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

Percentage Accurate: 97.9% → 98.6%

Time: 8.4s

Alternatives: 11

Speedup: 0.5×

• 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: 97.9% 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: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \left(x \cdot \frac{y}{z} + a \cdot \frac{b}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (* x y) (* z t)) 1e+302)
   (+ (fma x y (* z t)) (* a b))
   (* z (+ t (+ (* x (/ y z)) (* a (/ b z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) + (z * t)) <= 1e+302) {
		tmp = fma(x, y, (z * t)) + (a * b);
	} else {
		tmp = z * (t + ((x * (y / z)) + (a * (b / z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * y) + Float64(z * t)) <= 1e+302)
		tmp = Float64(fma(x, y, Float64(z * t)) + Float64(a * b));
	else
		tmp = Float64(z * Float64(t + Float64(Float64(x * Float64(y / z)) + Float64(a * Float64(b / z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], 1e+302], N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(t + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e302

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

   3. Simplified 100.0%

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

   if 1.0000000000000001e302 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 81.3%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 96.9%

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

      3. associate-/l* 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(t + \left(x \cdot \frac{y}{z} + a \cdot \frac{b}{z}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \left(x \cdot \frac{y}{z} + a \cdot \frac{b}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 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-define 98.0%

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

   3. fma-define 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. Add Preprocessing

5. Final simplification 98.4%

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

Alternative 3: 55.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{-77}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 0.145:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{+30}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.05e+54)
   (* x y)
   (if (<= (* x y) -5.5e-73)
     (* z t)
     (if (<= (* x y) 7.5e-77)
       (* a b)
       (if (<= (* x y) 0.145)
         (* z t)
         (if (<= (* x y) 1.35e+30) (* a b) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.05e+54) {
		tmp = x * y;
	} else if ((x * y) <= -5.5e-73) {
		tmp = z * t;
	} else if ((x * y) <= 7.5e-77) {
		tmp = a * b;
	} else if ((x * y) <= 0.145) {
		tmp = z * t;
	} else if ((x * y) <= 1.35e+30) {
		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) <= (-1.05d+54)) then
        tmp = x * y
    else if ((x * y) <= (-5.5d-73)) then
        tmp = z * t
    else if ((x * y) <= 7.5d-77) then
        tmp = a * b
    else if ((x * y) <= 0.145d0) then
        tmp = z * t
    else if ((x * y) <= 1.35d+30) 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) <= -1.05e+54) {
		tmp = x * y;
	} else if ((x * y) <= -5.5e-73) {
		tmp = z * t;
	} else if ((x * y) <= 7.5e-77) {
		tmp = a * b;
	} else if ((x * y) <= 0.145) {
		tmp = z * t;
	} else if ((x * y) <= 1.35e+30) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.05e+54:
		tmp = x * y
	elif (x * y) <= -5.5e-73:
		tmp = z * t
	elif (x * y) <= 7.5e-77:
		tmp = a * b
	elif (x * y) <= 0.145:
		tmp = z * t
	elif (x * y) <= 1.35e+30:
		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) <= -1.05e+54)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.5e-73)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 7.5e-77)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 0.145)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.35e+30)
		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) <= -1.05e+54)
		tmp = x * y;
	elseif ((x * y) <= -5.5e-73)
		tmp = z * t;
	elseif ((x * y) <= 7.5e-77)
		tmp = a * b;
	elseif ((x * y) <= 0.145)
		tmp = z * t;
	elseif ((x * y) <= 1.35e+30)
		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], -1.05e+54], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-73], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.5e-77], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.145], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.35e+30], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.04999999999999993e54 or 1.3499999999999999e30 < (*.f64 x y)

   1. Initial program 94.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.2%

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

   4. Taylor expanded in y around inf 86.2%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{a \cdot b}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in y around inf 73.8%

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

   if -1.04999999999999993e54 < (*.f64 x y) < -5.50000000000000006e-73 or 7.5000000000000006e-77 < (*.f64 x y) < 0.14499999999999999

   1. Initial program 99.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.4%

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

   4. Taylor expanded in a around 0 71.9%

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

   5. Taylor expanded in y around 0 66.3%

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

   if -5.50000000000000006e-73 < (*.f64 x y) < 7.5000000000000006e-77 or 0.14499999999999999 < (*.f64 x y) < 1.3499999999999999e30

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 68.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{-77}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 0.145:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{+30}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+41}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{z \cdot t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2e+112)
   (+ (* x y) (* a b))
   (if (<= (* x y) -5e-16)
     (+ (* x y) (* z t))
     (if (<= (* x y) 2e+41) (+ (* a b) (* z t)) (* y (+ x (/ (* z t) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -2e+112) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -5e-16) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 2e+41) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = y * (x + ((z * t) / 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) <= (-2d+112)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= (-5d-16)) then
        tmp = (x * y) + (z * t)
    else if ((x * y) <= 2d+41) then
        tmp = (a * b) + (z * t)
    else
        tmp = y * (x + ((z * t) / 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) <= -2e+112) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= -5e-16) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 2e+41) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = y * (x + ((z * t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -2e+112:
		tmp = (x * y) + (a * b)
	elif (x * y) <= -5e-16:
		tmp = (x * y) + (z * t)
	elif (x * y) <= 2e+41:
		tmp = (a * b) + (z * t)
	else:
		tmp = y * (x + ((z * t) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -2e+112)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= -5e-16)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(x * y) <= 2e+41)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(y * Float64(x + Float64(Float64(z * t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -2e+112)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= -5e-16)
		tmp = (x * y) + (z * t);
	elseif ((x * y) <= 2e+41)
		tmp = (a * b) + (z * t);
	else
		tmp = y * (x + ((z * t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+112], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-16], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+41], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e112

   1. Initial program 97.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.1%

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

   if -1.9999999999999999e112 < (*.f64 x y) < -5.0000000000000004e-16

   1. Initial program 99.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 90.3%

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

   4. Taylor expanded in a around 0 80.8%

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

   5. Taylor expanded in y around 0 90.5%

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

   if -5.0000000000000004e-16 < (*.f64 x y) < 2.00000000000000001e41

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.4%

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

   if 2.00000000000000001e41 < (*.f64 x y)

   1. Initial program 91.6%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.8%

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

   4. Taylor expanded in a around 0 87.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{t \cdot z}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+41}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{z \cdot t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -2e+112)
   (+ (* x y) (* a b))
   (if (or (<= (* x y) -5e-16) (not (<= (* x y) 2e+28)))
     (+ (* 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 ((x * y) <= -2e+112) {
		tmp = (x * y) + (a * b);
	} else if (((x * y) <= -5e-16) || !((x * y) <= 2e+28)) {
		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 ((x * y) <= (-2d+112)) then
        tmp = (x * y) + (a * b)
    else if (((x * y) <= (-5d-16)) .or. (.not. ((x * y) <= 2d+28))) 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 ((x * y) <= -2e+112) {
		tmp = (x * y) + (a * b);
	} else if (((x * y) <= -5e-16) || !((x * y) <= 2e+28)) {
		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 (x * y) <= -2e+112:
		tmp = (x * y) + (a * b)
	elif ((x * y) <= -5e-16) or not ((x * y) <= 2e+28):
		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(x * y) <= -2e+112)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif ((Float64(x * y) <= -5e-16) || !(Float64(x * y) <= 2e+28))
		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 ((x * y) <= -2e+112)
		tmp = (x * y) + (a * b);
	elseif (((x * y) <= -5e-16) || ~(((x * y) <= 2e+28)))
		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[(x * y), $MachinePrecision], -2e+112], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e-16], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+28]], $MachinePrecision]], 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 x y) < -1.9999999999999999e112

   1. Initial program 97.9%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 94.1%

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

   if -1.9999999999999999e112 < (*.f64 x y) < -5.0000000000000004e-16 or 1.99999999999999992e28 < (*.f64 x y)

   1. Initial program 94.4%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.4%

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

   4. Taylor expanded in a around 0 85.1%

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

   5. Taylor expanded in y around 0 88.1%

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

   if -5.0000000000000004e-16 < (*.f64 x y) < 1.99999999999999992e28

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.3%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_1 \leq 10^{+302}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \left(x \cdot \frac{y}{z} + a \cdot \frac{b}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= t_1 1e+302)
     (+ (* a b) t_1)
     (* z (+ t (+ (* x (/ y z)) (* a (/ b z))))))))

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 (t_1 <= 1e+302) {
		tmp = (a * b) + t_1;
	} else {
		tmp = z * (t + ((x * (y / z)) + (a * (b / z))));
	}
	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 (t_1 <= 1d+302) then
        tmp = (a * b) + t_1
    else
        tmp = z * (t + ((x * (y / z)) + (a * (b / z))))
    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 (t_1 <= 1e+302) {
		tmp = (a * b) + t_1;
	} else {
		tmp = z * (t + ((x * (y / z)) + (a * (b / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if t_1 <= 1e+302:
		tmp = (a * b) + t_1
	else:
		tmp = z * (t + ((x * (y / z)) + (a * (b / z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_1 <= 1e+302)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(z * Float64(t + Float64(Float64(x * Float64(y / z)) + Float64(a * Float64(b / z)))));
	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 (t_1 <= 1e+302)
		tmp = (a * b) + t_1;
	else
		tmp = z * (t + ((x * (y / z)) + (a * (b / z))));
	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[t$95$1, 1e+302], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(z * N[(t + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e302

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   if 1.0000000000000001e302 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 81.3%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 96.9%

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

      3. associate-/l* 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(t + \left(x \cdot \frac{y}{z} + a \cdot \frac{b}{z}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq 10^{+302}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t + \left(x \cdot \frac{y}{z} + a \cdot \frac{b}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_1 \leq 10^{+302}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\frac{x}{t} + \frac{z}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= t_1 1e+302) (+ (* a b) t_1) (* t (* y (+ (/ x t) (/ z y)))))))

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 (t_1 <= 1e+302) {
		tmp = (a * b) + t_1;
	} else {
		tmp = t * (y * ((x / t) + (z / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (t_1 <= 1d+302) then
        tmp = (a * b) + t_1
    else
        tmp = t * (y * ((x / t) + (z / 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 t_1 = (x * y) + (z * t);
	double tmp;
	if (t_1 <= 1e+302) {
		tmp = (a * b) + t_1;
	} else {
		tmp = t * (y * ((x / t) + (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if t_1 <= 1e+302:
		tmp = (a * b) + t_1
	else:
		tmp = t * (y * ((x / t) + (z / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (t_1 <= 1e+302)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(t * Float64(y * Float64(Float64(x / t) + Float64(z / y))));
	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 (t_1 <= 1e+302)
		tmp = (a * b) + t_1;
	else
		tmp = t * (y * ((x / t) + (z / y)));
	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[t$95$1, 1e+302], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t * N[(y * N[(N[(x / t), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e302

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   if 1.0000000000000001e302 < (+.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 81.3%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 90.6%

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

   4. Taylor expanded in y around inf 93.8%

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

   5. Taylor expanded in a around 0 96.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y + z \cdot t \leq 10^{+302}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\frac{x}{t} + \frac{z}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+124} \lor \neg \left(x \cdot y \leq 3.6 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -3.8e+124) (not (<= (* x y) 3.6e+94)))
   (* x y)
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -3.8e+124) || !((x * y) <= 3.6e+94)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((x * y) <= (-3.8d+124)) .or. (.not. ((x * y) <= 3.6d+94))) then
        tmp = x * y
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -3.8e+124) || !((x * y) <= 3.6e+94)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -3.8e+124) or not ((x * y) <= 3.6e+94):
		tmp = x * y
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -3.8e+124) || !(Float64(x * y) <= 3.6e+94))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -3.8e+124) || ~(((x * y) <= 3.6e+94)))
		tmp = x * y;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.8e+124], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.6e+94]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.7999999999999998e124 or 3.59999999999999992e94 < (*.f64 x y)

   1. Initial program 93.8%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.1%

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

   4. Taylor expanded in y around inf 91.1%

      \[\leadsto \color{blue}{y \cdot \left(x + \frac{a \cdot b}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in y around inf 81.0%

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

   if -3.7999999999999998e124 < (*.f64 x y) < 3.59999999999999992e94

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+124} \lor \neg \left(x \cdot y \leq 3.6 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.9 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -5.9e-16) (not (<= (* x y) 4.2e+30)))
   (+ (* 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 (((x * y) <= -5.9e-16) || !((x * y) <= 4.2e+30)) {
		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 (((x * y) <= (-5.9d-16)) .or. (.not. ((x * y) <= 4.2d+30))) 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 (((x * y) <= -5.9e-16) || !((x * y) <= 4.2e+30)) {
		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 ((x * y) <= -5.9e-16) or not ((x * y) <= 4.2e+30):
		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(x * y) <= -5.9e-16) || !(Float64(x * y) <= 4.2e+30))
		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 (((x * y) <= -5.9e-16) || ~(((x * y) <= 4.2e+30)))
		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[Or[LessEqual[N[(x * y), $MachinePrecision], -5.9e-16], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.2e+30]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 x y) < -5.90000000000000022e-16 or 4.2e30 < (*.f64 x y)

   1. Initial program 95.6%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 93.6%

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

   4. Taylor expanded in a around 0 82.3%

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

   5. Taylor expanded in y around 0 84.3%

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

   if -5.90000000000000022e-16 < (*.f64 x y) < 4.2e30

   1. Initial program 100.0%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.9 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq 4.2 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+139} \lor \neg \left(z \leq 7.2 \cdot 10^{-136}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.1e+139) (not (<= z 7.2e-136))) (* z t) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+139) || !(z <= 7.2e-136)) {
		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 ((z <= (-3.1d+139)) .or. (.not. (z <= 7.2d-136))) 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 ((z <= -3.1e+139) || !(z <= 7.2e-136)) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.1e+139) or not (z <= 7.2e-136):
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.1e+139) || !(z <= 7.2e-136))
		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 ((z <= -3.1e+139) || ~((z <= 7.2e-136)))
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.1e+139], N[Not[LessEqual[z, 7.2e-136]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e139 or 7.1999999999999996e-136 < z

   1. Initial program 96.1%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.7%

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

   4. Taylor expanded in a around 0 69.0%

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

   5. Taylor expanded in y around 0 43.2%

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

   if -3.1e139 < z < 7.1999999999999996e-136

   1. Initial program 99.2%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.4%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+139} \lor \neg \left(z \leq 7.2 \cdot 10^{-136}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.9% 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. Add Preprocessing

3. Taylor expanded in a around inf 36.7%

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

4. Final simplification 36.7%

   \[\leadsto a \cdot b \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(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)))