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

Percentage Accurate: 97.8% → 99.6%

Time: 7.4s

Alternatives: 9

Speedup: 0.4×

• 33.2% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (+ (* z t) (* x y)) (* a b)) INFINITY)
   (+ (fma x y (* z t)) (* a b))
   (* z (+ t (+ (* x (/ y z)) (* a (/ b z)))))))

C

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(z * t) + Float64(x * y)) + Float64(a * b)) <= Inf)
		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

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], Infinity], 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 (*.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. Step-by-step derivation

      1. fma-define 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in z around inf 30.0%

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

      1. +-commutative 30.0%

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

      2. associate-/l* 70.0%

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

      3. associate-/l* 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 99.6%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (fma a b (fma x y (* z t))))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(a * b + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-define 96.9%

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

   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. Add Preprocessing

Alternative 3: 99.6% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* z t) (* x y)) (* a b))))
   (if (<= t_1 INFINITY) t_1 (* z (+ t (+ (* x (/ y z)) (* a (/ b z))))))))

C

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

Java

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

Python

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * t) + Float64(x * y)) + Float64(a * b))
	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

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * t) + (x * y)) + (a * b);
	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

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $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. Step-by-step derivation

      1. fma-define 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in z around inf 30.0%

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

      1. +-commutative 30.0%

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

      2. associate-/l* 70.0%

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

      3. associate-/l* 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 99.6%

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

Alternative 4: 99.3% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* z t) (* x y)) (* a b))))
   (if (<= t_1 INFINITY) t_1 (* z (+ t (* a (/ b z)))))))

C

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

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * t) + (x * y)) + (a * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (t + (a * (b / z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(t + N[(a * N[(b / 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. Step-by-step derivation

      1. fma-define 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in x around 0 50.0%

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

   6. Taylor expanded in z around inf 60.0%

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

      1. associate-*r/ 70.0%

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

   8. Simplified 70.0%

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

4. Final simplification 98.8%

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

Alternative 5: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+95}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -0.041:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+92}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -8.2e+95)
   (* x y)
   (if (<= (* x y) -0.041) (* z t) (if (<= (* x y) 2.5e+92) (* a b) (* x y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -8.2e+95) {
		tmp = x * y;
	} else if ((x * y) <= -0.041) {
		tmp = z * t;
	} else if ((x * y) <= 2.5e+92) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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) <= (-8.2d+95)) then
        tmp = x * y
    else if ((x * y) <= (-0.041d0)) then
        tmp = z * t
    else if ((x * y) <= 2.5d+92) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -8.2e+95) {
		tmp = x * y;
	} else if ((x * y) <= -0.041) {
		tmp = z * t;
	} else if ((x * y) <= 2.5e+92) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -8.2e+95:
		tmp = x * y
	elif (x * y) <= -0.041:
		tmp = z * t
	elif (x * y) <= 2.5e+92:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -8.2e+95)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -0.041)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.5e+92)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -8.2e+95)
		tmp = x * y;
	elseif ((x * y) <= -0.041)
		tmp = z * t;
	elseif ((x * y) <= 2.5e+92)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+95], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -0.041], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+92], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.19999999999999972e95 or 2.50000000000000011e92 < (*.f64 x y)

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 87.5%

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

   4. Taylor expanded in b around inf 74.5%

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

   5. Taylor expanded in b around 0 75.4%

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

   if -8.19999999999999972e95 < (*.f64 x y) < -0.0410000000000000017

   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

   5. Taylor expanded in x around 0 82.3%

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

   6. Taylor expanded in z around inf 75.9%

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

      1. associate-*r/ 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in t around inf 61.4%

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

   if -0.0410000000000000017 < (*.f64 x y) < 2.50000000000000011e92

   1. Initial program 99.3%

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

      1. fma-define 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in a around inf 50.0%

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

Alternative 6: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+96} \lor \neg \left(x \cdot y \leq 400000000000\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.3e+96) (not (<= (* x y) 400000000000.0)))
   (+ (* x y) (* a b))
   (+ (* z t) (* a b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.3e+96) || !((x * y) <= 400000000000.0)) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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) <= (-1.3d+96)) .or. (.not. ((x * y) <= 400000000000.0d0))) then
        tmp = (x * y) + (a * b)
    else
        tmp = (z * t) + (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.3e+96) || !((x * y) <= 400000000000.0)) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -1.3e+96) or not ((x * y) <= 400000000000.0):
		tmp = (x * y) + (a * b)
	else:
		tmp = (z * t) + (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -1.3e+96) || !(Float64(x * y) <= 400000000000.0))
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = Float64(Float64(z * t) + Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -1.3e+96) || ~(((x * y) <= 400000000000.0)))
		tmp = (x * y) + (a * b);
	else
		tmp = (z * t) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.3e+96], N[Not[LessEqual[N[(x * y), $MachinePrecision], 400000000000.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.3e96 or 4e11 < (*.f64 x y)

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 85.2%

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

   if -1.3e96 < (*.f64 x y) < 4e11

   1. Initial program 99.3%

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

      1. fma-define 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 89.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+96} \lor \neg \left(x \cdot y \leq 400000000000\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+96} \lor \neg \left(x \cdot y \leq 1.46 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.65e+96) (not (<= (* x y) 1.46e+134)))
   (* x y)
   (+ (* z t) (* a b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.65e+96) || !((x * y) <= 1.46e+134)) {
		tmp = x * y;
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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) <= (-1.65d+96)) .or. (.not. ((x * y) <= 1.46d+134))) then
        tmp = x * y
    else
        tmp = (z * t) + (a * b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -1.65e+96) || !((x * y) <= 1.46e+134)) {
		tmp = x * y;
	} else {
		tmp = (z * t) + (a * b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -1.65e+96) or not ((x * y) <= 1.46e+134):
		tmp = x * y
	else:
		tmp = (z * t) + (a * b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -1.65e+96) || !(Float64(x * y) <= 1.46e+134))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(z * t) + Float64(a * b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -1.65e+96) || ~(((x * y) <= 1.46e+134)))
		tmp = x * y;
	else
		tmp = (z * t) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.65e+96], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.46e+134]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.64999999999999992e96 or 1.46e134 < (*.f64 x y)

   1. Initial program 89.9%

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

   3. Taylor expanded in x around inf 89.0%

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

   4. Taylor expanded in b around inf 76.4%

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

   5. Taylor expanded in b around 0 77.4%

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

   if -1.64999999999999992e96 < (*.f64 x y) < 1.46e134

   1. Initial program 99.4%

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

      1. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 86.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+96} \lor \neg \left(x \cdot y \leq 1.46 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+95} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -9.5e+95) (not (<= (* x y) 1.35e+91))) (* x y) (* a b)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -9.5e+95) || !((x * y) <= 1.35e+91)) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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) <= (-9.5d+95)) .or. (.not. ((x * y) <= 1.35d+91))) then
        tmp = x * y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * y) <= -9.5e+95) || !((x * y) <= 1.35e+91)) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * y) <= -9.5e+95) or not ((x * y) <= 1.35e+91):
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(x * y) <= -9.5e+95) || !(Float64(x * y) <= 1.35e+91))
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * y) <= -9.5e+95) || ~(((x * y) <= 1.35e+91)))
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -9.5e+95], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.35e+91]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.5000000000000004e95 or 1.35e91 < (*.f64 x y)

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 87.5%

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

   4. Taylor expanded in b around inf 74.5%

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

   5. Taylor expanded in b around 0 75.4%

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

   if -9.5000000000000004e95 < (*.f64 x y) < 1.35e91

   1. Initial program 99.4%

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

      1. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around inf 47.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+95} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.6% accurate, 3.7× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* a b))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return a * b

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(a * b)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = a * b;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(a * b), $MachinePrecision]

Derivation

1. Initial program 96.1%

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

   1. fma-define 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in a around inf 36.7%

   \[\leadsto \color{blue}{a \cdot b} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024137 
(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)))