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

Percentage Accurate: 97.8% → 99.5%

Time: 8.4s

Alternatives: 11

Speedup: 0.4×

• 33.6% 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: 97.8% 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: 99.5% accurate, 0.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (* a b) (+ (* x y) (* z t))) INFINITY)
   (fma a b (fma x y (* z t)))
   (* 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 (((a * b) + ((x * y) + (z * t))) <= ((double) INFINITY)) {
		tmp = fma(a, b, fma(x, y, (z * t)));
	} 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(a * b) + Float64(Float64(x * y) + Float64(z * t))) <= Inf)
		tmp = fma(a, b, fma(x, y, Float64(z * t)));
	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[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(a * b + N[(x * y + N[(z * t), $MachinePrecision]), $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 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 85.7%

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

      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%

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

Alternative 2: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-+l+ 97.2%

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

   2. fma-define 97.6%

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

   3. fma-define 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. Add Preprocessing

5. Final simplification 98.4%

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

Alternative 3: 99.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (* a b) (+ (* x y) (* z t))) INFINITY)
   (+ (* a b) (fma x y (* z t)))
   (* 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 (((a * b) + ((x * y) + (z * t))) <= ((double) INFINITY)) {
		tmp = (a * b) + fma(x, y, (z * t));
	} 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(a * b) + Float64(Float64(x * y) + Float64(z * t))) <= Inf)
		tmp = Float64(Float64(a * b) + fma(x, y, Float64(z * t)));
	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[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(a * b), $MachinePrecision] + N[(x * y + N[(z * t), $MachinePrecision]), $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 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 85.7%

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

      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%

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

Alternative 4: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -1.85 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -3.05 \cdot 10^{+75}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* a b) -5.2e+137)
     t_2
     (if (<= (* a b) -1.85e+88)
       t_1
       (if (<= (* a b) -3.05e+75)
         (* a b)
         (if (<= (* a b) -1.05e+32)
           (* x y)
           (if (<= (* a b) 8e+48) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -5.2e+137) {
		tmp = t_2;
	} else if ((a * b) <= -1.85e+88) {
		tmp = t_1;
	} else if ((a * b) <= -3.05e+75) {
		tmp = a * b;
	} else if ((a * b) <= -1.05e+32) {
		tmp = x * y;
	} else if ((a * b) <= 8e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (a * b) + (z * t)
    if ((a * b) <= (-5.2d+137)) then
        tmp = t_2
    else if ((a * b) <= (-1.85d+88)) then
        tmp = t_1
    else if ((a * b) <= (-3.05d+75)) then
        tmp = a * b
    else if ((a * b) <= (-1.05d+32)) then
        tmp = x * y
    else if ((a * b) <= 8d+48) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -5.2e+137) {
		tmp = t_2;
	} else if ((a * b) <= -1.85e+88) {
		tmp = t_1;
	} else if ((a * b) <= -3.05e+75) {
		tmp = a * b;
	} else if ((a * b) <= -1.05e+32) {
		tmp = x * y;
	} else if ((a * b) <= 8e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (a * b) <= -5.2e+137:
		tmp = t_2
	elif (a * b) <= -1.85e+88:
		tmp = t_1
	elif (a * b) <= -3.05e+75:
		tmp = a * b
	elif (a * b) <= -1.05e+32:
		tmp = x * y
	elif (a * b) <= 8e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5.2e+137)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.85e+88)
		tmp = t_1;
	elseif (Float64(a * b) <= -3.05e+75)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.05e+32)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 8e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -5.2e+137)
		tmp = t_2;
	elseif ((a * b) <= -1.85e+88)
		tmp = t_1;
	elseif ((a * b) <= -3.05e+75)
		tmp = a * b;
	elseif ((a * b) <= -1.05e+32)
		tmp = x * y;
	elseif ((a * b) <= 8e+48)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5.2e+137], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.85e+88], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -3.05e+75], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.05e+32], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8e+48], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.1999999999999998e137 or 8.00000000000000035e48 < (*.f64 a b)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 89.0%

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

   if -5.1999999999999998e137 < (*.f64 a b) < -1.84999999999999997e88 or -1.05e32 < (*.f64 a b) < 8.00000000000000035e48

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 79.5%

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

   4. Taylor expanded in a around 0 74.6%

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

   5. Taylor expanded in b around 0 95.1%

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

   if -1.84999999999999997e88 < (*.f64 a b) < -3.05000000000000005e75

   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 100.0%

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

   if -3.05000000000000005e75 < (*.f64 a b) < -1.05e32

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 71.2%

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

   4. Taylor expanded in a around 0 71.2%

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

   5. Taylor expanded in t around 0 85.8%

      \[\leadsto \color{blue}{x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+137}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.85 \cdot 10^{+88}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -3.05 \cdot 10^{+75}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+145}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-316}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{-307}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -3e+145)
   (* a b)
   (if (<= (* a b) -5e-316)
     (* x y)
     (if (<= (* a b) 3.2e-307)
       (* z t)
       (if (<= (* a b) 7.5e-205)
         (* x y)
         (if (<= (* a b) 4.2e+63) (* z t) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -3e+145) {
		tmp = a * b;
	} else if ((a * b) <= -5e-316) {
		tmp = x * y;
	} else if ((a * b) <= 3.2e-307) {
		tmp = z * t;
	} else if ((a * b) <= 7.5e-205) {
		tmp = x * y;
	} else if ((a * b) <= 4.2e+63) {
		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) <= (-3d+145)) then
        tmp = a * b
    else if ((a * b) <= (-5d-316)) then
        tmp = x * y
    else if ((a * b) <= 3.2d-307) then
        tmp = z * t
    else if ((a * b) <= 7.5d-205) then
        tmp = x * y
    else if ((a * b) <= 4.2d+63) 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) <= -3e+145) {
		tmp = a * b;
	} else if ((a * b) <= -5e-316) {
		tmp = x * y;
	} else if ((a * b) <= 3.2e-307) {
		tmp = z * t;
	} else if ((a * b) <= 7.5e-205) {
		tmp = x * y;
	} else if ((a * b) <= 4.2e+63) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -3e+145:
		tmp = a * b
	elif (a * b) <= -5e-316:
		tmp = x * y
	elif (a * b) <= 3.2e-307:
		tmp = z * t
	elif (a * b) <= 7.5e-205:
		tmp = x * y
	elif (a * b) <= 4.2e+63:
		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) <= -3e+145)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -5e-316)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.2e-307)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 7.5e-205)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 4.2e+63)
		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) <= -3e+145)
		tmp = a * b;
	elseif ((a * b) <= -5e-316)
		tmp = x * y;
	elseif ((a * b) <= 3.2e-307)
		tmp = z * t;
	elseif ((a * b) <= 7.5e-205)
		tmp = x * y;
	elseif ((a * b) <= 4.2e+63)
		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], -3e+145], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-316], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.2e-307], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.5e-205], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.2e+63], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.0000000000000002e145 or 4.2000000000000004e63 < (*.f64 a b)

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 78.3%

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

   if -3.0000000000000002e145 < (*.f64 a b) < -5.000000017e-316 or 3.20000000000000011e-307 < (*.f64 a b) < 7.4999999999999996e-205

   1. Initial program 97.7%

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

   3. Taylor expanded in b around inf 85.9%

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

   4. Taylor expanded in a around 0 75.3%

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

   5. Taylor expanded in t around 0 58.1%

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

   if -5.000000017e-316 < (*.f64 a b) < 3.20000000000000011e-307 or 7.4999999999999996e-205 < (*.f64 a b) < 4.2000000000000004e63

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 73.0%

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

   4. Taylor expanded in a around 0 69.3%

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

   5. Taylor expanded in t around inf 66.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+145}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-316}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{-307}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+152} \lor \neg \left(x \cdot y \leq 1.05 \cdot 10^{+119}\right) \land \left(x \cdot y \leq 5.6 \cdot 10^{+184} \lor \neg \left(x \cdot y \leq 7.7 \cdot 10^{+245}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -5e+152)
         (and (not (<= (* x y) 1.05e+119))
              (or (<= (* x y) 5.6e+184) (not (<= (* x y) 7.7e+245)))))
   (* 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) <= -5e+152) || (!((x * y) <= 1.05e+119) && (((x * y) <= 5.6e+184) || !((x * y) <= 7.7e+245)))) {
		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) <= (-5d+152)) .or. (.not. ((x * y) <= 1.05d+119)) .and. ((x * y) <= 5.6d+184) .or. (.not. ((x * y) <= 7.7d+245))) 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) <= -5e+152) || (!((x * y) <= 1.05e+119) && (((x * y) <= 5.6e+184) || !((x * y) <= 7.7e+245)))) {
		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) <= -5e+152) or (not ((x * y) <= 1.05e+119) and (((x * y) <= 5.6e+184) or not ((x * y) <= 7.7e+245))):
		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) <= -5e+152) || (!(Float64(x * y) <= 1.05e+119) && ((Float64(x * y) <= 5.6e+184) || !(Float64(x * y) <= 7.7e+245))))
		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) <= -5e+152) || (~(((x * y) <= 1.05e+119)) && (((x * y) <= 5.6e+184) || ~(((x * y) <= 7.7e+245)))))
		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], -5e+152], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.05e+119]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 5.6e+184], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.7e+245]], $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) < -5e152 or 1.04999999999999991e119 < (*.f64 x y) < 5.5999999999999998e184 or 7.6999999999999998e245 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in b around inf 74.4%

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

   4. Taylor expanded in a around 0 70.5%

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

   5. Taylor expanded in t around 0 86.1%

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

   if -5e152 < (*.f64 x y) < 1.04999999999999991e119 or 5.5999999999999998e184 < (*.f64 x y) < 7.6999999999999998e245

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 88.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+152} \lor \neg \left(x \cdot y \leq 1.05 \cdot 10^{+119}\right) \land \left(x \cdot y \leq 5.6 \cdot 10^{+184} \lor \neg \left(x \cdot y \leq 7.7 \cdot 10^{+245}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -4.5 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -2.7 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{+20}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* a b) -4.5e+137)
     t_2
     (if (<= (* a b) -2.7e+92)
       t_1
       (if (<= (* a b) -1.4e+20)
         (+ (* a b) (* x y))
         (if (<= (* a b) 9e+48) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -4.5e+137) {
		tmp = t_2;
	} else if ((a * b) <= -2.7e+92) {
		tmp = t_1;
	} else if ((a * b) <= -1.4e+20) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 9e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (a * b) + (z * t)
    if ((a * b) <= (-4.5d+137)) then
        tmp = t_2
    else if ((a * b) <= (-2.7d+92)) then
        tmp = t_1
    else if ((a * b) <= (-1.4d+20)) then
        tmp = (a * b) + (x * y)
    else if ((a * b) <= 9d+48) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -4.5e+137) {
		tmp = t_2;
	} else if ((a * b) <= -2.7e+92) {
		tmp = t_1;
	} else if ((a * b) <= -1.4e+20) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 9e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (a * b) <= -4.5e+137:
		tmp = t_2
	elif (a * b) <= -2.7e+92:
		tmp = t_1
	elif (a * b) <= -1.4e+20:
		tmp = (a * b) + (x * y)
	elif (a * b) <= 9e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -4.5e+137)
		tmp = t_2;
	elseif (Float64(a * b) <= -2.7e+92)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.4e+20)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(a * b) <= 9e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -4.5e+137)
		tmp = t_2;
	elseif ((a * b) <= -2.7e+92)
		tmp = t_1;
	elseif ((a * b) <= -1.4e+20)
		tmp = (a * b) + (x * y);
	elseif ((a * b) <= 9e+48)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4.5e+137], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2.7e+92], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.4e+20], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9e+48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.5000000000000001e137 or 8.99999999999999991e48 < (*.f64 a b)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 89.0%

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

   if -4.5000000000000001e137 < (*.f64 a b) < -2.6999999999999999e92 or -1.4e20 < (*.f64 a b) < 8.99999999999999991e48

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 79.9%

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

   4. Taylor expanded in a around 0 75.6%

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

   5. Taylor expanded in b around 0 95.7%

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

   if -2.6999999999999999e92 < (*.f64 a b) < -1.4e20

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 85.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.5 \cdot 10^{+137}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2.7 \cdot 10^{+92}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.4 \cdot 10^{+20}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))))
   (if (<= t_1 INFINITY) 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 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (t + ((x * (y / z)) + (a * (b / z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 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 = (a * b) + ((x * y) + (z * t))
	tmp = 0
	if t_1 <= math.inf:
		tmp = 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(a * b) + Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = 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 = (a * b) + ((x * y) + (z * t));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = 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[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * 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 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. associate-/l* 85.7%

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

      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%

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

Alternative 9: 99.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (t + (y * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * b) + ((x * y) + (z * t))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (t + (y * (x / z)))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + ((x * y) + (z * t));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (t + (y * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

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

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf 42.9%

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

   4. Taylor expanded in a around 0 57.1%

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

      1. clear-num 57.1%

         \[\leadsto z \cdot \left(t + \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\right) \]

      2. inv-pow 57.1%

         \[\leadsto z \cdot \left(t + \color{blue}{{\left(\frac{z}{x \cdot y}\right)}^{-1}}\right) \]

   6. Applied egg-rr 57.1%

      \[\leadsto z \cdot \left(t + \color{blue}{{\left(\frac{z}{x \cdot y}\right)}^{-1}}\right) \]
   7. Step-by-step derivation

      1. unpow-1 57.1%

         \[\leadsto z \cdot \left(t + \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\right) \]

      2. associate-/r* 71.4%

         \[\leadsto z \cdot \left(t + \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\right) \]

   8. Simplified 71.4%

      \[\leadsto z \cdot \left(t + \color{blue}{\frac{1}{\frac{\frac{z}{x}}{y}}}\right) \]
   9. Step-by-step derivation

      1. associate-/r/ 71.4%

         \[\leadsto z \cdot \left(t + \color{blue}{\frac{1}{\frac{z}{x}} \cdot y}\right) \]

      2. clear-num 71.4%

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

   10. Applied egg-rr 71.4%

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

4. Final simplification 99.2%

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

Alternative 10: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+123} \lor \neg \left(a \cdot b \leq 1.9 \cdot 10^{+63}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -3.5e+123) (not (<= (* a b) 1.9e+63))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -3.5e+123) || !((a * b) <= 1.9e+63)) {
		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) <= (-3.5d+123)) .or. (.not. ((a * b) <= 1.9d+63))) 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) <= -3.5e+123) || !((a * b) <= 1.9e+63)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -3.5e+123) or not ((a * b) <= 1.9e+63):
		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) <= -3.5e+123) || !(Float64(a * b) <= 1.9e+63))
		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) <= -3.5e+123) || ~(((a * b) <= 1.9e+63)))
		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], -3.5e+123], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.9e+63]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -3.5e123 or 1.9000000000000001e63 < (*.f64 a b)

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 76.8%

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

   if -3.5e123 < (*.f64 a b) < 1.9000000000000001e63

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf 79.3%

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

   4. Taylor expanded in a around 0 72.5%

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

   5. Taylor expanded in t around inf 49.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+123} \lor \neg \left(a \cdot b \leq 1.9 \cdot 10^{+63}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in a around inf 31.8%

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

4. Final simplification 31.8%

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

Reproduce

herbie shell --seed 2024077 
(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)))