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

Percentage Accurate: 98.0% → 98.9%

Time: 5.4s

Alternatives: 8

Speedup: 1.0×

• 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: 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: 98.9% 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 99.2%

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

   1. associate-+l+ 99.2%

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

   2. fma-def 99.2%

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

   3. +-commutative 99.2%

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

   4. fma-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 3: 53.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+115}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-69}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -4.45 \cdot 10^{-116}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-320}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2.7e+115)
   (* x y)
   (if (<= (* x y) -9.2e+20)
     (* a b)
     (if (<= (* x y) -1.65e-39)
       (* z t)
       (if (<= (* x y) -4.1e-69)
         (* a b)
         (if (<= (* x y) -4.45e-116)
           (* z t)
           (if (<= (* x y) -4e-320)
             (* a b)
             (if (<= (* x y) 2.4e+24) (* z t) (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -2.7e+115) {
		tmp = x * y;
	} else if ((x * y) <= -9.2e+20) {
		tmp = a * b;
	} else if ((x * y) <= -1.65e-39) {
		tmp = z * t;
	} else if ((x * y) <= -4.1e-69) {
		tmp = a * b;
	} else if ((x * y) <= -4.45e-116) {
		tmp = z * t;
	} else if ((x * y) <= -4e-320) {
		tmp = a * b;
	} else if ((x * y) <= 2.4e+24) {
		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) <= (-2.7d+115)) then
        tmp = x * y
    else if ((x * y) <= (-9.2d+20)) then
        tmp = a * b
    else if ((x * y) <= (-1.65d-39)) then
        tmp = z * t
    else if ((x * y) <= (-4.1d-69)) then
        tmp = a * b
    else if ((x * y) <= (-4.45d-116)) then
        tmp = z * t
    else if ((x * y) <= (-4d-320)) then
        tmp = a * b
    else if ((x * y) <= 2.4d+24) 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) <= -2.7e+115) {
		tmp = x * y;
	} else if ((x * y) <= -9.2e+20) {
		tmp = a * b;
	} else if ((x * y) <= -1.65e-39) {
		tmp = z * t;
	} else if ((x * y) <= -4.1e-69) {
		tmp = a * b;
	} else if ((x * y) <= -4.45e-116) {
		tmp = z * t;
	} else if ((x * y) <= -4e-320) {
		tmp = a * b;
	} else if ((x * y) <= 2.4e+24) {
		tmp = z * t;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -2.7e+115:
		tmp = x * y
	elif (x * y) <= -9.2e+20:
		tmp = a * b
	elif (x * y) <= -1.65e-39:
		tmp = z * t
	elif (x * y) <= -4.1e-69:
		tmp = a * b
	elif (x * y) <= -4.45e-116:
		tmp = z * t
	elif (x * y) <= -4e-320:
		tmp = a * b
	elif (x * y) <= 2.4e+24:
		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) <= -2.7e+115)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -9.2e+20)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -1.65e-39)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -4.1e-69)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -4.45e-116)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -4e-320)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 2.4e+24)
		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) <= -2.7e+115)
		tmp = x * y;
	elseif ((x * y) <= -9.2e+20)
		tmp = a * b;
	elseif ((x * y) <= -1.65e-39)
		tmp = z * t;
	elseif ((x * y) <= -4.1e-69)
		tmp = a * b;
	elseif ((x * y) <= -4.45e-116)
		tmp = z * t;
	elseif ((x * y) <= -4e-320)
		tmp = a * b;
	elseif ((x * y) <= 2.4e+24)
		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], -2.7e+115], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -9.2e+20], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.65e-39], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.1e-69], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.45e-116], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-320], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.4e+24], N[(z * t), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.70000000000000004e115 or 2.4000000000000001e24 < (*.f64 x y)

   1. Initial program 97.5%

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

   2. Taylor expanded in x around inf 89.1%

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

   3. Taylor expanded in x around inf 70.6%

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

   if -2.70000000000000004e115 < (*.f64 x y) < -9.2e20 or -1.64999999999999992e-39 < (*.f64 x y) < -4.0999999999999999e-69 or -4.45000000000000016e-116 < (*.f64 x y) < -3.99996e-320

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 60.7%

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

   if -9.2e20 < (*.f64 x y) < -1.64999999999999992e-39 or -4.0999999999999999e-69 < (*.f64 x y) < -4.45000000000000016e-116 or -3.99996e-320 < (*.f64 x y) < 2.4000000000000001e24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.0%

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

   3. Taylor expanded in t around inf 62.2%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+115}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-69}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -4.45 \cdot 10^{-116}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-320}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.6 \cdot 10^{+60} \lor \neg \left(a \cdot b \leq 3.05 \cdot 10^{+28} \lor \neg \left(a \cdot b \leq 6.5 \cdot 10^{+69}\right) \land a \cdot b \leq 6 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -4.6e+60)
         (not
          (or (<= (* a b) 3.05e+28)
              (and (not (<= (* a b) 6.5e+69)) (<= (* a b) 6e+95)))))
   (* a b)
   (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -4.6e+60) || !(((a * b) <= 3.05e+28) || (!((a * b) <= 6.5e+69) && ((a * b) <= 6e+95)))) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a * b) <= (-4.6d+60)) .or. (.not. ((a * b) <= 3.05d+28) .or. (.not. ((a * b) <= 6.5d+69)) .and. ((a * b) <= 6d+95))) then
        tmp = a * b
    else
        tmp = z * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -4.6e+60) || !(((a * b) <= 3.05e+28) || (!((a * b) <= 6.5e+69) && ((a * b) <= 6e+95)))) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -4.6e+60) or not (((a * b) <= 3.05e+28) or (not ((a * b) <= 6.5e+69) and ((a * b) <= 6e+95))):
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -4.6e+60) || !((Float64(a * b) <= 3.05e+28) || (!(Float64(a * b) <= 6.5e+69) && (Float64(a * b) <= 6e+95))))
		tmp = Float64(a * b);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a * b) <= -4.6e+60) || ~((((a * b) <= 3.05e+28) || (~(((a * b) <= 6.5e+69)) && ((a * b) <= 6e+95)))))
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -4.6e+60], N[Not[Or[LessEqual[N[(a * b), $MachinePrecision], 3.05e+28], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 6.5e+69]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 6e+95]]]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.60000000000000034e60 or 3.0500000000000001e28 < (*.f64 a b) < 6.5000000000000001e69 or 5.99999999999999982e95 < (*.f64 a b)

   1. Initial program 99.0%

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

   2. Taylor expanded in a around inf 70.8%

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

   if -4.60000000000000034e60 < (*.f64 a b) < 3.0500000000000001e28 or 6.5000000000000001e69 < (*.f64 a b) < 5.99999999999999982e95

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 58.6%

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

   3. Taylor expanded in t around inf 49.3%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.6 \cdot 10^{+60} \lor \neg \left(a \cdot b \leq 3.05 \cdot 10^{+28} \lor \neg \left(a \cdot b \leq 6.5 \cdot 10^{+69}\right) \land a \cdot b \leq 6 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 5: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.4e+116) (not (<= (* x y) 7.5e+174)))
   (* 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+116) || !((x * y) <= 7.5e+174)) {
		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+116)) .or. (.not. ((x * y) <= 7.5d+174))) 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+116) || !((x * y) <= 7.5e+174)) {
		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+116) or not ((x * y) <= 7.5e+174):
		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+116) || !(Float64(x * y) <= 7.5e+174))
		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+116) || ~(((x * y) <= 7.5e+174)))
		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+116], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.5e+174]], $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) < -3.40000000000000023e116 or 7.5000000000000004e174 < (*.f64 x y)

   1. Initial program 96.7%

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

   2. Taylor expanded in x around inf 91.5%

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

   3. Taylor expanded in x around inf 82.7%

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

   if -3.40000000000000023e116 < (*.f64 x y) < 7.5000000000000004e174

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+25} \lor \neg \left(x \cdot y \leq 1.65 \cdot 10^{+24}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.55e+25) (not (<= (* x y) 1.65e+24)))
   (+ (* 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 * y) <= -1.55e+25) || !((x * y) <= 1.65e+24)) {
		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 * y) <= (-1.55d+25)) .or. (.not. ((x * y) <= 1.65d+24))) 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 * y) <= -1.55e+25) || !((x * y) <= 1.65e+24)) {
		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 * y) <= -1.55e+25) or not ((x * y) <= 1.65e+24):
		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 ((Float64(x * y) <= -1.55e+25) || !(Float64(x * y) <= 1.65e+24))
		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 * y) <= -1.55e+25) || ~(((x * y) <= 1.65e+24)))
		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[N[(x * y), $MachinePrecision], -1.55e+25], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.65e+24]], $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 (*.f64 x y) < -1.5499999999999999e25 or 1.6499999999999999e24 < (*.f64 x y)

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 89.8%

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

   if -1.5499999999999999e25 < (*.f64 x y) < 1.6499999999999999e24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+25} \lor \neg \left(x \cdot y \leq 1.65 \cdot 10^{+24}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 7: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((x * y) + (z * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 8: 35.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Taylor expanded in a around inf 34.9%

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

3. Final simplification 34.9%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023322 
(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)))