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

Percentage Accurate: 97.6% → 99.2%

Time: 10.4s

Alternatives: 8

Speedup: 0.4×

• 32.5% 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: 97.6% 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: 99.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(x + N[(b * N[(a / y), $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 inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+206}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;t \cdot z + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.95e+206)
   (* x y)
   (if (<= (* x y) 2.6e+47)
     (+ (* t z) (* a b))
     (if (<= (* x y) 1.5e+73)
       (* x y)
       (if (<= (* x y) 1.6e+111) (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.95e+206) {
		tmp = x * y;
	} else if ((x * y) <= 2.6e+47) {
		tmp = (t * z) + (a * b);
	} else if ((x * y) <= 1.5e+73) {
		tmp = x * y;
	} else if ((x * y) <= 1.6e+111) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * y) <= (-1.95d+206)) then
        tmp = x * y
    else if ((x * y) <= 2.6d+47) then
        tmp = (t * z) + (a * b)
    else if ((x * y) <= 1.5d+73) then
        tmp = x * y
    else if ((x * y) <= 1.6d+111) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.95e+206) {
		tmp = x * y;
	} else if ((x * y) <= 2.6e+47) {
		tmp = (t * z) + (a * b);
	} else if ((x * y) <= 1.5e+73) {
		tmp = x * y;
	} else if ((x * y) <= 1.6e+111) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.95e+206:
		tmp = x * y
	elif (x * y) <= 2.6e+47:
		tmp = (t * z) + (a * b)
	elif (x * y) <= 1.5e+73:
		tmp = x * y
	elif (x * y) <= 1.6e+111:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -1.95e+206)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.6e+47)
		tmp = Float64(Float64(t * z) + Float64(a * b));
	elseif (Float64(x * y) <= 1.5e+73)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.6e+111)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -1.95e+206)
		tmp = x * y;
	elseif ((x * y) <= 2.6e+47)
		tmp = (t * z) + (a * b);
	elseif ((x * y) <= 1.5e+73)
		tmp = x * y;
	elseif ((x * y) <= 1.6e+111)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.95e+206], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.6e+47], N[(N[(t * z), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.5e+73], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.6e+111], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.95e206 or 2.60000000000000003e47 < (*.f64 x y) < 1.50000000000000005e73 or 1.6e111 < (*.f64 x y)

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.95e206 < (*.f64 x y) < 2.60000000000000003e47

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.50000000000000005e73 < (*.f64 x y) < 1.6e111

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.7:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -2.05 \cdot 10^{-281}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;x \cdot y \leq 1.16 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1.5e+77)
   (* x y)
   (if (<= (* x y) -3.7)
     (* a b)
     (if (<= (* x y) -2.05e-281)
       (* t z)
       (if (<= (* x y) 1.16e+47) (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.5e+77) {
		tmp = x * y;
	} else if ((x * y) <= -3.7) {
		tmp = a * b;
	} else if ((x * y) <= -2.05e-281) {
		tmp = t * z;
	} else if ((x * y) <= 1.16e+47) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * y) <= (-1.5d+77)) then
        tmp = x * y
    else if ((x * y) <= (-3.7d0)) then
        tmp = a * b
    else if ((x * y) <= (-2.05d-281)) then
        tmp = t * z
    else if ((x * y) <= 1.16d+47) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1.5e+77) {
		tmp = x * y;
	} else if ((x * y) <= -3.7) {
		tmp = a * b;
	} else if ((x * y) <= -2.05e-281) {
		tmp = t * z;
	} else if ((x * y) <= 1.16e+47) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1.5e+77:
		tmp = x * y
	elif (x * y) <= -3.7:
		tmp = a * b
	elif (x * y) <= -2.05e-281:
		tmp = t * z
	elif (x * y) <= 1.16e+47:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -1.5e+77)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.7)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -2.05e-281)
		tmp = Float64(t * z);
	elseif (Float64(x * y) <= 1.16e+47)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -1.5e+77)
		tmp = x * y;
	elseif ((x * y) <= -3.7)
		tmp = a * b;
	elseif ((x * y) <= -2.05e-281)
		tmp = t * z;
	elseif ((x * y) <= 1.16e+47)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.5e+77], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.7], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.05e-281], N[(t * z), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.16e+47], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.4999999999999999e77 or 1.1600000000000001e47 < (*.f64 x y)

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.4999999999999999e77 < (*.f64 x y) < -3.7000000000000002 or -2.05e-281 < (*.f64 x y) < 1.1600000000000001e47

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.7000000000000002 < (*.f64 x y) < -2.05e-281

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+18}:\\ \;\;\;\;t \cdot z + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + b \cdot \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* x y) -1e+83)
   (+ (* x y) (* a b))
   (if (<= (* x y) 2e+18) (+ (* t z) (* a b)) (* y (+ x (* b (/ a y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1e+83) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= 2e+18) {
		tmp = (t * z) + (a * b);
	} else {
		tmp = y * (x + (b * (a / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x * y) <= (-1d+83)) then
        tmp = (x * y) + (a * b)
    else if ((x * y) <= 2d+18) then
        tmp = (t * z) + (a * b)
    else
        tmp = y * (x + (b * (a / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x * y) <= -1e+83) {
		tmp = (x * y) + (a * b);
	} else if ((x * y) <= 2e+18) {
		tmp = (t * z) + (a * b);
	} else {
		tmp = y * (x + (b * (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x * y) <= -1e+83:
		tmp = (x * y) + (a * b)
	elif (x * y) <= 2e+18:
		tmp = (t * z) + (a * b)
	else:
		tmp = y * (x + (b * (a / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x * y) <= -1e+83)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	elseif (Float64(x * y) <= 2e+18)
		tmp = Float64(Float64(t * z) + Float64(a * b));
	else
		tmp = Float64(y * Float64(x + Float64(b * Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x * y) <= -1e+83)
		tmp = (x * y) + (a * b);
	elseif ((x * y) <= 2e+18)
		tmp = (t * z) + (a * b);
	else
		tmp = y * (x + (b * (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+83], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+18], N[(N[(t * z), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000003e83

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.00000000000000003e83 < (*.f64 x y) < 2e18

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2e18 < (*.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -2.85 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.5 \cdot 10^{-160}:\\ \;\;\;\;t \cdot z + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))))
   (if (<= (* x y) -2.85e+72)
     t_1
     (if (<= (* x y) 1.5e-160) (+ (* t z) (* a b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -2.85e+72) {
		tmp = t_1;
	} else if ((x * y) <= 1.5e-160) {
		tmp = (t * z) + (a * b);
	} 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 = (x * y) + (a * b)
    if ((x * y) <= (-2.85d+72)) then
        tmp = t_1
    else if ((x * y) <= 1.5d-160) then
        tmp = (t * z) + (a * b)
    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 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -2.85e+72) {
		tmp = t_1;
	} else if ((x * y) <= 1.5e-160) {
		tmp = (t * z) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -2.85e+72:
		tmp = t_1
	elif (x * y) <= 1.5e-160:
		tmp = (t * z) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -2.85e+72)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.5e-160)
		tmp = Float64(Float64(t * z) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -2.85e+72)
		tmp = t_1;
	elseif ((x * y) <= 1.5e-160)
		tmp = (t * z) + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.85e+72], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.5e-160], N[(N[(t * z), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.8499999999999998e72 or 1.49999999999999998e-160 < (*.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.8499999999999998e72 < (*.f64 x y) < 1.49999999999999998e-160

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z + a \cdot b\\ \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 0.00025:\\ \;\;\;\;t \cdot z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* t z) (* a b))))
   (if (<= (* a b) -4.4e-53)
     t_1
     (if (<= (* a b) 0.00025) (+ (* t z) (* x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * z) + (a * b);
	double tmp;
	if ((a * b) <= -4.4e-53) {
		tmp = t_1;
	} else if ((a * b) <= 0.00025) {
		tmp = (t * z) + (x * y);
	} 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 = (t * z) + (a * b)
    if ((a * b) <= (-4.4d-53)) then
        tmp = t_1
    else if ((a * b) <= 0.00025d0) then
        tmp = (t * z) + (x * y)
    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 = (t * z) + (a * b);
	double tmp;
	if ((a * b) <= -4.4e-53) {
		tmp = t_1;
	} else if ((a * b) <= 0.00025) {
		tmp = (t * z) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * z) + (a * b)
	tmp = 0
	if (a * b) <= -4.4e-53:
		tmp = t_1
	elif (a * b) <= 0.00025:
		tmp = (t * z) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * z) + Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -4.4e-53)
		tmp = t_1;
	elseif (Float64(a * b) <= 0.00025)
		tmp = Float64(Float64(t * z) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * z) + (a * b);
	tmp = 0.0;
	if ((a * b) <= -4.4e-53)
		tmp = t_1;
	elseif ((a * b) <= 0.00025)
		tmp = (t * z) + (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4.4e-53], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 0.00025], N[(N[(t * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.40000000000000037e-53 or 2.5000000000000001e-4 < (*.f64 a b)

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.40000000000000037e-53 < (*.f64 a b) < 2.5000000000000001e-4

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 53.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.95 \cdot 10^{+24}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-26}:\\ \;\;\;\;t \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* a b) -2.95e+24) (* a b) (if (<= (* a b) 4e-26) (* t z) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a * b) <= -2.95e+24) {
		tmp = a * b;
	} else if ((a * b) <= 4e-26) {
		tmp = t * z;
	} 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) <= (-2.95d+24)) then
        tmp = a * b
    else if ((a * b) <= 4d-26) then
        tmp = t * z
    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) <= -2.95e+24) {
		tmp = a * b;
	} else if ((a * b) <= 4e-26) {
		tmp = t * z;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a * b) <= -2.95e+24:
		tmp = a * b
	elif (a * b) <= 4e-26:
		tmp = t * z
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a * b) <= -2.95e+24)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 4e-26)
		tmp = Float64(t * z);
	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) <= -2.95e+24)
		tmp = a * b;
	elseif ((a * b) <= 4e-26)
		tmp = t * z;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.95e+24], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4e-26], N[(t * z), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.94999999999999987e24 or 4.0000000000000002e-26 < (*.f64 a b)

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.94999999999999987e24 < (*.f64 a b) < 4.0000000000000002e-26

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 34.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in a around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))