y
    else if ((x * y) <= (-2.9d-250)) then
        tmp = z * t
    else if ((x * y) <= 5.1d-288) then
        tmp = a * b
    else if ((x * y) <= 1.65d-112) then
        tmp = z * t
    else if ((x * y) <= 1.6d+50) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -4.8e-31) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e-250) {
		tmp = z * t;
	} else if ((x * y) <= 5.1e-288) {
		tmp = a * b;
	} else if ((x * y) <= 1.65e-112) {
		tmp = z * t;
	} else if ((x * y) <= 1.6e+50) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -4.8e-31:
		tmp = x * y
	elif (x * y) <= -2.9e-250:
		tmp = z * t
	elif (x * y) <= 5.1e-288:
		tmp = a * b
	elif (x * y) <= 1.65e-112:
		tmp = z * t
	elif (x * y) <= 1.6e+50:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -4.8e-31)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.9e-250)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 5.1e-288)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 1.65e-112)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.6e+50)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -4.8e-31)
		tmp = x * y;
	elseif ((x * y) <= -2.9e-250)
		tmp = z * t;
	elseif ((x * y) <= 5.1e-288)
		tmp = a * b;
	elseif ((x * y) <= 1.65e-112)
		tmp = z * t;
	elseif ((x * y) <= 1.6e+50)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.8e-31], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.9e-250], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.1e-288], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.65e-112], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.6e+50], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.8e-31 or 1.59999999999999991e50 < (*.f64 x y)

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 86.5%

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

   4. Taylor expanded in x around inf 71.9%

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

   if -4.8e-31 < (*.f64 x y) < -2.9000000000000002e-250 or 5.09999999999999995e-288 < (*.f64 x y) < 1.65e-112

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.0%

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

   4. Taylor expanded in t around inf 61.4%

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

   if -2.9000000000000002e-250 < (*.f64 x y) < 5.09999999999999995e-288 or 1.65e-112 < (*.f64 x y) < 1.59999999999999991e50

   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 55.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-250}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.1 \cdot 10^{-288}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{-112}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.2 \cdot 10^{+136} \lor \neg \left(x \cdot y \leq 9.8 \cdot 10^{+72}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -4.2e+136) (not (<= (* x y) 9.8e+72)))
   (* 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) <= -4.2e+136) || !((x * y) <= 9.8e+72)) {
		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) <= (-4.2d+136)) .or. (.not. ((x * y) <= 9.8d+72))) 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) <= -4.2e+136) || !((x * y) <= 9.8e+72)) {
		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) <= -4.2e+136) or not ((x * y) <= 9.8e+72):
		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) <= -4.2e+136) || !(Float64(x * y) <= 9.8e+72))
		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) <= -4.2e+136) || ~(((x * y) <= 9.8e+72)))
		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], -4.2e+136], N[Not[LessEqual[N[(x * y), $MachinePrecision], 9.8e+72]], $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) < -4.1999999999999998e136 or 9.80000000000000012e72 < (*.f64 x y)

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 94.4%

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

   4. Taylor expanded in x around inf 84.0%

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

   if -4.1999999999999998e136 < (*.f64 x y) < 9.80000000000000012e72

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.2 \cdot 10^{+136} \lor \neg \left(x \cdot y \leq 9.8 \cdot 10^{+72}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{-29} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -6e-29) (not (<= (* x y) 7.5e+54)))
   (+ (* 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 (((x * y) <= -6e-29) || !((x * y) <= 7.5e+54)) {
		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 (((x * y) <= (-6d-29)) .or. (.not. ((x * y) <= 7.5d+54))) 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 (((x * y) <= -6e-29) || !((x * y) <= 7.5e+54)) {
		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 ((x * y) <= -6e-29) or not ((x * y) <= 7.5e+54):
		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(x * y) <= -6e-29) || !(Float64(x * y) <= 7.5e+54))
		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 (((x * y) <= -6e-29) || ~(((x * y) <= 7.5e+54)))
		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[Or[LessEqual[N[(x * y), $MachinePrecision], -6e-29], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.5e+54]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 x y) < -6.0000000000000005e-29 or 7.50000000000000042e54 < (*.f64 x y)

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. fma-def 96.9%

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

      3. +-commutative 96.9%

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

      4. fma-def 96.9%

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

   3. Simplified 96.9%

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

      1. fma-udef 96.2%

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

      2. +-commutative 96.2%

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

      3. fma-udef 96.1%

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

      4. associate-+r+ 96.1%

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

      5. +-commutative 96.1%

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

      6. associate-+r+ 96.1%

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

      7. fma-def 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in a around 0 82.8%

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

   if -6.0000000000000005e-29 < (*.f64 x y) < 7.50000000000000042e54

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{-29} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{-20} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -7e-20) (not (<= (* x y) 4.8e+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) <= -7e-20) || !((x * y) <= 4.8e+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) <= (-7d-20)) .or. (.not. ((x * y) <= 4.8d+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) <= -7e-20) || !((x * y) <= 4.8e+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) <= -7e-20) or not ((x * y) <= 4.8e+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) <= -7e-20) || !(Float64(x * y) <= 4.8e+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) <= -7e-20) || ~(((x * y) <= 4.8e+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], -7e-20], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.8e+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) < -7.00000000000000007e-20 or 4.80000000000000009e26 < (*.f64 x y)

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 87.1%

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

   if -7.00000000000000007e-20 < (*.f64 x y) < 4.80000000000000009e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{-20} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-73} \lor \neg \left(t \leq 2.2 \cdot 10^{+73}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e-73) (not (<= t 2.2e+73))) (* z t) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e-73) || !(t <= 2.2e+73)) {
		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 ((t <= (-3d-73)) .or. (.not. (t <= 2.2d+73))) 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 ((t <= -3e-73) || !(t <= 2.2e+73)) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e-73) or not (t <= 2.2e+73):
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e-73) || !(t <= 2.2e+73))
		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 ((t <= -3e-73) || ~((t <= 2.2e+73)))
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e-73], N[Not[LessEqual[t, 2.2e+73]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e-73 or 2.2e73 < t

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 69.8%

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

   4. Taylor expanded in t around inf 44.9%

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

   if -3e-73 < t < 2.2e73

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 37.2%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-73} \lor \neg \left(t \leq 2.2 \cdot 10^{+73}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.4% 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 98.0%

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

3. Taylor expanded in a around inf 33.8%

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

4. Final simplification 33.8%

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

Reproduce

herbie shell --seed 2024029 
(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)))