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

Percentage Accurate: 97.9% → 99.0%

Time: 4.8s

Alternatives: 9

Speedup: 1.0×

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 99.2%

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

   3. fma-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * b + N[(z * t), $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 33.3%

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

      1. fma-def 66.7%

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

   4. Simplified 66.7%

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

4. Final simplification 99.2%

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

Alternative 3: 98.2% 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 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%

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

Alternative 4: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-201}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+47}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -3.2e+58)
   (* a b)
   (if (<= (* a b) -2.2e-162)
     (* z t)
     (if (<= (* a b) 0.0)
       (* x y)
       (if (<= (* a b) 8.5e-201)
         (* z t)
         (if (<= (* a b) 2.8e-39)
           (* x y)
           (if (<= (* a b) 4e+47) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -3.2e+58) {
		tmp = a * b;
	} else if ((a * b) <= -2.2e-162) {
		tmp = z * t;
	} else if ((a * b) <= 0.0) {
		tmp = x * y;
	} else if ((a * b) <= 8.5e-201) {
		tmp = z * t;
	} else if ((a * b) <= 2.8e-39) {
		tmp = x * y;
	} else if ((a * b) <= 4e+47) {
		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) <= (-3.2d+58)) then
        tmp = a * b
    else if ((a * b) <= (-2.2d-162)) then
        tmp = z * t
    else if ((a * b) <= 0.0d0) then
        tmp = x * y
    else if ((a * b) <= 8.5d-201) then
        tmp = z * t
    else if ((a * b) <= 2.8d-39) then
        tmp = x * y
    else if ((a * b) <= 4d+47) 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) <= -3.2e+58) {
		tmp = a * b;
	} else if ((a * b) <= -2.2e-162) {
		tmp = z * t;
	} else if ((a * b) <= 0.0) {
		tmp = x * y;
	} else if ((a * b) <= 8.5e-201) {
		tmp = z * t;
	} else if ((a * b) <= 2.8e-39) {
		tmp = x * y;
	} else if ((a * b) <= 4e+47) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -3.2e+58:
		tmp = a * b
	elif (a * b) <= -2.2e-162:
		tmp = z * t
	elif (a * b) <= 0.0:
		tmp = x * y
	elif (a * b) <= 8.5e-201:
		tmp = z * t
	elif (a * b) <= 2.8e-39:
		tmp = x * y
	elif (a * b) <= 4e+47:
		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) <= -3.2e+58)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.2e-162)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 8.5e-201)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.8e-39)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 4e+47)
		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) <= -3.2e+58)
		tmp = a * b;
	elseif ((a * b) <= -2.2e-162)
		tmp = z * t;
	elseif ((a * b) <= 0.0)
		tmp = x * y;
	elseif ((a * b) <= 8.5e-201)
		tmp = z * t;
	elseif ((a * b) <= 2.8e-39)
		tmp = x * y;
	elseif ((a * b) <= 4e+47)
		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], -3.2e+58], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.2e-162], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.5e-201], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.8e-39], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4e+47], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.20000000000000015e58 or 4.0000000000000002e47 < (*.f64 a b)

   1. Initial program 95.6%

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

   2. Taylor expanded in a around inf 69.8%

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

   if -3.20000000000000015e58 < (*.f64 a b) < -2.1999999999999999e-162 or -0.0 < (*.f64 a b) < 8.5000000000000007e-201 or 2.8000000000000001e-39 < (*.f64 a b) < 4.0000000000000002e47

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 63.1%

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

   if -2.1999999999999999e-162 < (*.f64 a b) < -0.0 or 8.5000000000000007e-201 < (*.f64 a b) < 2.8000000000000001e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.2 \cdot 10^{-162}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-201}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+47}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 5: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -85000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+133} \lor \neg \left(y \leq 1.9 \cdot 10^{+157}\right) \land y \leq 10^{+204}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -85000.0)
   (* x y)
   (if (or (<= y 1.75e+133) (and (not (<= y 1.9e+157)) (<= y 1e+204)))
     (+ (* 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 <= -85000.0) {
		tmp = x * y;
	} else if ((y <= 1.75e+133) || (!(y <= 1.9e+157) && (y <= 1e+204))) {
		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 <= (-85000.0d0)) then
        tmp = x * y
    else if ((y <= 1.75d+133) .or. (.not. (y <= 1.9d+157)) .and. (y <= 1d+204)) 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 <= -85000.0) {
		tmp = x * y;
	} else if ((y <= 1.75e+133) || (!(y <= 1.9e+157) && (y <= 1e+204))) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -85000.0:
		tmp = x * y
	elif (y <= 1.75e+133) or (not (y <= 1.9e+157) and (y <= 1e+204)):
		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 <= -85000.0)
		tmp = Float64(x * y);
	elseif ((y <= 1.75e+133) || (!(y <= 1.9e+157) && (y <= 1e+204)))
		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 <= -85000.0)
		tmp = x * y;
	elseif ((y <= 1.75e+133) || (~((y <= 1.9e+157)) && (y <= 1e+204)))
		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, -85000.0], N[(x * y), $MachinePrecision], If[Or[LessEqual[y, 1.75e+133], And[N[Not[LessEqual[y, 1.9e+157]], $MachinePrecision], LessEqual[y, 1e+204]]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -85000 or 1.7499999999999999e133 < y < 1.9e157 or 9.99999999999999989e203 < y

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf 56.2%

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

   if -85000 < y < 1.7499999999999999e133 or 1.9e157 < y < 9.99999999999999989e203

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0 80.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -85000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+133} \lor \neg \left(y \leq 1.9 \cdot 10^{+157}\right) \land y \leq 10^{+204}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-132} \lor \neg \left(t \leq 1.2 \cdot 10^{+111}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-132) (not (<= t 1.2e+111)))
   (+ (* a b) (* z t))
   (+ (* a b) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-132) || !(t <= 1.2e+111)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (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 <= (-1d-132)) .or. (.not. (t <= 1.2d+111))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (a * b) + (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 <= -1e-132) || !(t <= 1.2e+111)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-132) or not (t <= 1.2e+111):
		tmp = (a * b) + (z * t)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-132) || !(t <= 1.2e+111))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-132) || ~((t <= 1.2e+111)))
		tmp = (a * b) + (z * t);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-132], N[Not[LessEqual[t, 1.2e+111]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999999e-133 or 1.20000000000000003e111 < t

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 74.7%

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

   if -9.9999999999999999e-133 < t < 1.20000000000000003e111

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 83.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-132} \lor \neg \left(t \leq 1.2 \cdot 10^{+111}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 7: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.5 \cdot 10^{+59}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{+46}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -8.5e+59) (* a b) (if (<= (* a b) 1.55e+46) (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -8.5e+59) {
		tmp = a * b;
	} else if ((a * b) <= 1.55e+46) {
		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) <= (-8.5d+59)) then
        tmp = a * b
    else if ((a * b) <= 1.55d+46) 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) <= -8.5e+59) {
		tmp = a * b;
	} else if ((a * b) <= 1.55e+46) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -8.5e+59:
		tmp = a * b
	elif (a * b) <= 1.55e+46:
		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) <= -8.5e+59)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.55e+46)
		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) <= -8.5e+59)
		tmp = a * b;
	elseif ((a * b) <= 1.55e+46)
		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], -8.5e+59], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.55e+46], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8.4999999999999999e59 or 1.54999999999999988e46 < (*.f64 a b)

   1. Initial program 95.6%

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

   2. Taylor expanded in a around inf 69.8%

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

   if -8.4999999999999999e59 < (*.f64 a b) < 1.54999999999999988e46

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 50.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.5 \cdot 10^{+59}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.55 \cdot 10^{+46}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 9: 36.0% 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 97.6%

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

2. Taylor expanded in a around inf 36.9%

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

3. Final simplification 36.9%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023268 
(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)))