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

Percentage Accurate: 97.9% → 99.0%

Time: 6.6s

Alternatives: 8

Speedup: 1.0×

• 32.5% 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: 97.9% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. +-commutative 98.4%

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

   2. *-commutative 98.4%

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

   3. fma-define 99.2%

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

   4. fma-define 99.6%

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

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-315}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{-323}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \cdot a \leq 7.6 \cdot 10^{-107}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* b a) -1.25e+33)
   (* b a)
   (if (<= (* b a) -1e-315)
     (* x y)
     (if (<= (* b a) 4e-323)
       (* z t)
       (if (<= (* b a) 7.6e-107)
         (* x y)
         (if (<= (* b a) 1.95e+37) (* z t) (* b a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b * a) <= -1.25e+33) {
		tmp = b * a;
	} else if ((b * a) <= -1e-315) {
		tmp = x * y;
	} else if ((b * a) <= 4e-323) {
		tmp = z * t;
	} else if ((b * a) <= 7.6e-107) {
		tmp = x * y;
	} else if ((b * a) <= 1.95e+37) {
		tmp = z * t;
	} else {
		tmp = b * a;
	}
	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 ((b * a) <= (-1.25d+33)) then
        tmp = b * a
    else if ((b * a) <= (-1d-315)) then
        tmp = x * y
    else if ((b * a) <= 4d-323) then
        tmp = z * t
    else if ((b * a) <= 7.6d-107) then
        tmp = x * y
    else if ((b * a) <= 1.95d+37) then
        tmp = z * t
    else
        tmp = b * a
    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 ((b * a) <= -1.25e+33) {
		tmp = b * a;
	} else if ((b * a) <= -1e-315) {
		tmp = x * y;
	} else if ((b * a) <= 4e-323) {
		tmp = z * t;
	} else if ((b * a) <= 7.6e-107) {
		tmp = x * y;
	} else if ((b * a) <= 1.95e+37) {
		tmp = z * t;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b * a) <= -1.25e+33:
		tmp = b * a
	elif (b * a) <= -1e-315:
		tmp = x * y
	elif (b * a) <= 4e-323:
		tmp = z * t
	elif (b * a) <= 7.6e-107:
		tmp = x * y
	elif (b * a) <= 1.95e+37:
		tmp = z * t
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(b * a) <= -1.25e+33)
		tmp = Float64(b * a);
	elseif (Float64(b * a) <= -1e-315)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 4e-323)
		tmp = Float64(z * t);
	elseif (Float64(b * a) <= 7.6e-107)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 1.95e+37)
		tmp = Float64(z * t);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b * a) <= -1.25e+33)
		tmp = b * a;
	elseif ((b * a) <= -1e-315)
		tmp = x * y;
	elseif ((b * a) <= 4e-323)
		tmp = z * t;
	elseif ((b * a) <= 7.6e-107)
		tmp = x * y;
	elseif ((b * a) <= 1.95e+37)
		tmp = z * t;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(b * a), $MachinePrecision], -1.25e+33], N[(b * a), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -1e-315], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 4e-323], N[(z * t), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 7.6e-107], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1.95e+37], N[(z * t), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.24999999999999993e33 or 1.9499999999999999e37 < (*.f64 a b)

   1. Initial program 96.6%

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

   3. Taylor expanded in a around inf 72.5%

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

   if -1.24999999999999993e33 < (*.f64 a b) < -9.999999985e-316 or 3.95253e-323 < (*.f64 a b) < 7.6000000000000004e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.6%

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

   if -9.999999985e-316 < (*.f64 a b) < 3.95253e-323 or 7.6000000000000004e-107 < (*.f64 a b) < 1.9499999999999999e37

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 59.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-315}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{-323}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \cdot a \leq 7.6 \cdot 10^{-107}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq 5.2 \cdot 10^{+41}\right) \land \left(x \cdot y \leq 2.4 \cdot 10^{+84} \lor \neg \left(x \cdot y \leq 4.7 \cdot 10^{+100}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -4.8e+175)
         (and (not (<= (* x y) 5.2e+41))
              (or (<= (* x y) 2.4e+84) (not (<= (* x y) 4.7e+100)))))
   (* x y)
   (+ (* b a) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -4.8e+175) || (!((x * y) <= 5.2e+41) && (((x * y) <= 2.4e+84) || !((x * y) <= 4.7e+100)))) {
		tmp = x * y;
	} else {
		tmp = (b * a) + (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) <= (-4.8d+175)) .or. (.not. ((x * y) <= 5.2d+41)) .and. ((x * y) <= 2.4d+84) .or. (.not. ((x * y) <= 4.7d+100))) then
        tmp = x * y
    else
        tmp = (b * a) + (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) <= -4.8e+175) || (!((x * y) <= 5.2e+41) && (((x * y) <= 2.4e+84) || !((x * y) <= 4.7e+100)))) {
		tmp = x * y;
	} else {
		tmp = (b * a) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -4.8e+175) or (not ((x * y) <= 5.2e+41) and (((x * y) <= 2.4e+84) or not ((x * y) <= 4.7e+100))):
		tmp = x * y
	else:
		tmp = (b * a) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -4.8e+175) || (!(Float64(x * y) <= 5.2e+41) && ((Float64(x * y) <= 2.4e+84) || !(Float64(x * y) <= 4.7e+100))))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(b * a) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -4.8e+175) || (~(((x * y) <= 5.2e+41)) && (((x * y) <= 2.4e+84) || ~(((x * y) <= 4.7e+100)))))
		tmp = x * y;
	else
		tmp = (b * a) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.8e+175], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.2e+41]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 2.4e+84], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.7e+100]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], N[(N[(b * a), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.8e175 or 5.2000000000000001e41 < (*.f64 x y) < 2.4e84 or 4.7e100 < (*.f64 x y)

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 83.5%

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

   if -4.8e175 < (*.f64 x y) < 5.2000000000000001e41 or 2.4e84 < (*.f64 x y) < 4.7e100

   1. Initial program 98.8%

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

   3. 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 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.8 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq 5.2 \cdot 10^{+41}\right) \land \left(x \cdot y \leq 2.4 \cdot 10^{+84} \lor \neg \left(x \cdot y \leq 4.7 \cdot 10^{+100}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+34} \lor \neg \left(x \cdot y \leq 5.4 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot y + b \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot a + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.2e+34) (not (<= (* x y) 5.4e-86)))
   (+ (* x y) (* b a))
   (+ (* b a) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -3.2e+34) || !((x * y) <= 5.4e-86)) {
		tmp = (x * y) + (b * a);
	} else {
		tmp = (b * a) + (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) <= (-3.2d+34)) .or. (.not. ((x * y) <= 5.4d-86))) then
        tmp = (x * y) + (b * a)
    else
        tmp = (b * a) + (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) <= -3.2e+34) || !((x * y) <= 5.4e-86)) {
		tmp = (x * y) + (b * a);
	} else {
		tmp = (b * a) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -3.2e+34) or not ((x * y) <= 5.4e-86):
		tmp = (x * y) + (b * a)
	else:
		tmp = (b * a) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -3.2e+34) || !(Float64(x * y) <= 5.4e-86))
		tmp = Float64(Float64(x * y) + Float64(b * a));
	else
		tmp = Float64(Float64(b * a) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -3.2e+34) || ~(((x * y) <= 5.4e-86)))
		tmp = (x * y) + (b * a);
	else
		tmp = (b * a) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.2e+34], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.4e-86]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(N[(b * a), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.1999999999999998e34 or 5.39999999999999985e-86 < (*.f64 x y)

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 87.6%

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

   if -3.1999999999999998e34 < (*.f64 x y) < 5.39999999999999985e-86

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 95.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+34} \lor \neg \left(x \cdot y \leq 5.4 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot y + b \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot a + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2.9 \cdot 10^{+30} \lor \neg \left(b \cdot a \leq 1.85 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot y + b \cdot a\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* b a) -2.9e+30) (not (<= (* b a) 1.85e+36)))
   (+ (* x y) (* b a))
   (+ (* x y) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((b * a) <= -2.9e+30) || !((b * a) <= 1.85e+36)) {
		tmp = (x * y) + (b * a);
	} 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 (((b * a) <= (-2.9d+30)) .or. (.not. ((b * a) <= 1.85d+36))) then
        tmp = (x * y) + (b * a)
    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 (((b * a) <= -2.9e+30) || !((b * a) <= 1.85e+36)) {
		tmp = (x * y) + (b * a);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((b * a) <= -2.9e+30) or not ((b * a) <= 1.85e+36):
		tmp = (x * y) + (b * a)
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(b * a) <= -2.9e+30) || !(Float64(b * a) <= 1.85e+36))
		tmp = Float64(Float64(x * y) + Float64(b * a));
	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 (((b * a) <= -2.9e+30) || ~(((b * a) <= 1.85e+36)))
		tmp = (x * y) + (b * a);
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -2.9e+30], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.85e+36]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(b * a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.8999999999999998e30 or 1.85000000000000014e36 < (*.f64 a b)

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 88.2%

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

   if -2.8999999999999998e30 < (*.f64 a b) < 1.85000000000000014e36

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 93.7%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2.9 \cdot 10^{+30} \lor \neg \left(b \cdot a \leq 1.85 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot y + b \cdot a\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -18500000 \lor \neg \left(b \cdot a \leq 3.8 \cdot 10^{+36}\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* b a) -18500000.0) (not (<= (* b a) 3.8e+36))) (* b a) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((b * a) <= -18500000.0) || !((b * a) <= 3.8e+36)) {
		tmp = b * a;
	} 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 (((b * a) <= (-18500000.0d0)) .or. (.not. ((b * a) <= 3.8d+36))) then
        tmp = b * a
    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 (((b * a) <= -18500000.0) || !((b * a) <= 3.8e+36)) {
		tmp = b * a;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((b * a) <= -18500000.0) or not ((b * a) <= 3.8e+36):
		tmp = b * a
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(b * a) <= -18500000.0) || !(Float64(b * a) <= 3.8e+36))
		tmp = Float64(b * a);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((b * a) <= -18500000.0) || ~(((b * a) <= 3.8e+36)))
		tmp = b * a;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -18500000.0], N[Not[LessEqual[N[(b * a), $MachinePrecision], 3.8e+36]], $MachinePrecision]], N[(b * a), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.85e7 or 3.80000000000000025e36 < (*.f64 a b)

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 71.3%

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

   if -1.85e7 < (*.f64 a b) < 3.80000000000000025e36

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 42.6%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -18500000 \lor \neg \left(b \cdot a \leq 3.8 \cdot 10^{+36}\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (b * a) + ((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 = (b * a) + ((x * y) + (z * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 8: 35.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

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 = b * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in a around inf 39.2%

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

4. Final simplification 39.2%

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

Reproduce

herbie shell --seed 2024048 
(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)))