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

Percentage Accurate: 97.7% → 98.9%

Time: 4.5s

Alternatives: 9

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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 37.5%

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

      1. fma-def 62.5%

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

   4. Simplified 62.5%

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

4. Final simplification 98.8%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-+l+ 96.9%

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

   2. fma-def 98.0%

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

   3. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 52.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+197}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.65 \cdot 10^{-213}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -5.2 \cdot 10^{-255}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.6 \cdot 10^{-247}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.45 \cdot 10^{+148}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -4.2e+197)
   (* a b)
   (if (<= (* a b) -2.5e-19)
     (* x y)
     (if (<= (* a b) -6.2e-130)
       (* z t)
       (if (<= (* a b) -1.65e-213)
         (* x y)
         (if (<= (* a b) -5.2e-255)
           (* z t)
           (if (<= (* a b) 5.6e-247)
             (* x y)
             (if (<= (* a b) 7.5e-88)
               (* z t)
               (if (<= (* a b) 8.6e-36)
                 (* x y)
                 (if (<= (* a b) 1.45e+148) (* z t) (* a b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -4.2e+197) {
		tmp = a * b;
	} else if ((a * b) <= -2.5e-19) {
		tmp = x * y;
	} else if ((a * b) <= -6.2e-130) {
		tmp = z * t;
	} else if ((a * b) <= -1.65e-213) {
		tmp = x * y;
	} else if ((a * b) <= -5.2e-255) {
		tmp = z * t;
	} else if ((a * b) <= 5.6e-247) {
		tmp = x * y;
	} else if ((a * b) <= 7.5e-88) {
		tmp = z * t;
	} else if ((a * b) <= 8.6e-36) {
		tmp = x * y;
	} else if ((a * b) <= 1.45e+148) {
		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) <= (-4.2d+197)) then
        tmp = a * b
    else if ((a * b) <= (-2.5d-19)) then
        tmp = x * y
    else if ((a * b) <= (-6.2d-130)) then
        tmp = z * t
    else if ((a * b) <= (-1.65d-213)) then
        tmp = x * y
    else if ((a * b) <= (-5.2d-255)) then
        tmp = z * t
    else if ((a * b) <= 5.6d-247) then
        tmp = x * y
    else if ((a * b) <= 7.5d-88) then
        tmp = z * t
    else if ((a * b) <= 8.6d-36) then
        tmp = x * y
    else if ((a * b) <= 1.45d+148) 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) <= -4.2e+197) {
		tmp = a * b;
	} else if ((a * b) <= -2.5e-19) {
		tmp = x * y;
	} else if ((a * b) <= -6.2e-130) {
		tmp = z * t;
	} else if ((a * b) <= -1.65e-213) {
		tmp = x * y;
	} else if ((a * b) <= -5.2e-255) {
		tmp = z * t;
	} else if ((a * b) <= 5.6e-247) {
		tmp = x * y;
	} else if ((a * b) <= 7.5e-88) {
		tmp = z * t;
	} else if ((a * b) <= 8.6e-36) {
		tmp = x * y;
	} else if ((a * b) <= 1.45e+148) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -4.2e+197:
		tmp = a * b
	elif (a * b) <= -2.5e-19:
		tmp = x * y
	elif (a * b) <= -6.2e-130:
		tmp = z * t
	elif (a * b) <= -1.65e-213:
		tmp = x * y
	elif (a * b) <= -5.2e-255:
		tmp = z * t
	elif (a * b) <= 5.6e-247:
		tmp = x * y
	elif (a * b) <= 7.5e-88:
		tmp = z * t
	elif (a * b) <= 8.6e-36:
		tmp = x * y
	elif (a * b) <= 1.45e+148:
		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) <= -4.2e+197)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.5e-19)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -6.2e-130)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -1.65e-213)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -5.2e-255)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.6e-247)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 7.5e-88)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 8.6e-36)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.45e+148)
		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) <= -4.2e+197)
		tmp = a * b;
	elseif ((a * b) <= -2.5e-19)
		tmp = x * y;
	elseif ((a * b) <= -6.2e-130)
		tmp = z * t;
	elseif ((a * b) <= -1.65e-213)
		tmp = x * y;
	elseif ((a * b) <= -5.2e-255)
		tmp = z * t;
	elseif ((a * b) <= 5.6e-247)
		tmp = x * y;
	elseif ((a * b) <= 7.5e-88)
		tmp = z * t;
	elseif ((a * b) <= 8.6e-36)
		tmp = x * y;
	elseif ((a * b) <= 1.45e+148)
		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], -4.2e+197], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.5e-19], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -6.2e-130], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.65e-213], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5.2e-255], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.6e-247], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.5e-88], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.6e-36], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.45e+148], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.20000000000000013e197 or 1.45e148 < (*.f64 a b)

   1. Initial program 89.7%

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

   2. Taylor expanded in a around inf 81.8%

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

   if -4.20000000000000013e197 < (*.f64 a b) < -2.5000000000000002e-19 or -6.20000000000000021e-130 < (*.f64 a b) < -1.65000000000000016e-213 or -5.20000000000000041e-255 < (*.f64 a b) < 5.59999999999999973e-247 or 7.50000000000000041e-88 < (*.f64 a b) < 8.6000000000000004e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 62.6%

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

   if -2.5000000000000002e-19 < (*.f64 a b) < -6.20000000000000021e-130 or -1.65000000000000016e-213 < (*.f64 a b) < -5.20000000000000041e-255 or 5.59999999999999973e-247 < (*.f64 a b) < 7.50000000000000041e-88 or 8.6000000000000004e-36 < (*.f64 a b) < 1.45e148

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 62.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+197}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.65 \cdot 10^{-213}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -5.2 \cdot 10^{-255}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.6 \cdot 10^{-247}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.5 \cdot 10^{-88}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.45 \cdot 10^{+148}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 4: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 50.0%

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

4. Final simplification 98.4%

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

Alternative 5: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.5e-19)
   (+ (* a b) (* x y))
   (if (<= (* a b) 2.3e+24) (+ (* z t) (* x y)) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.5e-19) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 2.3e+24) {
		tmp = (z * t) + (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 ((a * b) <= (-1.5d-19)) then
        tmp = (a * b) + (x * y)
    else if ((a * b) <= 2.3d+24) then
        tmp = (z * t) + (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 ((a * b) <= -1.5e-19) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 2.3e+24) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.5e-19:
		tmp = (a * b) + (x * y)
	elif (a * b) <= 2.3e+24:
		tmp = (z * t) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -1.5e-19)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(a * b) <= 2.3e+24)
		tmp = Float64(Float64(z * t) + 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 ((a * b) <= -1.5e-19)
		tmp = (a * b) + (x * y);
	elseif ((a * b) <= 2.3e+24)
		tmp = (z * t) + (x * y);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.5e-19], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.3e+24], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.49999999999999996e-19

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 84.5%

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

   if -1.49999999999999996e-19 < (*.f64 a b) < 2.2999999999999999e24

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 91.2%

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

   if 2.2999999999999999e24 < (*.f64 a b)

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 83.8%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 6: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+144} \lor \neg \left(x \leq 1.5 \cdot 10^{-157}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -7e+144) (not (<= x 1.5e-157)))
   (+ (* a b) (* x y))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7e+144) || !(x <= 1.5e-157)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-7d+144)) .or. (.not. (x <= 1.5d-157))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -7e+144) || !(x <= 1.5e-157)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -7e+144) or not (x <= 1.5e-157):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -7e+144) || !(x <= 1.5e-157))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -7e+144) || ~((x <= 1.5e-157)))
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -7e+144], N[Not[LessEqual[x, 1.5e-157]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.9999999999999996e144 or 1.5e-157 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 76.5%

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

   if -6.9999999999999996e144 < x < 1.5e-157

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 81.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+144} \lor \neg \left(x \leq 1.5 \cdot 10^{-157}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 7: 52.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5.3 \cdot 10^{+150}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -1.7e-19) (* a b) (if (<= (* a b) 5.3e+150) (* z t) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -1.7e-19) {
		tmp = a * b;
	} else if ((a * b) <= 5.3e+150) {
		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) <= (-1.7d-19)) then
        tmp = a * b
    else if ((a * b) <= 5.3d+150) 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) <= -1.7e-19) {
		tmp = a * b;
	} else if ((a * b) <= 5.3e+150) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -1.7e-19:
		tmp = a * b
	elif (a * b) <= 5.3e+150:
		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) <= -1.7e-19)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 5.3e+150)
		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) <= -1.7e-19)
		tmp = a * b;
	elseif ((a * b) <= 5.3e+150)
		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], -1.7e-19], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.3e+150], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.7000000000000001e-19 or 5.30000000000000013e150 < (*.f64 a b)

   1. Initial program 92.9%

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

   2. Taylor expanded in a around inf 65.7%

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

   if -1.7000000000000001e-19 < (*.f64 a b) < 5.30000000000000013e150

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 47.3%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 5.3 \cdot 10^{+150}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+156}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-16}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.5e+156)
   (* x y)
   (if (<= x 1.46e-16) (+ (* a b) (* z t)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+156) {
		tmp = x * y;
	} else if (x <= 1.46e-16) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.5d+156)) then
        tmp = x * y
    else if (x <= 1.46d-16) then
        tmp = (a * b) + (z * t)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+156) {
		tmp = x * y;
	} else if (x <= 1.46e-16) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.5e+156:
		tmp = x * y
	elif x <= 1.46e-16:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.5e+156)
		tmp = Float64(x * y);
	elseif (x <= 1.46e-16)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.5e+156)
		tmp = x * y;
	elseif (x <= 1.46e-16)
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.5e+156], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.46e-16], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999948e156 or 1.4600000000000001e-16 < x

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 61.7%

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

   if -8.49999999999999948e156 < x < 1.4600000000000001e-16

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 80.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+156}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-16}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 35.2% 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 96.9%

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

2. Taylor expanded in a around inf 36.2%

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

3. Final simplification 36.2%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023257 
(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)))