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

Percentage Accurate: 98.0% → 98.9%

Time: 8.7s

Alternatives: 9

Speedup: 1.0×

• 33.0% 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: 98.9% 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 98.0%

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

   1. associate-+l+ 98.0%

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

   2. fma-def 98.4%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 98.3% 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 98.0%

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

   1. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+91} \lor \neg \left(y \leq 1.5 \cdot 10^{+134}\right) \land y \leq 3.2 \cdot 10^{+142}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -16000.0)
   (* x y)
   (if (or (<= y 8.5e+91) (and (not (<= y 1.5e+134)) (<= y 3.2e+142)))
     (+ (* a b) (* z t))
     (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -16000.0) {
		tmp = x * y;
	} else if ((y <= 8.5e+91) || (!(y <= 1.5e+134) && (y <= 3.2e+142))) {
		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 (y <= (-16000.0d0)) then
        tmp = x * y
    else if ((y <= 8.5d+91) .or. (.not. (y <= 1.5d+134)) .and. (y <= 3.2d+142)) 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 (y <= -16000.0) {
		tmp = x * y;
	} else if ((y <= 8.5e+91) || (!(y <= 1.5e+134) && (y <= 3.2e+142))) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -16000.0:
		tmp = x * y
	elif (y <= 8.5e+91) or (not (y <= 1.5e+134) and (y <= 3.2e+142)):
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -16000.0)
		tmp = Float64(x * y);
	elseif ((y <= 8.5e+91) || (!(y <= 1.5e+134) && (y <= 3.2e+142)))
		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 (y <= -16000.0)
		tmp = x * y;
	elseif ((y <= 8.5e+91) || (~((y <= 1.5e+134)) && (y <= 3.2e+142)))
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -16000.0], N[(x * y), $MachinePrecision], If[Or[LessEqual[y, 8.5e+91], And[N[Not[LessEqual[y, 1.5e+134]], $MachinePrecision], LessEqual[y, 3.2e+142]]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -16000 or 8.4999999999999995e91 < y < 1.49999999999999998e134 or 3.20000000000000005e142 < y

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 70.1%

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

   if -16000 < y < 8.4999999999999995e91 or 1.49999999999999998e134 < y < 3.20000000000000005e142

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 84.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+91} \lor \neg \left(y \leq 1.5 \cdot 10^{+134}\right) \land y \leq 3.2 \cdot 10^{+142}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 54.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -2.05e+90)
   (* a b)
   (if (<= (* a b) -6.2e-288)
     (* z t)
     (if (<= (* a b) 5.8e-37) (* x y) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -2.05e+90) {
		tmp = a * b;
	} else if ((a * b) <= -6.2e-288) {
		tmp = z * t;
	} else if ((a * b) <= 5.8e-37) {
		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) <= (-2.05d+90)) then
        tmp = a * b
    else if ((a * b) <= (-6.2d-288)) then
        tmp = z * t
    else if ((a * b) <= 5.8d-37) 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) <= -2.05e+90) {
		tmp = a * b;
	} else if ((a * b) <= -6.2e-288) {
		tmp = z * t;
	} else if ((a * b) <= 5.8e-37) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -2.05e+90:
		tmp = a * b
	elif (a * b) <= -6.2e-288:
		tmp = z * t
	elif (a * b) <= 5.8e-37:
		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) <= -2.05e+90)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -6.2e-288)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.8e-37)
		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) <= -2.05e+90)
		tmp = a * b;
	elseif ((a * b) <= -6.2e-288)
		tmp = z * t;
	elseif ((a * b) <= 5.8e-37)
		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], -2.05e+90], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -6.2e-288], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.8e-37], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.05000000000000021e90 or 5.80000000000000009e-37 < (*.f64 a b)

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 64.9%

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

   if -2.05000000000000021e90 < (*.f64 a b) < -6.19999999999999967e-288

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 51.6%

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

   if -6.19999999999999967e-288 < (*.f64 a b) < 5.80000000000000009e-37

   1. Initial program 98.8%

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

   2. Taylor expanded in x around inf 59.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-288}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{-37}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 5: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3200000000 \lor \neg \left(x \leq 3.5 \cdot 10^{-115}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -3200000000.0) (not (<= x 3.5e-115)))
   (+ (* 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 <= -3200000000.0) || !(x <= 3.5e-115)) {
		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 <= (-3200000000.0d0)) .or. (.not. (x <= 3.5d-115))) 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 <= -3200000000.0) || !(x <= 3.5e-115)) {
		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 <= -3200000000.0) or not (x <= 3.5e-115):
		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 <= -3200000000.0) || !(x <= 3.5e-115))
		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 <= -3200000000.0) || ~((x <= 3.5e-115)))
		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, -3200000000.0], N[Not[LessEqual[x, 3.5e-115]], $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 < -3.2e9 or 3.5000000000000002e-115 < x

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 81.9%

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

   if -3.2e9 < x < 3.5000000000000002e-115

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3200000000 \lor \neg \left(x \leq 3.5 \cdot 10^{-115}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.3e-66)
   (+ (* a b) (* z t))
   (if (<= t 2.8e+72) (+ (* a b) (* x y)) (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e-66) {
		tmp = (a * b) + (z * t);
	} else if (t <= 2.8e+72) {
		tmp = (a * b) + (x * y);
	} 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 (t <= (-1.3d-66)) then
        tmp = (a * b) + (z * t)
    else if (t <= 2.8d+72) then
        tmp = (a * b) + (x * y)
    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 (t <= -1.3e-66) {
		tmp = (a * b) + (z * t);
	} else if (t <= 2.8e+72) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (z * t) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.3e-66:
		tmp = (a * b) + (z * t)
	elif t <= 2.8e+72:
		tmp = (a * b) + (x * y)
	else:
		tmp = (z * t) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.3e-66)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (t <= 2.8e+72)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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 (t <= -1.3e-66)
		tmp = (a * b) + (z * t);
	elseif (t <= 2.8e+72)
		tmp = (a * b) + (x * y);
	else
		tmp = (z * t) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.3e-66], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+72], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2999999999999999e-66

   1. Initial program 94.6%

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

   2. Taylor expanded in x around 0 73.7%

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

   if -1.2999999999999999e-66 < t < 2.7999999999999999e72

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.2%

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

   if 2.7999999999999999e72 < t

   1. Initial program 97.6%

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

   2. Taylor expanded in a around 0 89.7%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \end{array} \]

Alternative 7: 98.0% 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 98.0%

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

2. Final simplification 98.0%

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

Alternative 8: 48.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-85}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.9e-85) (* z t) (if (<= t 2.8e+72) (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e-85) {
		tmp = z * t;
	} else if (t <= 2.8e+72) {
		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 (t <= (-4.9d-85)) then
        tmp = z * t
    else if (t <= 2.8d+72) 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 (t <= -4.9e-85) {
		tmp = z * t;
	} else if (t <= 2.8e+72) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.9e-85:
		tmp = z * t
	elif t <= 2.8e+72:
		tmp = a * b
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.9e-85)
		tmp = Float64(z * t);
	elseif (t <= 2.8e+72)
		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 (t <= -4.9e-85)
		tmp = z * t;
	elseif (t <= 2.8e+72)
		tmp = a * b;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.9e-85], N[(z * t), $MachinePrecision], If[LessEqual[t, 2.8e+72], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.90000000000000015e-85 or 2.7999999999999999e72 < t

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 53.6%

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

   if -4.90000000000000015e-85 < t < 2.7999999999999999e72

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 43.2%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-85}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 9: 35.8% 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 98.0%

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

2. Taylor expanded in a around inf 33.7%

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

3. Final simplification 33.7%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023278 
(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)))