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

Percentage Accurate: 97.5% → 98.9%

Time: 5.2s

Alternatives: 9

Speedup: 1.0×

• 33.1% 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: 97.5% 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 98.8%

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

   1. associate-+l+ 98.8%

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

   2. fma-def 99.6%

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

   3. +-commutative 99.6%

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

   4. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 98.0% 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-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: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-299}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-140}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 680:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+77} \lor \neg \left(x \cdot y \leq 2.2 \cdot 10^{+142}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -6e+39)
   (* x y)
   (if (<= (* x y) -8.5e-50)
     (* z t)
     (if (<= (* x y) -6e-299)
       (* a b)
       (if (<= (* x y) 4e-140)
         (* z t)
         (if (<= (* x y) 680.0)
           (* a b)
           (if (<= (* x y) 7.4e+22)
             (* z t)
             (if (or (<= (* x y) 1.85e+77) (not (<= (* x y) 2.2e+142)))
               (* x y)
               (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -6e+39) {
		tmp = x * y;
	} else if ((x * y) <= -8.5e-50) {
		tmp = z * t;
	} else if ((x * y) <= -6e-299) {
		tmp = a * b;
	} else if ((x * y) <= 4e-140) {
		tmp = z * t;
	} else if ((x * y) <= 680.0) {
		tmp = a * b;
	} else if ((x * y) <= 7.4e+22) {
		tmp = z * t;
	} else if (((x * y) <= 1.85e+77) || !((x * y) <= 2.2e+142)) {
		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 ((x * y) <= (-6d+39)) then
        tmp = x * y
    else if ((x * y) <= (-8.5d-50)) then
        tmp = z * t
    else if ((x * y) <= (-6d-299)) then
        tmp = a * b
    else if ((x * y) <= 4d-140) then
        tmp = z * t
    else if ((x * y) <= 680.0d0) then
        tmp = a * b
    else if ((x * y) <= 7.4d+22) then
        tmp = z * t
    else if (((x * y) <= 1.85d+77) .or. (.not. ((x * y) <= 2.2d+142))) 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 ((x * y) <= -6e+39) {
		tmp = x * y;
	} else if ((x * y) <= -8.5e-50) {
		tmp = z * t;
	} else if ((x * y) <= -6e-299) {
		tmp = a * b;
	} else if ((x * y) <= 4e-140) {
		tmp = z * t;
	} else if ((x * y) <= 680.0) {
		tmp = a * b;
	} else if ((x * y) <= 7.4e+22) {
		tmp = z * t;
	} else if (((x * y) <= 1.85e+77) || !((x * y) <= 2.2e+142)) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -6e+39:
		tmp = x * y
	elif (x * y) <= -8.5e-50:
		tmp = z * t
	elif (x * y) <= -6e-299:
		tmp = a * b
	elif (x * y) <= 4e-140:
		tmp = z * t
	elif (x * y) <= 680.0:
		tmp = a * b
	elif (x * y) <= 7.4e+22:
		tmp = z * t
	elif ((x * y) <= 1.85e+77) or not ((x * y) <= 2.2e+142):
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -6e+39)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -8.5e-50)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -6e-299)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 4e-140)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 680.0)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 7.4e+22)
		tmp = Float64(z * t);
	elseif ((Float64(x * y) <= 1.85e+77) || !(Float64(x * y) <= 2.2e+142))
		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 ((x * y) <= -6e+39)
		tmp = x * y;
	elseif ((x * y) <= -8.5e-50)
		tmp = z * t;
	elseif ((x * y) <= -6e-299)
		tmp = a * b;
	elseif ((x * y) <= 4e-140)
		tmp = z * t;
	elseif ((x * y) <= 680.0)
		tmp = a * b;
	elseif ((x * y) <= 7.4e+22)
		tmp = z * t;
	elseif (((x * y) <= 1.85e+77) || ~(((x * y) <= 2.2e+142)))
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -6e+39], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.5e-50], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -6e-299], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-140], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 680.0], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.4e+22], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 1.85e+77], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.2e+142]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.9999999999999999e39 or 7.3999999999999996e22 < (*.f64 x y) < 1.84999999999999997e77 or 2.19999999999999987e142 < (*.f64 x y)

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 67.3%

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

   if -5.9999999999999999e39 < (*.f64 x y) < -8.50000000000000012e-50 or -5.99999999999999969e-299 < (*.f64 x y) < 3.9999999999999999e-140 or 680 < (*.f64 x y) < 7.3999999999999996e22

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 66.5%

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

   if -8.50000000000000012e-50 < (*.f64 x y) < -5.99999999999999969e-299 or 3.9999999999999999e-140 < (*.f64 x y) < 680 or 1.84999999999999997e77 < (*.f64 x y) < 2.19999999999999987e142

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 62.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-299}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-140}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 680:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+77} \lor \neg \left(x \cdot y \leq 2.2 \cdot 10^{+142}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 4: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.8 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* a b) -3e+74)
     t_2
     (if (<= (* a b) 2.9e-19)
       t_1
       (if (<= (* a b) 1.8e+57)
         t_2
         (if (<= (* a b) 2e+159) t_1 (+ (* a b) (* z t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -3e+74) {
		tmp = t_2;
	} else if ((a * b) <= 2.9e-19) {
		tmp = t_1;
	} else if ((a * b) <= 1.8e+57) {
		tmp = t_2;
	} else if ((a * b) <= 2e+159) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((a * b) <= (-3d+74)) then
        tmp = t_2
    else if ((a * b) <= 2.9d-19) then
        tmp = t_1
    else if ((a * b) <= 1.8d+57) then
        tmp = t_2
    else if ((a * b) <= 2d+159) then
        tmp = t_1
    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 t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -3e+74) {
		tmp = t_2;
	} else if ((a * b) <= 2.9e-19) {
		tmp = t_1;
	} else if ((a * b) <= 1.8e+57) {
		tmp = t_2;
	} else if ((a * b) <= 2e+159) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (a * b) <= -3e+74:
		tmp = t_2
	elif (a * b) <= 2.9e-19:
		tmp = t_1
	elif (a * b) <= 1.8e+57:
		tmp = t_2
	elif (a * b) <= 2e+159:
		tmp = t_1
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -3e+74)
		tmp = t_2;
	elseif (Float64(a * b) <= 2.9e-19)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.8e+57)
		tmp = t_2;
	elseif (Float64(a * b) <= 2e+159)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -3e+74)
		tmp = t_2;
	elseif ((a * b) <= 2.9e-19)
		tmp = t_1;
	elseif ((a * b) <= 1.8e+57)
		tmp = t_2;
	elseif ((a * b) <= 2e+159)
		tmp = t_1;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3e+74], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2.9e-19], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.8e+57], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2e+159], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3e74 or 2.9e-19 < (*.f64 a b) < 1.8000000000000001e57

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 87.2%

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

   if -3e74 < (*.f64 a b) < 2.9e-19 or 1.8000000000000001e57 < (*.f64 a b) < 1.9999999999999999e159

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 90.6%

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

   if 1.9999999999999999e159 < (*.f64 a b)

   1. Initial program 94.6%

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

   2. Taylor expanded in x around 0 92.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+74}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.8 \cdot 10^{+57}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+159}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 5: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+67} \lor \neg \left(a \cdot b \leq 2.9 \cdot 10^{-19} \lor \neg \left(a \cdot b \leq 2.95 \cdot 10^{+57}\right) \land a \cdot b \leq 4.5 \cdot 10^{+219}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -4.4e+67)
         (not
          (or (<= (* a b) 2.9e-19)
              (and (not (<= (* a b) 2.95e+57)) (<= (* a b) 4.5e+219)))))
   (* a b)
   (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -4.4e+67) || !(((a * b) <= 2.9e-19) || (!((a * b) <= 2.95e+57) && ((a * b) <= 4.5e+219)))) {
		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) <= (-4.4d+67)) .or. (.not. ((a * b) <= 2.9d-19) .or. (.not. ((a * b) <= 2.95d+57)) .and. ((a * b) <= 4.5d+219))) 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) <= -4.4e+67) || !(((a * b) <= 2.9e-19) || (!((a * b) <= 2.95e+57) && ((a * b) <= 4.5e+219)))) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -4.4e+67) or not (((a * b) <= 2.9e-19) or (not ((a * b) <= 2.95e+57) and ((a * b) <= 4.5e+219))):
		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) <= -4.4e+67) || !((Float64(a * b) <= 2.9e-19) || (!(Float64(a * b) <= 2.95e+57) && (Float64(a * b) <= 4.5e+219))))
		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) <= -4.4e+67) || ~((((a * b) <= 2.9e-19) || (~(((a * b) <= 2.95e+57)) && ((a * b) <= 4.5e+219)))))
		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], -4.4e+67], N[Not[Or[LessEqual[N[(a * b), $MachinePrecision], 2.9e-19], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.95e+57]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 4.5e+219]]]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.4e67 or 2.9e-19 < (*.f64 a b) < 2.95000000000000006e57 or 4.50000000000000023e219 < (*.f64 a b)

   1. Initial program 97.8%

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

   2. Taylor expanded in a around inf 73.6%

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

   if -4.4e67 < (*.f64 a b) < 2.9e-19 or 2.95000000000000006e57 < (*.f64 a b) < 4.50000000000000023e219

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 47.9%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+67} \lor \neg \left(a \cdot b \leq 2.9 \cdot 10^{-19} \lor \neg \left(a \cdot b \leq 2.95 \cdot 10^{+57}\right) \land a \cdot b \leq 4.5 \cdot 10^{+219}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 6: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+221} \lor \neg \left(x \cdot y \leq 3.35 \cdot 10^{+146}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.4e+221) (not (<= (* x y) 3.35e+146)))
   (* 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+221) || !((x * y) <= 3.35e+146)) {
		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+221)) .or. (.not. ((x * y) <= 3.35d+146))) 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+221) || !((x * y) <= 3.35e+146)) {
		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+221) or not ((x * y) <= 3.35e+146):
		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+221) || !(Float64(x * y) <= 3.35e+146))
		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+221) || ~(((x * y) <= 3.35e+146)))
		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+221], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.35e+146]], $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) < -3.3999999999999998e221 or 3.35000000000000003e146 < (*.f64 x y)

   1. Initial program 96.9%

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

   2. Taylor expanded in x around inf 86.1%

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

   if -3.3999999999999998e221 < (*.f64 x y) < 3.35000000000000003e146

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 83.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+221} \lor \neg \left(x \cdot y \leq 3.35 \cdot 10^{+146}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 7: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+91} \lor \neg \left(x \leq 2.4 \cdot 10^{-71}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.35e+91) (not (<= x 2.4e-71)))
   (+ (* 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 <= -1.35e+91) || !(x <= 2.4e-71)) {
		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 <= (-1.35d+91)) .or. (.not. (x <= 2.4d-71))) 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 <= -1.35e+91) || !(x <= 2.4e-71)) {
		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 <= -1.35e+91) or not (x <= 2.4e-71):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.35e+91) || !(x <= 2.4e-71))
		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 <= -1.35e+91) || ~((x <= 2.4e-71)))
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.35e+91], N[Not[LessEqual[x, 2.4e-71]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e91 or 2.4e-71 < x

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 76.4%

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

   if -1.35e91 < x < 2.4e-71

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 82.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+91} \lor \neg \left(x \leq 2.4 \cdot 10^{-71}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 8: 97.5% 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 98.8%

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

2. Final simplification 98.8%

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

Alternative 9: 36.3% 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. Taylor expanded in a around inf 34.5%

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

3. Final simplification 34.5%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023320 
(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)))