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

Percentage Accurate: 97.9% → 99.1%

Time: 7.8s

Alternatives: 8

Speedup: 1.0×

• 32.7% 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: 99.1% 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 98.8%

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

   1. +-commutative 98.8%

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

   2. fma-define 99.2%

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

   3. fma-define 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

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 98.8%

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

   1. fma-define 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. Add Preprocessing

5. Final simplification 99.2%

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

Alternative 3: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.55 \cdot 10^{-20}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.6 \cdot 10^{-261}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.6 \cdot 10^{-159}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 14500000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.55e-20)
   (* a b)
   (if (<= (* a b) 2.6e-261)
     (* x y)
     (if (<= (* a b) 5.6e-159)
       (* z t)
       (if (<= (* a b) 14500000000000.0) (* x y) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.55e-20) {
		tmp = a * b;
	} else if ((a * b) <= 2.6e-261) {
		tmp = x * y;
	} else if ((a * b) <= 5.6e-159) {
		tmp = z * t;
	} else if ((a * b) <= 14500000000000.0) {
		tmp = x * y;
	} 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) <= (-1.55d-20)) then
        tmp = a * b
    else if ((a * b) <= 2.6d-261) then
        tmp = x * y
    else if ((a * b) <= 5.6d-159) then
        tmp = z * t
    else if ((a * b) <= 14500000000000.0d0) then
        tmp = x * y
    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) <= -1.55e-20) {
		tmp = a * b;
	} else if ((a * b) <= 2.6e-261) {
		tmp = x * y;
	} else if ((a * b) <= 5.6e-159) {
		tmp = z * t;
	} else if ((a * b) <= 14500000000000.0) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.55e-20:
		tmp = a * b
	elif (a * b) <= 2.6e-261:
		tmp = x * y
	elif (a * b) <= 5.6e-159:
		tmp = z * t
	elif (a * b) <= 14500000000000.0:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -1.55e-20)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 2.6e-261)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 5.6e-159)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 14500000000000.0)
		tmp = Float64(x * y);
	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) <= -1.55e-20)
		tmp = a * b;
	elseif ((a * b) <= 2.6e-261)
		tmp = x * y;
	elseif ((a * b) <= 5.6e-159)
		tmp = z * t;
	elseif ((a * b) <= 14500000000000.0)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.55e-20], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.6e-261], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.6e-159], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 14500000000000.0], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.55e-20 or 1.45e13 < (*.f64 a b)

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 66.6%

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

   if -1.55e-20 < (*.f64 a b) < 2.6000000000000001e-261 or 5.6000000000000004e-159 < (*.f64 a b) < 1.45e13

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 64.1%

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

   4. Taylor expanded in y around inf 64.1%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{a \cdot b}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in x around inf 59.7%

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

   if 2.6000000000000001e-261 < (*.f64 a b) < 5.6000000000000004e-159

   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 0 69.1%

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

   4. Taylor expanded in z around inf 69.1%

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

   5. Taylor expanded in t around inf 69.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.55 \cdot 10^{-20}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 2.6 \cdot 10^{-261}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.6 \cdot 10^{-159}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 14500000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-9} \lor \neg \left(a \cdot b \leq 5000000000000\right):\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -2e-9) (not (<= (* a b) 5000000000000.0)))
   (+ (* z t) (* a b))
   (+ (* z t) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -2e-9) || !((a * b) <= 5000000000000.0)) {
		tmp = (z * t) + (a * b);
	} else {
		tmp = (z * t) + (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 (((a * b) <= (-2d-9)) .or. (.not. ((a * b) <= 5000000000000.0d0))) then
        tmp = (z * t) + (a * b)
    else
        tmp = (z * t) + (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 (((a * b) <= -2e-9) || !((a * b) <= 5000000000000.0)) {
		tmp = (z * t) + (a * b);
	} else {
		tmp = (z * t) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -2e-9) or not ((a * b) <= 5000000000000.0):
		tmp = (z * t) + (a * b)
	else:
		tmp = (z * t) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -2e-9) || !(Float64(a * b) <= 5000000000000.0))
		tmp = Float64(Float64(z * t) + Float64(a * b));
	else
		tmp = Float64(Float64(z * t) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a * b) <= -2e-9) || ~(((a * b) <= 5000000000000.0)))
		tmp = (z * t) + (a * b);
	else
		tmp = (z * t) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e-9], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5000000000000.0]], $MachinePrecision]], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.00000000000000012e-9 or 5e12 < (*.f64 a b)

   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 84.8%

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

   if -2.00000000000000012e-9 < (*.f64 a b) < 5e12

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 93.1%

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

   4. Taylor expanded in a around 0 88.7%

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

   5. Taylor expanded in y around 0 94.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-9} \lor \neg \left(a \cdot b \leq 5000000000000\right):\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.55 \cdot 10^{-20} \lor \neg \left(a \cdot b \leq 14500000000000\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -1.55e-20) (not (<= (* a b) 14500000000000.0)))
   (* a b)
   (* x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -1.55e-20) || !((a * b) <= 14500000000000.0)) {
		tmp = a * b;
	} 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 (((a * b) <= (-1.55d-20)) .or. (.not. ((a * b) <= 14500000000000.0d0))) then
        tmp = a * b
    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 (((a * b) <= -1.55e-20) || !((a * b) <= 14500000000000.0)) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -1.55e-20) or not ((a * b) <= 14500000000000.0):
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -1.55e-20) || !(Float64(a * b) <= 14500000000000.0))
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a * b) <= -1.55e-20) || ~(((a * b) <= 14500000000000.0)))
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.55e-20], N[Not[LessEqual[N[(a * b), $MachinePrecision], 14500000000000.0]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.55e-20 or 1.45e13 < (*.f64 a b)

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 66.6%

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

   if -1.55e-20 < (*.f64 a b) < 1.45e13

   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 inf 59.7%

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

   4. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{a \cdot b}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in x around inf 55.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.55 \cdot 10^{-20} \lor \neg \left(a \cdot b \leq 14500000000000\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+62} \lor \neg \left(y \leq 1.9 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e+62) (not (<= y 1.9e+131))) (* x y) (+ (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e+62) || !(y <= 1.9e+131)) {
		tmp = x * y;
	} else {
		tmp = (z * t) + (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 ((y <= (-1.4d+62)) .or. (.not. (y <= 1.9d+131))) then
        tmp = x * y
    else
        tmp = (z * t) + (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 ((y <= -1.4e+62) || !(y <= 1.9e+131)) {
		tmp = x * y;
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4e+62) or not (y <= 1.9e+131):
		tmp = x * y
	else:
		tmp = (z * t) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4e+62) || !(y <= 1.9e+131))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(z * t) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4e+62) || ~((y <= 1.9e+131)))
		tmp = x * y;
	else
		tmp = (z * t) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4e+62], N[Not[LessEqual[y, 1.9e+131]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000007e62 or 1.9000000000000002e131 < y

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 81.5%

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

   4. Taylor expanded in y around inf 81.5%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{a \cdot b}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in x around inf 60.9%

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

   if -1.40000000000000007e62 < y < 1.9000000000000002e131

   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 73.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+62} \lor \neg \left(y \leq 1.9 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 8: 35.0% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in a around inf 34.6%

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

4. Final simplification 34.6%

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

Reproduce

herbie shell --seed 2024085 
(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)))