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

Percentage Accurate: 97.8% → 98.5%

Time: 5.1s

Alternatives: 9

Speedup: 0.5×

• 33.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% 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: 98.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

   3. Simplified 100.0%

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

   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. Taylor expanded in a around 0 66.7%

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

4. Final simplification 99.2%

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

Alternative 2: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * y + N[(a * b + 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. associate-+l+ 97.6%

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

   2. fma-def 98.0%

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

   3. +-commutative 98.0%

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

   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. Final simplification 98.4%

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

Alternative 3: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+108} \lor \neg \left(x \cdot y \leq 0.011 \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+60}\right) \land x \cdot y \leq 2.55 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -2.2e+108)
         (not
          (or (<= (* x y) 0.011)
              (and (not (<= (* x y) 2.9e+60)) (<= (* x y) 2.55e+135)))))
   (+ (* 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) <= -2.2e+108) || !(((x * y) <= 0.011) || (!((x * y) <= 2.9e+60) && ((x * y) <= 2.55e+135)))) {
		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) <= (-2.2d+108)) .or. (.not. ((x * y) <= 0.011d0) .or. (.not. ((x * y) <= 2.9d+60)) .and. ((x * y) <= 2.55d+135))) 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) <= -2.2e+108) || !(((x * y) <= 0.011) || (!((x * y) <= 2.9e+60) && ((x * y) <= 2.55e+135)))) {
		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) <= -2.2e+108) or not (((x * y) <= 0.011) or (not ((x * y) <= 2.9e+60) and ((x * y) <= 2.55e+135))):
		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) <= -2.2e+108) || !((Float64(x * y) <= 0.011) || (!(Float64(x * y) <= 2.9e+60) && (Float64(x * y) <= 2.55e+135))))
		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) <= -2.2e+108) || ~((((x * y) <= 0.011) || (~(((x * y) <= 2.9e+60)) && ((x * y) <= 2.55e+135)))))
		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], -2.2e+108], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], 0.011], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+60]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 2.55e+135]]]], $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) < -2.2000000000000001e108 or 0.010999999999999999 < (*.f64 x y) < 2.9e60 or 2.54999999999999991e135 < (*.f64 x y)

   1. Initial program 95.8%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in z around 0 87.5%

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

   if -2.2000000000000001e108 < (*.f64 x y) < 0.010999999999999999 or 2.9e60 < (*.f64 x y) < 2.54999999999999991e135

   1. Initial program 98.7%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in x around 0 91.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+108} \lor \neg \left(x \cdot y \leq 0.011 \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+60}\right) \land x \cdot y \leq 2.55 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 4: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + t_1\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) t_1)))
   (if (<= t_2 INFINITY) t_2 t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + t_1;
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + t_1;
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + t_1)
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + t_1;
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

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%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   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. Taylor expanded in a around 0 66.7%

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

4. Final simplification 99.2%

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

Alternative 5: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.18 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.36 \cdot 10^{+135}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.18e+98)
   (* x y)
   (if (<= (* x y) 2.5e+15)
     (* z t)
     (if (<= (* x y) 5.2e+42)
       (* a b)
       (if (<= (* x y) 1.36e+135) (* z t) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.18e+98) {
		tmp = x * y;
	} else if ((x * y) <= 2.5e+15) {
		tmp = z * t;
	} else if ((x * y) <= 5.2e+42) {
		tmp = a * b;
	} else if ((x * y) <= 1.36e+135) {
		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) <= (-1.18d+98)) then
        tmp = x * y
    else if ((x * y) <= 2.5d+15) then
        tmp = z * t
    else if ((x * y) <= 5.2d+42) then
        tmp = a * b
    else if ((x * y) <= 1.36d+135) 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) <= -1.18e+98) {
		tmp = x * y;
	} else if ((x * y) <= 2.5e+15) {
		tmp = z * t;
	} else if ((x * y) <= 5.2e+42) {
		tmp = a * b;
	} else if ((x * y) <= 1.36e+135) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.18e+98:
		tmp = x * y
	elif (x * y) <= 2.5e+15:
		tmp = z * t
	elif (x * y) <= 5.2e+42:
		tmp = a * b
	elif (x * y) <= 1.36e+135:
		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) <= -1.18e+98)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.5e+15)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 5.2e+42)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 1.36e+135)
		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) <= -1.18e+98)
		tmp = x * y;
	elseif ((x * y) <= 2.5e+15)
		tmp = z * t;
	elseif ((x * y) <= 5.2e+42)
		tmp = a * b;
	elseif ((x * y) <= 1.36e+135)
		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], -1.18e+98], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+15], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.2e+42], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.36e+135], N[(z * t), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.18000000000000002e98 or 1.36000000000000007e135 < (*.f64 x y)

   1. Initial program 95.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in x around inf 80.4%

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

   if -1.18000000000000002e98 < (*.f64 x y) < 2.5e15 or 5.1999999999999998e42 < (*.f64 x y) < 1.36000000000000007e135

   1. Initial program 98.8%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in z around inf 51.6%

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

   if 2.5e15 < (*.f64 x y) < 5.1999999999999998e42

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in a around inf 66.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.18 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{+42}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.36 \cdot 10^{+135}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+104} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.4e+104) (not (<= (* x y) 3e+154)))
   (* 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) <= -3.4e+104) || !((x * y) <= 3e+154)) {
		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) <= (-3.4d+104)) .or. (.not. ((x * y) <= 3d+154))) 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) <= -3.4e+104) || !((x * y) <= 3e+154)) {
		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) <= -3.4e+104) or not ((x * y) <= 3e+154):
		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) <= -3.4e+104) || !(Float64(x * y) <= 3e+154))
		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) <= -3.4e+104) || ~(((x * y) <= 3e+154)))
		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], -3.4e+104], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3e+154]], $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) < -3.3999999999999997e104 or 3.00000000000000026e154 < (*.f64 x y)

   1. Initial program 94.6%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in x around inf 83.9%

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

   if -3.3999999999999997e104 < (*.f64 x y) < 3.00000000000000026e154

   1. Initial program 98.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in x around 0 87.0%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+104} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 7: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= y -3.4e-111)
     t_1
     (if (<= y 4.3e+92)
       (+ (* a b) (* z t))
       (if (<= y 2e+132) (+ (* x y) (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (y <= -3.4e-111) {
		tmp = t_1;
	} else if (y <= 4.3e+92) {
		tmp = (a * b) + (z * t);
	} else if (y <= 2e+132) {
		tmp = (x * y) + (a * b);
	} 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 = (x * y) + (z * t)
    if (y <= (-3.4d-111)) then
        tmp = t_1
    else if (y <= 4.3d+92) then
        tmp = (a * b) + (z * t)
    else if (y <= 2d+132) then
        tmp = (x * y) + (a * b)
    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 = (x * y) + (z * t);
	double tmp;
	if (y <= -3.4e-111) {
		tmp = t_1;
	} else if (y <= 4.3e+92) {
		tmp = (a * b) + (z * t);
	} else if (y <= 2e+132) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if y <= -3.4e-111:
		tmp = t_1
	elif y <= 4.3e+92:
		tmp = (a * b) + (z * t)
	elif y <= 2e+132:
		tmp = (x * y) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (y <= -3.4e-111)
		tmp = t_1;
	elseif (y <= 4.3e+92)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (y <= 2e+132)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (y <= -3.4e-111)
		tmp = t_1;
	elseif (y <= 4.3e+92)
		tmp = (a * b) + (z * t);
	elseif (y <= 2e+132)
		tmp = (x * y) + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e-111], t$95$1, If[LessEqual[y, 4.3e+92], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+132], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999997e-111 or 1.99999999999999998e132 < y

   1. Initial program 96.7%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in a around 0 74.9%

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

   if -3.39999999999999997e-111 < y < 4.2999999999999998e92

   1. Initial program 99.2%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in x around 0 84.9%

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

   if 4.2999999999999998e92 < y < 1.99999999999999998e132

   1. Initial program 88.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in z around 0 88.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-111}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 8: 48.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+93} \lor \neg \left(z \leq 8.6 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e+93) (not (<= z 8.6e-8))) (* z t) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+93) || !(z <= 8.6e-8)) {
		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 ((z <= (-3.5d+93)) .or. (.not. (z <= 8.6d-8))) 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 ((z <= -3.5e+93) || !(z <= 8.6e-8)) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e+93) or not (z <= 8.6e-8):
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e+93) || !(z <= 8.6e-8))
		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 ((z <= -3.5e+93) || ~((z <= 8.6e-8)))
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e+93], N[Not[LessEqual[z, 8.6e-8]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999998e93 or 8.6000000000000002e-8 < z

   1. Initial program 98.2%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in z around inf 64.7%

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

   if -3.49999999999999998e93 < z < 8.6000000000000002e-8

   1. Initial program 97.3%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]

   2. Taylor expanded in a around inf 43.0%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+93} \lor \neg \left(z \leq 8.6 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 9: 35.0% 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. Taylor expanded in a around inf 35.5%

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

3. Final simplification 35.5%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023308 
(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)))