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

Percentage Accurate: 97.9% → 98.5%

Time: 6.5s

Alternatives: 8

Speedup: 0.4×

• 32.6% 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: 98.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* x y) (* z t)) (* a b))))
   (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 = ((x * y) + (z * t)) + (a * b);
	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 = ((x * y) + (z * t)) + (a * b);
	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 = ((x * y) + (z * t)) + (a * b)
	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(Float64(x * y) + Float64(z * t)) + Float64(a * b))
	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 = ((x * y) + (z * t)) + (a * b);
	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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $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 56.3%

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

Alternative 2: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.3%

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

   3. fma-define 97.7%

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

3. Simplified 97.7%

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

Alternative 3: 55.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.45 \cdot 10^{+119}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -4.05 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-304}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{-63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{+52}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.45e+119)
   (* a b)
   (if (<= (* a b) -4.05e-109)
     (* x y)
     (if (<= (* a b) 2.9e-304)
       (* z t)
       (if (<= (* a b) 3.4e-63)
         (* x y)
         (if (<= (* a b) 1e+52) (* z t) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.45e+119) {
		tmp = a * b;
	} else if ((a * b) <= -4.05e-109) {
		tmp = x * y;
	} else if ((a * b) <= 2.9e-304) {
		tmp = z * t;
	} else if ((a * b) <= 3.4e-63) {
		tmp = x * y;
	} else if ((a * b) <= 1e+52) {
		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) <= (-1.45d+119)) then
        tmp = a * b
    else if ((a * b) <= (-4.05d-109)) then
        tmp = x * y
    else if ((a * b) <= 2.9d-304) then
        tmp = z * t
    else if ((a * b) <= 3.4d-63) then
        tmp = x * y
    else if ((a * b) <= 1d+52) 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) <= -1.45e+119) {
		tmp = a * b;
	} else if ((a * b) <= -4.05e-109) {
		tmp = x * y;
	} else if ((a * b) <= 2.9e-304) {
		tmp = z * t;
	} else if ((a * b) <= 3.4e-63) {
		tmp = x * y;
	} else if ((a * b) <= 1e+52) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.45e+119:
		tmp = a * b
	elif (a * b) <= -4.05e-109:
		tmp = x * y
	elif (a * b) <= 2.9e-304:
		tmp = z * t
	elif (a * b) <= 3.4e-63:
		tmp = x * y
	elif (a * b) <= 1e+52:
		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) <= -1.45e+119)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -4.05e-109)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.9e-304)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 3.4e-63)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1e+52)
		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) <= -1.45e+119)
		tmp = a * b;
	elseif ((a * b) <= -4.05e-109)
		tmp = x * y;
	elseif ((a * b) <= 2.9e-304)
		tmp = z * t;
	elseif ((a * b) <= 3.4e-63)
		tmp = x * y;
	elseif ((a * b) <= 1e+52)
		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], -1.45e+119], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.05e-109], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.9e-304], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.4e-63], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+52], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.45000000000000004e119 or 9.9999999999999999e51 < (*.f64 a b)

   1. Initial program 94.7%

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

   3. Taylor expanded in a around inf 70.2%

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

   if -1.45000000000000004e119 < (*.f64 a b) < -4.0500000000000001e-109 or 2.9e-304 < (*.f64 a b) < 3.39999999999999998e-63

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 56.1%

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

   if -4.0500000000000001e-109 < (*.f64 a b) < 2.9e-304 or 3.39999999999999998e-63 < (*.f64 a b) < 9.9999999999999999e51

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 59.6%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.45 \cdot 10^{+119}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -4.05 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-304}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{-63}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 10^{+52}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+144} \lor \neg \left(x \cdot y \leq -6 \cdot 10^{+58}\right) \land \left(x \cdot y \leq -2.3 \cdot 10^{-29} \lor \neg \left(x \cdot y \leq 3.15 \cdot 10^{+130}\right)\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -4.5e+144)
         (and (not (<= (* x y) -6e+58))
              (or (<= (* x y) -2.3e-29) (not (<= (* x y) 3.15e+130)))))
   (+ (* 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) <= -4.5e+144) || (!((x * y) <= -6e+58) && (((x * y) <= -2.3e-29) || !((x * y) <= 3.15e+130)))) {
		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) <= (-4.5d+144)) .or. (.not. ((x * y) <= (-6d+58))) .and. ((x * y) <= (-2.3d-29)) .or. (.not. ((x * y) <= 3.15d+130))) 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) <= -4.5e+144) || (!((x * y) <= -6e+58) && (((x * y) <= -2.3e-29) || !((x * y) <= 3.15e+130)))) {
		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) <= -4.5e+144) or (not ((x * y) <= -6e+58) and (((x * y) <= -2.3e-29) or not ((x * y) <= 3.15e+130))):
		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) <= -4.5e+144) || (!(Float64(x * y) <= -6e+58) && ((Float64(x * y) <= -2.3e-29) || !(Float64(x * y) <= 3.15e+130))))
		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) <= -4.5e+144) || (~(((x * y) <= -6e+58)) && (((x * y) <= -2.3e-29) || ~(((x * y) <= 3.15e+130)))))
		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], -4.5e+144], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -6e+58]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -2.3e-29], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.15e+130]], $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) < -4.49999999999999967e144 or -6.0000000000000005e58 < (*.f64 x y) < -2.29999999999999991e-29 or 3.15e130 < (*.f64 x y)

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0 87.1%

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

   if -4.49999999999999967e144 < (*.f64 x y) < -6.0000000000000005e58 or -2.29999999999999991e-29 < (*.f64 x y) < 3.15e130

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 89.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+144} \lor \neg \left(x \cdot y \leq -6 \cdot 10^{+58}\right) \land \left(x \cdot y \leq -2.3 \cdot 10^{-29} \lor \neg \left(x \cdot y \leq 3.15 \cdot 10^{+130}\right)\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq -8.5 \cdot 10^{+56}\right) \land \left(x \cdot y \leq -3.65 \cdot 10^{+18} \lor \neg \left(x \cdot y \leq 6.3 \cdot 10^{+153}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.4e+145)
         (and (not (<= (* x y) -8.5e+56))
              (or (<= (* x y) -3.65e+18) (not (<= (* x y) 6.3e+153)))))
   (* x y)
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.4e+145) || (!((x * y) <= -8.5e+56) && (((x * y) <= -3.65e+18) || !((x * y) <= 6.3e+153)))) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((x * y) <= (-1.4d+145)) .or. (.not. ((x * y) <= (-8.5d+56))) .and. ((x * y) <= (-3.65d+18)) .or. (.not. ((x * y) <= 6.3d+153))) then
        tmp = x * y
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.4e+145) || (!((x * y) <= -8.5e+56) && (((x * y) <= -3.65e+18) || !((x * y) <= 6.3e+153)))) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -1.4e+145) or (not ((x * y) <= -8.5e+56) and (((x * y) <= -3.65e+18) or not ((x * y) <= 6.3e+153))):
		tmp = x * y
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -1.4e+145) || (!(Float64(x * y) <= -8.5e+56) && ((Float64(x * y) <= -3.65e+18) || !(Float64(x * y) <= 6.3e+153))))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -1.4e+145) || (~(((x * y) <= -8.5e+56)) && (((x * y) <= -3.65e+18) || ~(((x * y) <= 6.3e+153)))))
		tmp = x * y;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.4e+145], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -8.5e+56]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], -3.65e+18], N[Not[LessEqual[N[(x * y), $MachinePrecision], 6.3e+153]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.3999999999999999e145 or -8.4999999999999998e56 < (*.f64 x y) < -3.65e18 or 6.3000000000000001e153 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 81.7%

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

   if -1.3999999999999999e145 < (*.f64 x y) < -8.4999999999999998e56 or -3.65e18 < (*.f64 x y) < 6.3000000000000001e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 86.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq -8.5 \cdot 10^{+56}\right) \land \left(x \cdot y \leq -3.65 \cdot 10^{+18} \lor \neg \left(x \cdot y \leq 6.3 \cdot 10^{+153}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{-41}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.1 \cdot 10^{-8} \lor \neg \left(x \cdot y \leq 1.75 \cdot 10^{+51}\right) \land x \cdot y \leq 1.72 \cdot 10^{+131}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2.05e-41)
   (+ (* x y) (* z t))
   (if (or (<= (* x y) 5.1e-8)
           (and (not (<= (* x y) 1.75e+51)) (<= (* x y) 1.72e+131)))
     (+ (* 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 ((x * y) <= -2.05e-41) {
		tmp = (x * y) + (z * t);
	} else if (((x * y) <= 5.1e-8) || (!((x * y) <= 1.75e+51) && ((x * y) <= 1.72e+131))) {
		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 ((x * y) <= (-2.05d-41)) then
        tmp = (x * y) + (z * t)
    else if (((x * y) <= 5.1d-8) .or. (.not. ((x * y) <= 1.75d+51)) .and. ((x * y) <= 1.72d+131)) 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 ((x * y) <= -2.05e-41) {
		tmp = (x * y) + (z * t);
	} else if (((x * y) <= 5.1e-8) || (!((x * y) <= 1.75e+51) && ((x * y) <= 1.72e+131))) {
		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 (x * y) <= -2.05e-41:
		tmp = (x * y) + (z * t)
	elif ((x * y) <= 5.1e-8) or (not ((x * y) <= 1.75e+51) and ((x * y) <= 1.72e+131)):
		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(x * y) <= -2.05e-41)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif ((Float64(x * y) <= 5.1e-8) || (!(Float64(x * y) <= 1.75e+51) && (Float64(x * y) <= 1.72e+131)))
		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 ((x * y) <= -2.05e-41)
		tmp = (x * y) + (z * t);
	elseif (((x * y) <= 5.1e-8) || (~(((x * y) <= 1.75e+51)) && ((x * y) <= 1.72e+131)))
		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[LessEqual[N[(x * y), $MachinePrecision], -2.05e-41], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 5.1e-8], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.75e+51]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1.72e+131]]], 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 3 regimes

2. if (*.f64 x y) < -2.05000000000000007e-41

   1. Initial program 94.8%

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

   3. Taylor expanded in a around 0 81.7%

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

   if -2.05000000000000007e-41 < (*.f64 x y) < 5.10000000000000001e-8 or 1.75e51 < (*.f64 x y) < 1.71999999999999994e131

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 93.9%

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

   if 5.10000000000000001e-8 < (*.f64 x y) < 1.75e51 or 1.71999999999999994e131 < (*.f64 x y)

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 89.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{-41}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.1 \cdot 10^{-8} \lor \neg \left(x \cdot y \leq 1.75 \cdot 10^{+51}\right) \land x \cdot y \leq 1.72 \cdot 10^{+131}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-13} \lor \neg \left(t \leq 1.25 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9e-13) (not (<= t 1.25e+49))) (* z t) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e-13) || !(t <= 1.25e+49)) {
		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 <= (-9d-13)) .or. (.not. (t <= 1.25d+49))) 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 <= -9e-13) || !(t <= 1.25e+49)) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9e-13) or not (t <= 1.25e+49):
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9e-13) || !(t <= 1.25e+49))
		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 <= -9e-13) || ~((t <= 1.25e+49)))
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9e-13], N[Not[LessEqual[t, 1.25e+49]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9e-13 or 1.2500000000000001e49 < t

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 57.8%

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

   if -9e-13 < t < 1.2500000000000001e49

   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 45.9%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-13} \lor \neg \left(t \leq 1.25 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.9% 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 96.5%

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

3. Taylor expanded in a around inf 34.7%

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

Reproduce

herbie shell --seed 2024089 
(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)))