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

Percentage Accurate: 97.9% → 99.0%

Time: 4.0s

Alternatives: 10

Speedup: 0.5×

• 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: 97.9% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-+l+ 96.9%

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

   2. fma-def 98.0%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 3: 98.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-+l+ 96.9%

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

   2. fma-def 98.0%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 4: 98.8% accurate, 0.5× 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%

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

   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 x around inf 50.0%

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

4. Final simplification 98.4%

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

Alternative 5: 54.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{-305}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 48000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -5.4e+54)
   (* a b)
   (if (<= (* a b) 4.6e-305)
     (* z t)
     (if (<= (* a b) 2.3e-248)
       (* x y)
       (if (<= (* a b) 48000000000000.0) (* z t) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -5.4e+54) {
		tmp = a * b;
	} else if ((a * b) <= 4.6e-305) {
		tmp = z * t;
	} else if ((a * b) <= 2.3e-248) {
		tmp = x * y;
	} else if ((a * b) <= 48000000000000.0) {
		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) <= (-5.4d+54)) then
        tmp = a * b
    else if ((a * b) <= 4.6d-305) then
        tmp = z * t
    else if ((a * b) <= 2.3d-248) then
        tmp = x * y
    else if ((a * b) <= 48000000000000.0d0) 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) <= -5.4e+54) {
		tmp = a * b;
	} else if ((a * b) <= 4.6e-305) {
		tmp = z * t;
	} else if ((a * b) <= 2.3e-248) {
		tmp = x * y;
	} else if ((a * b) <= 48000000000000.0) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -5.4e+54:
		tmp = a * b
	elif (a * b) <= 4.6e-305:
		tmp = z * t
	elif (a * b) <= 2.3e-248:
		tmp = x * y
	elif (a * b) <= 48000000000000.0:
		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) <= -5.4e+54)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 4.6e-305)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.3e-248)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 48000000000000.0)
		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) <= -5.4e+54)
		tmp = a * b;
	elseif ((a * b) <= 4.6e-305)
		tmp = z * t;
	elseif ((a * b) <= 2.3e-248)
		tmp = x * y;
	elseif ((a * b) <= 48000000000000.0)
		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], -5.4e+54], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.6e-305], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.3e-248], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 48000000000000.0], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.40000000000000022e54 or 4.8e13 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 70.8%

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

   if -5.40000000000000022e54 < (*.f64 a b) < 4.5999999999999999e-305 or 2.3e-248 < (*.f64 a b) < 4.8e13

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 56.7%

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

   if 4.5999999999999999e-305 < (*.f64 a b) < 2.3e-248

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{-305}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-248}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 48000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 6: 77.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+244} \lor \neg \left(x \leq -1.8 \cdot 10^{+225}\right) \land \left(x \leq -9.8 \cdot 10^{+129} \lor \neg \left(x \leq 1.65 \cdot 10^{-94}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -7.5e+244)
         (and (not (<= x -1.8e+225))
              (or (<= x -9.8e+129) (not (<= x 1.65e-94)))))
   (+ (* a b) (* x y))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7.5e+244) || (!(x <= -1.8e+225) && ((x <= -9.8e+129) || !(x <= 1.65e-94)))) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-7.5d+244)) .or. (.not. (x <= (-1.8d+225))) .and. (x <= (-9.8d+129)) .or. (.not. (x <= 1.65d-94))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7.5e+244) || (!(x <= -1.8e+225) && ((x <= -9.8e+129) || !(x <= 1.65e-94)))) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -7.5e+244) or (not (x <= -1.8e+225) and ((x <= -9.8e+129) or not (x <= 1.65e-94))):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -7.5e+244) || (!(x <= -1.8e+225) && ((x <= -9.8e+129) || !(x <= 1.65e-94))))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -7.5e+244) || (~((x <= -1.8e+225)) && ((x <= -9.8e+129) || ~((x <= 1.65e-94)))))
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -7.5e+244], And[N[Not[LessEqual[x, -1.8e+225]], $MachinePrecision], Or[LessEqual[x, -9.8e+129], N[Not[LessEqual[x, 1.65e-94]], $MachinePrecision]]]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e244 or -1.7999999999999999e225 < x < -9.8e129 or 1.6500000000000001e-94 < x

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 70.3%

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

   if -7.5e244 < x < -1.7999999999999999e225 or -9.8e129 < x < 1.6500000000000001e-94

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 82.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+244} \lor \neg \left(x \leq -1.8 \cdot 10^{+225}\right) \land \left(x \leq -9.8 \cdot 10^{+129} \lor \neg \left(x \leq 1.65 \cdot 10^{-94}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 7: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+276}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+224} \lor \neg \left(x \leq -5.6 \cdot 10^{+182}\right) \land x \leq 1.25 \cdot 10^{-93}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+276)
   (* x y)
   (if (or (<= x -7.2e+224) (and (not (<= x -5.6e+182)) (<= x 1.25e-93)))
     (+ (* a b) (* z t))
     (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+276) {
		tmp = x * y;
	} else if ((x <= -7.2e+224) || (!(x <= -5.6e+182) && (x <= 1.25e-93))) {
		tmp = (a * b) + (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 <= (-9.5d+276)) then
        tmp = x * y
    else if ((x <= (-7.2d+224)) .or. (.not. (x <= (-5.6d+182))) .and. (x <= 1.25d-93)) then
        tmp = (a * b) + (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 <= -9.5e+276) {
		tmp = x * y;
	} else if ((x <= -7.2e+224) || (!(x <= -5.6e+182) && (x <= 1.25e-93))) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+276:
		tmp = x * y
	elif (x <= -7.2e+224) or (not (x <= -5.6e+182) and (x <= 1.25e-93)):
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+276)
		tmp = Float64(x * y);
	elseif ((x <= -7.2e+224) || (!(x <= -5.6e+182) && (x <= 1.25e-93)))
		tmp = Float64(Float64(a * b) + 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 <= -9.5e+276)
		tmp = x * y;
	elseif ((x <= -7.2e+224) || (~((x <= -5.6e+182)) && (x <= 1.25e-93)))
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+276], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, -7.2e+224], And[N[Not[LessEqual[x, -5.6e+182]], $MachinePrecision], LessEqual[x, 1.25e-93]]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000013e276 or -7.2e224 < x < -5.60000000000000013e182 or 1.24999999999999999e-93 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 46.8%

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

   if -9.50000000000000013e276 < x < -7.2e224 or -5.60000000000000013e182 < x < 1.24999999999999999e-93

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 79.8%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+276}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+224} \lor \neg \left(x \leq -5.6 \cdot 10^{+182}\right) \land x \leq 1.25 \cdot 10^{-93}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+51} \lor \neg \left(a \cdot b \leq 4.9 \cdot 10^{+14}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -1.8e+51) (not (<= (* a b) 4.9e+14)))
   (+ (* 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 (((a * b) <= -1.8e+51) || !((a * b) <= 4.9e+14)) {
		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 (((a * b) <= (-1.8d+51)) .or. (.not. ((a * b) <= 4.9d+14))) 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 (((a * b) <= -1.8e+51) || !((a * b) <= 4.9e+14)) {
		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 ((a * b) <= -1.8e+51) or not ((a * b) <= 4.9e+14):
		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(a * b) <= -1.8e+51) || !(Float64(a * b) <= 4.9e+14))
		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 (((a * b) <= -1.8e+51) || ~(((a * b) <= 4.9e+14)))
		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[Or[LessEqual[N[(a * b), $MachinePrecision], -1.8e+51], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.9e+14]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 a b) < -1.80000000000000005e51 or 4.9e14 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 86.5%

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

   if -1.80000000000000005e51 < (*.f64 a b) < 4.9e14

   1. Initial program 98.6%

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

   2. Taylor expanded in a around 0 91.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.8 \cdot 10^{+51} \lor \neg \left(a \cdot b \leq 4.9 \cdot 10^{+14}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 9: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 68000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -5.8e+54)
   (* a b)
   (if (<= (* a b) 68000000000000.0) (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -5.8e+54) {
		tmp = a * b;
	} else if ((a * b) <= 68000000000000.0) {
		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) <= (-5.8d+54)) then
        tmp = a * b
    else if ((a * b) <= 68000000000000.0d0) 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) <= -5.8e+54) {
		tmp = a * b;
	} else if ((a * b) <= 68000000000000.0) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -5.8e+54:
		tmp = a * b
	elif (a * b) <= 68000000000000.0:
		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) <= -5.8e+54)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 68000000000000.0)
		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) <= -5.8e+54)
		tmp = a * b;
	elseif ((a * b) <= 68000000000000.0)
		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], -5.8e+54], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 68000000000000.0], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.7999999999999997e54 or 6.8e13 < (*.f64 a b)

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 70.8%

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

   if -5.7999999999999997e54 < (*.f64 a b) < 6.8e13

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 54.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+54}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 68000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 10: 36.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in a around inf 35.8%

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

3. Final simplification 35.8%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023199 
(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)))