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

Percentage Accurate: 98.0% → 99.1%

Time: 6.8s

Alternatives: 10

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: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% 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 97.6%

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

   1. associate-+l+ 97.6%

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

   2. fma-def 98.8%

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

   3. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 98.4% 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 97.6%

   \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
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 3: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 98.4%

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

3. Applied egg-rr 98.4%

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

4. Final simplification 98.4%

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

Alternative 4: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.6 \cdot 10^{+85}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{-287}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.25 \cdot 10^{-206}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{+85}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -7.6e+85)
   (* a b)
   (if (<= (* a b) -2.9e-196)
     (* x y)
     (if (<= (* a b) 1.2e-287)
       (* z t)
       (if (<= (* a b) 2.25e-206)
         (* x y)
         (if (<= (* a b) 1.9e-138)
           (* z t)
           (if (<= (* a b) 2.5e-116)
             (* x y)
             (if (<= (* a b) 1.16e+85) (* z t) (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -7.6e+85) {
		tmp = a * b;
	} else if ((a * b) <= -2.9e-196) {
		tmp = x * y;
	} else if ((a * b) <= 1.2e-287) {
		tmp = z * t;
	} else if ((a * b) <= 2.25e-206) {
		tmp = x * y;
	} else if ((a * b) <= 1.9e-138) {
		tmp = z * t;
	} else if ((a * b) <= 2.5e-116) {
		tmp = x * y;
	} else if ((a * b) <= 1.16e+85) {
		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) <= (-7.6d+85)) then
        tmp = a * b
    else if ((a * b) <= (-2.9d-196)) then
        tmp = x * y
    else if ((a * b) <= 1.2d-287) then
        tmp = z * t
    else if ((a * b) <= 2.25d-206) then
        tmp = x * y
    else if ((a * b) <= 1.9d-138) then
        tmp = z * t
    else if ((a * b) <= 2.5d-116) then
        tmp = x * y
    else if ((a * b) <= 1.16d+85) 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) <= -7.6e+85) {
		tmp = a * b;
	} else if ((a * b) <= -2.9e-196) {
		tmp = x * y;
	} else if ((a * b) <= 1.2e-287) {
		tmp = z * t;
	} else if ((a * b) <= 2.25e-206) {
		tmp = x * y;
	} else if ((a * b) <= 1.9e-138) {
		tmp = z * t;
	} else if ((a * b) <= 2.5e-116) {
		tmp = x * y;
	} else if ((a * b) <= 1.16e+85) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -7.6e+85:
		tmp = a * b
	elif (a * b) <= -2.9e-196:
		tmp = x * y
	elif (a * b) <= 1.2e-287:
		tmp = z * t
	elif (a * b) <= 2.25e-206:
		tmp = x * y
	elif (a * b) <= 1.9e-138:
		tmp = z * t
	elif (a * b) <= 2.5e-116:
		tmp = x * y
	elif (a * b) <= 1.16e+85:
		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) <= -7.6e+85)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.9e-196)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.2e-287)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.25e-206)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.9e-138)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.5e-116)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.16e+85)
		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) <= -7.6e+85)
		tmp = a * b;
	elseif ((a * b) <= -2.9e-196)
		tmp = x * y;
	elseif ((a * b) <= 1.2e-287)
		tmp = z * t;
	elseif ((a * b) <= 2.25e-206)
		tmp = x * y;
	elseif ((a * b) <= 1.9e-138)
		tmp = z * t;
	elseif ((a * b) <= 2.5e-116)
		tmp = x * y;
	elseif ((a * b) <= 1.16e+85)
		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], -7.6e+85], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.9e-196], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.2e-287], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.25e-206], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.9e-138], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.5e-116], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.16e+85], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -7.59999999999999984e85 or 1.15999999999999995e85 < (*.f64 a b)

   1. Initial program 96.7%

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

   2. Taylor expanded in a around inf 84.4%

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

   if -7.59999999999999984e85 < (*.f64 a b) < -2.89999999999999987e-196 or 1.2e-287 < (*.f64 a b) < 2.2499999999999999e-206 or 1.9000000000000001e-138 < (*.f64 a b) < 2.5000000000000001e-116

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around inf 60.0%

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

   if -2.89999999999999987e-196 < (*.f64 a b) < 1.2e-287 or 2.2499999999999999e-206 < (*.f64 a b) < 1.9000000000000001e-138 or 2.5000000000000001e-116 < (*.f64 a b) < 1.15999999999999995e85

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-def 99.0%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in z around inf 62.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.6 \cdot 10^{+85}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.9 \cdot 10^{-196}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.2 \cdot 10^{-287}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.25 \cdot 10^{-206}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.9 \cdot 10^{-138}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{+85}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 5: 78.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+81} \lor \neg \left(x \cdot y \leq 1.4 \cdot 10^{+264}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.4e+81) (not (<= (* x y) 1.4e+264)))
   (* x y)
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.4e+81) || !((x * y) <= 1.4e+264)) {
		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) <= (-1.4d+81)) .or. (.not. ((x * y) <= 1.4d+264))) 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) <= -1.4e+81) || !((x * y) <= 1.4e+264)) {
		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) <= -1.4e+81) or not ((x * y) <= 1.4e+264):
		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) <= -1.4e+81) || !(Float64(x * y) <= 1.4e+264))
		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) <= -1.4e+81) || ~(((x * y) <= 1.4e+264)))
		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], -1.4e+81], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.4e+264]], $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) < -1.39999999999999997e81 or 1.39999999999999999e264 < (*.f64 x y)

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. fma-def 93.7%

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

   3. Applied egg-rr 93.7%

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

   4. Taylor expanded in x around inf 78.0%

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

   if -1.39999999999999997e81 < (*.f64 x y) < 1.39999999999999999e264

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+81} \lor \neg \left(x \cdot y \leq 1.4 \cdot 10^{+264}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.4 \cdot 10^{+86} \lor \neg \left(a \cdot b \leq 9.4 \cdot 10^{+58}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -1.4e+86) (not (<= (* a b) 9.4e+58)))
   (+ (* a b) (* z t))
   (+ (* x y) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -1.4e+86) || !((a * b) <= 9.4e+58)) {
		tmp = (a * b) + (z * t);
	} 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 (((a * b) <= (-1.4d+86)) .or. (.not. ((a * b) <= 9.4d+58))) then
        tmp = (a * b) + (z * t)
    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 (((a * b) <= -1.4e+86) || !((a * b) <= 9.4e+58)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -1.4e+86) or not ((a * b) <= 9.4e+58):
		tmp = (a * b) + (z * t)
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * b) <= -1.4e+86) || !(Float64(a * b) <= 9.4e+58))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	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 (((a * b) <= -1.4e+86) || ~(((a * b) <= 9.4e+58)))
		tmp = (a * b) + (z * t);
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.4e+86], N[Not[LessEqual[N[(a * b), $MachinePrecision], 9.4e+58]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.40000000000000002e86 or 9.39999999999999944e58 < (*.f64 a b)

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 91.1%

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

   if -1.40000000000000002e86 < (*.f64 a b) < 9.39999999999999944e58

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in a around 0 87.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.4 \cdot 10^{+86} \lor \neg \left(a \cdot b \leq 9.4 \cdot 10^{+58}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 7: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.4:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -6.4)
   (+ (* a b) (* x y))
   (if (<= (* a b) 1.5e+58) (+ (* x y) (* z t)) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -6.4) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 1.5e+58) {
		tmp = (x * y) + (z * t);
	} 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 ((a * b) <= (-6.4d0)) then
        tmp = (a * b) + (x * y)
    else if ((a * b) <= 1.5d+58) then
        tmp = (x * y) + (z * t)
    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 ((a * b) <= -6.4) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 1.5e+58) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -6.4:
		tmp = (a * b) + (x * y)
	elif (a * b) <= 1.5e+58:
		tmp = (x * y) + (z * t)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -6.4)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(a * b) <= 1.5e+58)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	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 ((a * b) <= -6.4)
		tmp = (a * b) + (x * y);
	elseif ((a * b) <= 1.5e+58)
		tmp = (x * y) + (z * t);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -6.4], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.5e+58], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.4000000000000004

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 90.3%

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

   if -6.4000000000000004 < (*.f64 a b) < 1.5000000000000001e58

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in a around 0 89.3%

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

   if 1.5000000000000001e58 < (*.f64 a b)

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 88.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.4:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 8: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -11 \lor \neg \left(a \cdot b \leq 1.05 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -11.0) (not (<= (* a b) 1.05e+87))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -11.0) || !((a * b) <= 1.05e+87)) {
		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) <= (-11.0d0)) .or. (.not. ((a * b) <= 1.05d+87))) 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) <= -11.0) || !((a * b) <= 1.05e+87)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -11.0) or not ((a * b) <= 1.05e+87):
		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) <= -11.0) || !(Float64(a * b) <= 1.05e+87))
		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) <= -11.0) || ~(((a * b) <= 1.05e+87)))
		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], -11.0], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.05e+87]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -11 or 1.05e87 < (*.f64 a b)

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 79.5%

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

   if -11 < (*.f64 a b) < 1.05e87

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-def 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in z around inf 49.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -11 \lor \neg \left(a \cdot b \leq 1.05 \cdot 10^{+87}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 9: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 10: 34.9% 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 97.6%

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

2. Taylor expanded in a around inf 39.3%

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

3. Final simplification 39.3%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023301 
(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)))