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

Percentage Accurate: 97.6% → 98.6%

Time: 6.8s

Alternatives: 12

Speedup: 1.0×

• 33.5% 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: 97.6% 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: 98.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-+l+ 97.2%

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

   2. fma-def 98.4%

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

   3. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 98.8% 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 97.2%

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

   1. +-commutative 97.2%

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

   2. fma-def 97.6%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 98.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))))
   (if (<= t_1 INFINITY) t_1 (fma z t (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(z, t, (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(z, t, Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 42.9%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]
   3. Step-by-step derivation

      1. fma-def 42.9%

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

   4. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, b, t \cdot z\right)} \]
   5. Step-by-step derivation

      1. fma-udef 42.9%

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

      2. +-commutative 42.9%

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

      3. *-commutative 42.9%

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

   6. Applied egg-rr 42.9%

      \[\leadsto \color{blue}{z \cdot t + a \cdot b} \]
   7. Step-by-step derivation

      1. fma-def 71.4%

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

   8. Applied egg-rr 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, t, a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

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

Alternative 4: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 5: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. fma-def 97.6%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)} \]
4. Step-by-step derivation

   1. fma-udef 98.0%

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

   2. +-commutative 98.0%

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

   3. fma-def 97.2%

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

   4. associate-+l+ 97.2%

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

   5. fma-udef 98.0%

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

   6. +-commutative 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 6: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.15 \cdot 10^{-49}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{-113}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -8.5e+98)
   (* x y)
   (if (<= (* x y) -1.15e-49)
     (* a b)
     (if (<= (* x y) -3.3e-113)
       (* z t)
       (if (<= (* x y) 7.8e+83) (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -8.5e+98) {
		tmp = x * y;
	} else if ((x * y) <= -1.15e-49) {
		tmp = a * b;
	} else if ((x * y) <= -3.3e-113) {
		tmp = z * t;
	} else if ((x * y) <= 7.8e+83) {
		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 ((x * y) <= (-8.5d+98)) then
        tmp = x * y
    else if ((x * y) <= (-1.15d-49)) then
        tmp = a * b
    else if ((x * y) <= (-3.3d-113)) then
        tmp = z * t
    else if ((x * y) <= 7.8d+83) 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 ((x * y) <= -8.5e+98) {
		tmp = x * y;
	} else if ((x * y) <= -1.15e-49) {
		tmp = a * b;
	} else if ((x * y) <= -3.3e-113) {
		tmp = z * t;
	} else if ((x * y) <= 7.8e+83) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -8.5e+98:
		tmp = x * y
	elif (x * y) <= -1.15e-49:
		tmp = a * b
	elif (x * y) <= -3.3e-113:
		tmp = z * t
	elif (x * y) <= 7.8e+83:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -8.5e+98)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.15e-49)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -3.3e-113)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 7.8e+83)
		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 ((x * y) <= -8.5e+98)
		tmp = x * y;
	elseif ((x * y) <= -1.15e-49)
		tmp = a * b;
	elseif ((x * y) <= -3.3e-113)
		tmp = z * t;
	elseif ((x * y) <= 7.8e+83)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -8.5e+98], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.15e-49], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.3e-113], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.8e+83], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.4999999999999996e98 or 7.8000000000000003e83 < (*.f64 x y)

   1. Initial program 94.6%

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

   2. Taylor expanded in x around inf 74.4%

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

   if -8.4999999999999996e98 < (*.f64 x y) < -1.15e-49 or -3.3000000000000002e-113 < (*.f64 x y) < 7.8000000000000003e83

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 61.3%

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

   if -1.15e-49 < (*.f64 x y) < -3.3000000000000002e-113

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 63.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.15 \cdot 10^{-49}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{-113}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.8 \cdot 10^{+83}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{-47}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* x y) -3.8e+103)
     t_1
     (if (<= (* x y) 2.15e-47)
       (+ (* a b) (* z t))
       (if (<= (* x y) 1.3e+86) (+ (* a b) (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -3.8e+103) {
		tmp = t_1;
	} else if ((x * y) <= 2.15e-47) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.3e+86) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (x * y) + (z * t)
    if ((x * y) <= (-3.8d+103)) then
        tmp = t_1
    else if ((x * y) <= 2.15d-47) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 1.3d+86) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    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 tmp;
	if ((x * y) <= -3.8e+103) {
		tmp = t_1;
	} else if ((x * y) <= 2.15e-47) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 1.3e+86) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (x * y) <= -3.8e+103:
		tmp = t_1
	elif (x * y) <= 2.15e-47:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 1.3e+86:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -3.8e+103)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.15e-47)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 1.3e+86)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -3.8e+103)
		tmp = t_1;
	elseif ((x * y) <= 2.15e-47)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 1.3e+86)
		tmp = (a * b) + (x * y);
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.8e+103], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.15e-47], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.3e+86], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.7999999999999997e103 or 1.2999999999999999e86 < (*.f64 x y)

   1. Initial program 94.5%

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

   2. Taylor expanded in a around 0 88.7%

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

   if -3.7999999999999997e103 < (*.f64 x y) < 2.1499999999999999e-47

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 93.5%

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

   if 2.1499999999999999e-47 < (*.f64 x y) < 1.2999999999999999e86

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 85.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{-47}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{+86}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 8: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.3 \cdot 10^{+138} \lor \neg \left(x \cdot y \leq 2.1 \cdot 10^{-47}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -5.3e+138) (not (<= (* x y) 2.1e-47)))
   (+ (* 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) <= -5.3e+138) || !((x * y) <= 2.1e-47)) {
		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) <= (-5.3d+138)) .or. (.not. ((x * y) <= 2.1d-47))) 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) <= -5.3e+138) || !((x * y) <= 2.1e-47)) {
		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) <= -5.3e+138) or not ((x * y) <= 2.1e-47):
		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) <= -5.3e+138) || !(Float64(x * y) <= 2.1e-47))
		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) <= -5.3e+138) || ~(((x * y) <= 2.1e-47)))
		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], -5.3e+138], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.1e-47]], $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) < -5.29999999999999984e138 or 2.1000000000000001e-47 < (*.f64 x y)

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 83.6%

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

   if -5.29999999999999984e138 < (*.f64 x y) < 2.1000000000000001e-47

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 92.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.3 \cdot 10^{+138} \lor \neg \left(x \cdot y \leq 2.1 \cdot 10^{-47}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 9: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+198}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.6e+198)
   (* x y)
   (if (<= (* x y) 1.9e+93) (+ (* a b) (* z t)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.6e+198) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e+93) {
		tmp = (a * b) + (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) <= (-1.6d+198)) then
        tmp = x * y
    else if ((x * y) <= 1.9d+93) then
        tmp = (a * b) + (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) <= -1.6e+198) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e+93) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.6e+198:
		tmp = x * y
	elif (x * y) <= 1.9e+93:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -1.6e+198)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.9e+93)
		tmp = Float64(Float64(a * b) + 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) <= -1.6e+198)
		tmp = x * y;
	elseif ((x * y) <= 1.9e+93)
		tmp = (a * b) + (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], -1.6e+198], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e+93], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.5999999999999999e198 or 1.8999999999999999e93 < (*.f64 x y)

   1. Initial program 93.3%

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

   2. Taylor expanded in x around inf 82.3%

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

   if -1.5999999999999999e198 < (*.f64 x y) < 1.8999999999999999e93

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 87.1%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+198}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 10: 53.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{-24}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -8e+51) (* a b) (if (<= (* a b) 9e-24) (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8e+51) {
		tmp = a * b;
	} else if ((a * b) <= 9e-24) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a * b) <= (-8d+51)) then
        tmp = a * b
    else if ((a * b) <= 9d-24) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8e+51) {
		tmp = a * b;
	} else if ((a * b) <= 9e-24) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -8e+51:
		tmp = a * b
	elif (a * b) <= 9e-24:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -8e+51)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 9e-24)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a * b) <= -8e+51)
		tmp = a * b;
	elseif ((a * b) <= 9e-24)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -8e+51], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9e-24], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8e51 or 8.9999999999999995e-24 < (*.f64 a b)

   1. Initial program 96.0%

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

   2. Taylor expanded in a around inf 71.6%

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

   if -8e51 < (*.f64 a b) < 8.9999999999999995e-24

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 45.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{-24}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 11: 97.6% 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 97.2%

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

2. Final simplification 97.2%

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

Alternative 12: 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 97.2%

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

2. Taylor expanded in a around inf 41.0%

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

3. Final simplification 41.0%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023271 
(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)))