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

Percentage Accurate: 98.0% → 98.8%

Time: 8.2s

Alternatives: 11

Speedup: 0.4×

• 31.9% 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: 98.0% 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: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -inf.0

   1. Initial program 73.9%

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

   3. Taylor expanded in x around 0 82.6%

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

   4. Taylor expanded in z around inf 91.3%

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

      1. associate-/l* 95.7%

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

   6. Simplified 95.7%

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

   if -inf.0 < (*.f64 a b)

   1. Initial program 99.1%

      \[\left(x \cdot y + z \cdot t\right) + a \cdot b \]
   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
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

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

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-define 98.4%

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

   3. fma-define 99.2%

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

3. Simplified 99.2%

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

Alternative 3: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 97.7%

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

   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 4: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.22 \cdot 10^{+117} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+122}\right) \land \left(x \cdot y \leq 1.3 \cdot 10^{+221} \lor \neg \left(x \cdot y \leq 1.55 \cdot 10^{+252}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* x y) -1.22e+117)
         (and (not (<= (* x y) 2.4e+122))
              (or (<= (* x y) 1.3e+221) (not (<= (* x y) 1.55e+252)))))
   (* 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) <= -1.22e+117) || (!((x * y) <= 2.4e+122) && (((x * y) <= 1.3e+221) || !((x * y) <= 1.55e+252)))) {
		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) <= (-1.22d+117)) .or. (.not. ((x * y) <= 2.4d+122)) .and. ((x * y) <= 1.3d+221) .or. (.not. ((x * y) <= 1.55d+252))) 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) <= -1.22e+117) || (!((x * y) <= 2.4e+122) && (((x * y) <= 1.3e+221) || !((x * y) <= 1.55e+252)))) {
		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) <= -1.22e+117) or (not ((x * y) <= 2.4e+122) and (((x * y) <= 1.3e+221) or not ((x * y) <= 1.55e+252))):
		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) <= -1.22e+117) || (!(Float64(x * y) <= 2.4e+122) && ((Float64(x * y) <= 1.3e+221) || !(Float64(x * y) <= 1.55e+252))))
		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) <= -1.22e+117) || (~(((x * y) <= 2.4e+122)) && (((x * y) <= 1.3e+221) || ~(((x * y) <= 1.55e+252)))))
		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], -1.22e+117], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.4e+122]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 1.3e+221], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.55e+252]], $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) < -1.22000000000000004e117 or 2.4000000000000002e122 < (*.f64 x y) < 1.30000000000000002e221 or 1.54999999999999991e252 < (*.f64 x y)

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 76.6%

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

   if -1.22000000000000004e117 < (*.f64 x y) < 2.4000000000000002e122 or 1.30000000000000002e221 < (*.f64 x y) < 1.54999999999999991e252

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 87.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.22 \cdot 10^{+117} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+122}\right) \land \left(x \cdot y \leq 1.3 \cdot 10^{+221} \lor \neg \left(x \cdot y \leq 1.55 \cdot 10^{+252}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -7.2 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{+71} \lor \neg \left(x \cdot y \leq 1.85 \cdot 10^{+171}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* x y) -7.2e+71)
     t_1
     (if (<= (* x y) 2e-22)
       (+ (* a b) (* z t))
       (if (or (<= (* x y) 9e+71) (not (<= (* x y) 1.85e+171)))
         t_1
         (+ (* x y) (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -7.2e+71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-22) {
		tmp = (a * b) + (z * t);
	} else if (((x * y) <= 9e+71) || !((x * y) <= 1.85e+171)) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((x * y) <= (-7.2d+71)) then
        tmp = t_1
    else if ((x * y) <= 2d-22) then
        tmp = (a * b) + (z * t)
    else if (((x * y) <= 9d+71) .or. (.not. ((x * y) <= 1.85d+171))) then
        tmp = t_1
    else
        tmp = (x * y) + (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 t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -7.2e+71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-22) {
		tmp = (a * b) + (z * t);
	} else if (((x * y) <= 9e+71) || !((x * y) <= 1.85e+171)) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -7.2e+71:
		tmp = t_1
	elif (x * y) <= 2e-22:
		tmp = (a * b) + (z * t)
	elif ((x * y) <= 9e+71) or not ((x * y) <= 1.85e+171):
		tmp = t_1
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -7.2e+71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-22)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif ((Float64(x * y) <= 9e+71) || !(Float64(x * y) <= 1.85e+171))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -7.2e+71)
		tmp = t_1;
	elseif ((x * y) <= 2e-22)
		tmp = (a * b) + (z * t);
	elseif (((x * y) <= 9e+71) || ~(((x * y) <= 1.85e+171)))
		tmp = t_1;
	else
		tmp = (x * y) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7.2e+71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-22], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 9e+71], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.85e+171]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.1999999999999999e71 or 2.0000000000000001e-22 < (*.f64 x y) < 9.00000000000000087e71 or 1.84999999999999999e171 < (*.f64 x y)

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 86.0%

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

   if -7.1999999999999999e71 < (*.f64 x y) < 2.0000000000000001e-22

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 93.5%

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

   if 9.00000000000000087e71 < (*.f64 x y) < 1.84999999999999999e171

   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 0 94.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.2 \cdot 10^{+71}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{+71} \lor \neg \left(x \cdot y \leq 1.85 \cdot 10^{+171}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{+83} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+106}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* x y) -3.2e+70)
     t_1
     (if (<= (* x y) 7e-22)
       (+ (* a b) (* z t))
       (if (or (<= (* x y) 8.2e+83) (not (<= (* x y) 5e+106))) t_1 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -3.2e+70) {
		tmp = t_1;
	} else if ((x * y) <= 7e-22) {
		tmp = (a * b) + (z * t);
	} else if (((x * y) <= 8.2e+83) || !((x * y) <= 5e+106)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((x * y) <= (-3.2d+70)) then
        tmp = t_1
    else if ((x * y) <= 7d-22) then
        tmp = (a * b) + (z * t)
    else if (((x * y) <= 8.2d+83) .or. (.not. ((x * y) <= 5d+106))) then
        tmp = t_1
    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 t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -3.2e+70) {
		tmp = t_1;
	} else if ((x * y) <= 7e-22) {
		tmp = (a * b) + (z * t);
	} else if (((x * y) <= 8.2e+83) || !((x * y) <= 5e+106)) {
		tmp = t_1;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -3.2e+70:
		tmp = t_1
	elif (x * y) <= 7e-22:
		tmp = (a * b) + (z * t)
	elif ((x * y) <= 8.2e+83) or not ((x * y) <= 5e+106):
		tmp = t_1
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -3.2e+70)
		tmp = t_1;
	elseif (Float64(x * y) <= 7e-22)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif ((Float64(x * y) <= 8.2e+83) || !(Float64(x * y) <= 5e+106))
		tmp = t_1;
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -3.2e+70)
		tmp = t_1;
	elseif ((x * y) <= 7e-22)
		tmp = (a * b) + (z * t);
	elseif (((x * y) <= 8.2e+83) || ~(((x * y) <= 5e+106)))
		tmp = t_1;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+70], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7e-22], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 8.2e+83], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+106]], $MachinePrecision]], t$95$1, N[(z * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.2000000000000002e70 or 7.00000000000000011e-22 < (*.f64 x y) < 8.2000000000000002e83 or 4.9999999999999998e106 < (*.f64 x y)

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 85.4%

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

   if -3.2000000000000002e70 < (*.f64 x y) < 7.00000000000000011e-22

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 93.5%

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

   if 8.2000000000000002e83 < (*.f64 x y) < 4.9999999999999998e106

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{-22}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{+83} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+106}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+171}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* x y) -2.1e+71)
     t_1
     (if (<= (* x y) 3.5e-24)
       (+ (* a b) (* z t))
       (if (<= (* x y) 6.8e+71)
         (* a (+ b (/ (* x y) a)))
         (if (<= (* x y) 1.85e+171) (+ (* x y) (* z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+71) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e-24) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 6.8e+71) {
		tmp = a * (b + ((x * y) / a));
	} else if ((x * y) <= 1.85e+171) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((x * y) <= (-2.1d+71)) then
        tmp = t_1
    else if ((x * y) <= 3.5d-24) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 6.8d+71) then
        tmp = a * (b + ((x * y) / a))
    else if ((x * y) <= 1.85d+171) then
        tmp = (x * y) + (z * t)
    else
        tmp = t_1
    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 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+71) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e-24) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 6.8e+71) {
		tmp = a * (b + ((x * y) / a));
	} else if ((x * y) <= 1.85e+171) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -2.1e+71:
		tmp = t_1
	elif (x * y) <= 3.5e-24:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 6.8e+71:
		tmp = a * (b + ((x * y) / a))
	elif (x * y) <= 1.85e+171:
		tmp = (x * y) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+71)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.5e-24)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 6.8e+71)
		tmp = Float64(a * Float64(b + Float64(Float64(x * y) / a)));
	elseif (Float64(x * y) <= 1.85e+171)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.1e+71)
		tmp = t_1;
	elseif ((x * y) <= 3.5e-24)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 6.8e+71)
		tmp = a * (b + ((x * y) / a));
	elseif ((x * y) <= 1.85e+171)
		tmp = (x * y) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e-24], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.8e+71], N[(a * N[(b + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.85e+171], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.09999999999999989e71 or 1.84999999999999999e171 < (*.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 z around 0 86.2%

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

   if -2.09999999999999989e71 < (*.f64 x y) < 3.4999999999999996e-24

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 93.5%

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

   if 3.4999999999999996e-24 < (*.f64 x y) < 6.7999999999999997e71

   1. Initial program 94.9%

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

   3. Taylor expanded in a around inf 90.1%

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

   4. Taylor expanded in t around 0 80.1%

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

   if 6.7999999999999997e71 < (*.f64 x y) < 1.84999999999999999e171

   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 0 94.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+71}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-24}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+171}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-11}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-221}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.65e+103)
   (* a b)
   (if (<= a -1.5e-11)
     (* z t)
     (if (<= a -1.2e-68)
       (* x y)
       (if (<= a -1.55e-221) (* z t) (if (<= a 6.2e-150) (* x y) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.65e+103) {
		tmp = a * b;
	} else if (a <= -1.5e-11) {
		tmp = z * t;
	} else if (a <= -1.2e-68) {
		tmp = x * y;
	} else if (a <= -1.55e-221) {
		tmp = z * t;
	} else if (a <= 6.2e-150) {
		tmp = x * y;
	} 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 <= (-1.65d+103)) then
        tmp = a * b
    else if (a <= (-1.5d-11)) then
        tmp = z * t
    else if (a <= (-1.2d-68)) then
        tmp = x * y
    else if (a <= (-1.55d-221)) then
        tmp = z * t
    else if (a <= 6.2d-150) then
        tmp = x * y
    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 <= -1.65e+103) {
		tmp = a * b;
	} else if (a <= -1.5e-11) {
		tmp = z * t;
	} else if (a <= -1.2e-68) {
		tmp = x * y;
	} else if (a <= -1.55e-221) {
		tmp = z * t;
	} else if (a <= 6.2e-150) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.65e+103:
		tmp = a * b
	elif a <= -1.5e-11:
		tmp = z * t
	elif a <= -1.2e-68:
		tmp = x * y
	elif a <= -1.55e-221:
		tmp = z * t
	elif a <= 6.2e-150:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.65e+103)
		tmp = Float64(a * b);
	elseif (a <= -1.5e-11)
		tmp = Float64(z * t);
	elseif (a <= -1.2e-68)
		tmp = Float64(x * y);
	elseif (a <= -1.55e-221)
		tmp = Float64(z * t);
	elseif (a <= 6.2e-150)
		tmp = Float64(x * y);
	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 <= -1.65e+103)
		tmp = a * b;
	elseif (a <= -1.5e-11)
		tmp = z * t;
	elseif (a <= -1.2e-68)
		tmp = x * y;
	elseif (a <= -1.55e-221)
		tmp = z * t;
	elseif (a <= 6.2e-150)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.65e+103], N[(a * b), $MachinePrecision], If[LessEqual[a, -1.5e-11], N[(z * t), $MachinePrecision], If[LessEqual[a, -1.2e-68], N[(x * y), $MachinePrecision], If[LessEqual[a, -1.55e-221], N[(z * t), $MachinePrecision], If[LessEqual[a, 6.2e-150], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65000000000000004e103 or 6.19999999999999996e-150 < a

   1. Initial program 96.7%

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

   3. Taylor expanded in a around inf 58.2%

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

   if -1.65000000000000004e103 < a < -1.5e-11 or -1.19999999999999996e-68 < a < -1.55e-221

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 54.0%

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

   if -1.5e-11 < a < -1.19999999999999996e-68 or -1.55e-221 < a < 6.19999999999999996e-150

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-11}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-221}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.3% accurate, 0.4× speedup

Math

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

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 (* 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 + (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 + (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 + (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(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 + (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[(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. Add Preprocessing

   3. Taylor expanded in x around 0 50.0%

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

   4. Taylor expanded in z around inf 75.0%

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

      1. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 99.6%

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

Alternative 10: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{-35} \lor \neg \left(a \cdot b \leq 1.45 \cdot 10^{+32}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* a b) -8.2e-35) (not (<= (* a b) 1.45e+32))) (* a b) (* z t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * b) <= -8.2e-35) || !((a * b) <= 1.45e+32)) {
		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) <= (-8.2d-35)) .or. (.not. ((a * b) <= 1.45d+32))) 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) <= -8.2e-35) || !((a * b) <= 1.45e+32)) {
		tmp = a * b;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * b) <= -8.2e-35) or not ((a * b) <= 1.45e+32):
		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) <= -8.2e-35) || !(Float64(a * b) <= 1.45e+32))
		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) <= -8.2e-35) || ~(((a * b) <= 1.45e+32)))
		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], -8.2e-35], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.45e+32]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8.20000000000000052e-35 or 1.45000000000000001e32 < (*.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 a around inf 65.9%

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

   if -8.20000000000000052e-35 < (*.f64 a b) < 1.45000000000000001e32

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 49.5%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.2 \cdot 10^{-35} \lor \neg \left(a \cdot b \leq 1.45 \cdot 10^{+32}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.4% 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. Add Preprocessing

3. Taylor expanded in a around inf 40.7%

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

Reproduce

herbie shell --seed 2024101 
(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)))