Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.6% → 97.9%

Time: 13.0s

Alternatives: 17

Speedup: 1.0×

• 41.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. +-commutative 98.8%

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

   2. fma-define 99.2%

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

   3. associate-+l+ 99.2%

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

   4. fma-define 99.2%

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

   5. fma-define 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 95.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate-+l+ 98.8%

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

   2. fma-define 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 65.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + z \cdot t\\ t_3 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -4.45 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.8 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{-226}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 280000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i)))
        (t_2 (+ (* a b) (* z t)))
        (t_3 (+ (* a b) (* x y))))
   (if (<= (* x y) -6.8e+92)
     t_3
     (if (<= (* x y) -4.45e-11)
       t_1
       (if (<= (* x y) -1.7e-64)
         t_2
         (if (<= (* x y) 1.8e-288)
           t_1
           (if (<= (* x y) 5.4e-226)
             t_2
             (if (<= (* x y) 280000000000.0) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (a * b) + (z * t);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -6.8e+92) {
		tmp = t_3;
	} else if ((x * y) <= -4.45e-11) {
		tmp = t_1;
	} else if ((x * y) <= -1.7e-64) {
		tmp = t_2;
	} else if ((x * y) <= 1.8e-288) {
		tmp = t_1;
	} else if ((x * y) <= 5.4e-226) {
		tmp = t_2;
	} else if ((x * y) <= 280000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (a * b) + (z * t)
    t_3 = (a * b) + (x * y)
    if ((x * y) <= (-6.8d+92)) then
        tmp = t_3
    else if ((x * y) <= (-4.45d-11)) then
        tmp = t_1
    else if ((x * y) <= (-1.7d-64)) then
        tmp = t_2
    else if ((x * y) <= 1.8d-288) then
        tmp = t_1
    else if ((x * y) <= 5.4d-226) then
        tmp = t_2
    else if ((x * y) <= 280000000000.0d0) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (a * b) + (z * t);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -6.8e+92) {
		tmp = t_3;
	} else if ((x * y) <= -4.45e-11) {
		tmp = t_1;
	} else if ((x * y) <= -1.7e-64) {
		tmp = t_2;
	} else if ((x * y) <= 1.8e-288) {
		tmp = t_1;
	} else if ((x * y) <= 5.4e-226) {
		tmp = t_2;
	} else if ((x * y) <= 280000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (a * b) + (z * t)
	t_3 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -6.8e+92:
		tmp = t_3
	elif (x * y) <= -4.45e-11:
		tmp = t_1
	elif (x * y) <= -1.7e-64:
		tmp = t_2
	elif (x * y) <= 1.8e-288:
		tmp = t_1
	elif (x * y) <= 5.4e-226:
		tmp = t_2
	elif (x * y) <= 280000000000.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -6.8e+92)
		tmp = t_3;
	elseif (Float64(x * y) <= -4.45e-11)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.7e-64)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.8e-288)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.4e-226)
		tmp = t_2;
	elseif (Float64(x * y) <= 280000000000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	t_2 = (a * b) + (z * t);
	t_3 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -6.8e+92)
		tmp = t_3;
	elseif ((x * y) <= -4.45e-11)
		tmp = t_1;
	elseif ((x * y) <= -1.7e-64)
		tmp = t_2;
	elseif ((x * y) <= 1.8e-288)
		tmp = t_1;
	elseif ((x * y) <= 5.4e-226)
		tmp = t_2;
	elseif ((x * y) <= 280000000000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.8e+92], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -4.45e-11], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.7e-64], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.8e-288], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.4e-226], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 280000000000.0], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.7999999999999996e92 or 2.8e11 < (*.f64 x y)

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 85.4%

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

   4. Taylor expanded in c around 0 74.5%

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

   if -6.7999999999999996e92 < (*.f64 x y) < -4.45e-11 or -1.70000000000000006e-64 < (*.f64 x y) < 1.8000000000000001e-288 or 5.40000000000000029e-226 < (*.f64 x y) < 2.8e11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 75.9%

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

   4. Taylor expanded in x around 0 70.1%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -4.45e-11 < (*.f64 x y) < -1.70000000000000006e-64 or 1.8000000000000001e-288 < (*.f64 x y) < 5.40000000000000029e-226

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 94.4%

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

   4. Taylor expanded in t around inf 94.4%

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

   5. Taylor expanded in c around 0 84.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{+92}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.45 \cdot 10^{-11}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-64}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.8 \cdot 10^{-288}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 5.4 \cdot 10^{-226}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 280000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq 280000000000\right) \land \left(x \cdot y \leq 2.4 \cdot 10^{+140} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+251}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.8e+175)
         (and (not (<= (* x y) 280000000000.0))
              (or (<= (* x y) 2.4e+140) (not (<= (* x y) 2e+251)))))
   (* x y)
   (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.8e+175) || (!((x * y) <= 280000000000.0) && (((x * y) <= 2.4e+140) || !((x * y) <= 2e+251)))) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2.8d+175)) .or. (.not. ((x * y) <= 280000000000.0d0)) .and. ((x * y) <= 2.4d+140) .or. (.not. ((x * y) <= 2d+251))) then
        tmp = x * y
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.8e+175) || (!((x * y) <= 280000000000.0) && (((x * y) <= 2.4e+140) || !((x * y) <= 2e+251)))) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2.8e+175) or (not ((x * y) <= 280000000000.0) and (((x * y) <= 2.4e+140) or not ((x * y) <= 2e+251))):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2.8e+175) || (!(Float64(x * y) <= 280000000000.0) && ((Float64(x * y) <= 2.4e+140) || !(Float64(x * y) <= 2e+251))))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2.8e+175) || (~(((x * y) <= 280000000000.0)) && (((x * y) <= 2.4e+140) || ~(((x * y) <= 2e+251)))))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.8e+175], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 280000000000.0]], $MachinePrecision], Or[LessEqual[N[(x * y), $MachinePrecision], 2.4e+140], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+251]], $MachinePrecision]]]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.8000000000000001e175 or 2.8e11 < (*.f64 x y) < 2.4e140 or 2.0000000000000001e251 < (*.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 74.6%

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

   if -2.8000000000000001e175 < (*.f64 x y) < 2.8e11 or 2.4e140 < (*.f64 x y) < 2.0000000000000001e251

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in x around 0 64.4%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq 280000000000\right) \land \left(x \cdot y \leq 2.4 \cdot 10^{+140} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+251}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1.25 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -23500000000 \lor \neg \left(c \cdot i \leq 5.5 \cdot 10^{+88}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* c i) -5.6e+141)
     t_1
     (if (<= (* c i) -1.25e+37)
       (* x y)
       (if (or (<= (* c i) -23500000000.0) (not (<= (* c i) 5.5e+88)))
         t_1
         (+ (* a b) (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -5.6e+141) {
		tmp = t_1;
	} else if ((c * i) <= -1.25e+37) {
		tmp = x * y;
	} else if (((c * i) <= -23500000000.0) || !((c * i) <= 5.5e+88)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((c * i) <= (-5.6d+141)) then
        tmp = t_1
    else if ((c * i) <= (-1.25d+37)) then
        tmp = x * y
    else if (((c * i) <= (-23500000000.0d0)) .or. (.not. ((c * i) <= 5.5d+88))) then
        tmp = t_1
    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 c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -5.6e+141) {
		tmp = t_1;
	} else if ((c * i) <= -1.25e+37) {
		tmp = x * y;
	} else if (((c * i) <= -23500000000.0) || !((c * i) <= 5.5e+88)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -5.6e+141:
		tmp = t_1
	elif (c * i) <= -1.25e+37:
		tmp = x * y
	elif ((c * i) <= -23500000000.0) or not ((c * i) <= 5.5e+88):
		tmp = t_1
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -5.6e+141)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.25e+37)
		tmp = Float64(x * y);
	elseif ((Float64(c * i) <= -23500000000.0) || !(Float64(c * i) <= 5.5e+88))
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -5.6e+141)
		tmp = t_1;
	elseif ((c * i) <= -1.25e+37)
		tmp = x * y;
	elseif (((c * i) <= -23500000000.0) || ~(((c * i) <= 5.5e+88)))
		tmp = t_1;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5.6e+141], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.25e+37], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], -23500000000.0], N[Not[LessEqual[N[(c * i), $MachinePrecision], 5.5e+88]], $MachinePrecision]], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.59999999999999982e141 or -1.24999999999999997e37 < (*.f64 c i) < -2.35e10 or 5.5e88 < (*.f64 c i)

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0 89.4%

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

   4. Taylor expanded in x around 0 76.9%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -5.59999999999999982e141 < (*.f64 c i) < -1.24999999999999997e37

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 52.0%

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

   if -2.35e10 < (*.f64 c i) < 5.5e88

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 91.3%

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

   4. Taylor expanded in t around inf 71.6%

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

   5. Taylor expanded in c around 0 65.3%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.25 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -23500000000 \lor \neg \left(c \cdot i \leq 5.5 \cdot 10^{+88}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{-155}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 225000000000:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4e+93)
   (* x y)
   (if (<= (* x y) 1.1e-285)
     (* c i)
     (if (<= (* x y) 3.4e-155)
       (* z t)
       (if (<= (* x y) 225000000000.0) (* c i) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4e+93) {
		tmp = x * y;
	} else if ((x * y) <= 1.1e-285) {
		tmp = c * i;
	} else if ((x * y) <= 3.4e-155) {
		tmp = z * t;
	} else if ((x * y) <= 225000000000.0) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-4d+93)) then
        tmp = x * y
    else if ((x * y) <= 1.1d-285) then
        tmp = c * i
    else if ((x * y) <= 3.4d-155) then
        tmp = z * t
    else if ((x * y) <= 225000000000.0d0) then
        tmp = c * i
    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 c, double i) {
	double tmp;
	if ((x * y) <= -4e+93) {
		tmp = x * y;
	} else if ((x * y) <= 1.1e-285) {
		tmp = c * i;
	} else if ((x * y) <= 3.4e-155) {
		tmp = z * t;
	} else if ((x * y) <= 225000000000.0) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4e+93:
		tmp = x * y
	elif (x * y) <= 1.1e-285:
		tmp = c * i
	elif (x * y) <= 3.4e-155:
		tmp = z * t
	elif (x * y) <= 225000000000.0:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4e+93)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.1e-285)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= 3.4e-155)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 225000000000.0)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4e+93)
		tmp = x * y;
	elseif ((x * y) <= 1.1e-285)
		tmp = c * i;
	elseif ((x * y) <= 3.4e-155)
		tmp = z * t;
	elseif ((x * y) <= 225000000000.0)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+93], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.1e-285], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.4e-155], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 225000000000.0], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.00000000000000017e93 or 2.25e11 < (*.f64 x y)

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 62.2%

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

   if -4.00000000000000017e93 < (*.f64 x y) < 1.1e-285 or 3.4e-155 < (*.f64 x y) < 2.25e11

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 45.4%

      \[\leadsto \color{blue}{c \cdot i} \]

   if 1.1e-285 < (*.f64 x y) < 3.4e-155

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf 54.4%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{-155}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 225000000000:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{-26}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 10^{-274}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+51}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2e-26)
   (+ (* c i) (* x y))
   (if (<= (* c i) 1e-274)
     (+ (* a b) (* z t))
     (if (<= (* c i) 2e+51) (+ (* a b) (* x y)) (+ (* c i) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2e-26) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= 1e-274) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 2e+51) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2d-26)) then
        tmp = (c * i) + (x * y)
    else if ((c * i) <= 1d-274) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 2d+51) then
        tmp = (a * b) + (x * y)
    else
        tmp = (c * i) + (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 c, double i) {
	double tmp;
	if ((c * i) <= -2e-26) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= 1e-274) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 2e+51) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2e-26:
		tmp = (c * i) + (x * y)
	elif (c * i) <= 1e-274:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 2e+51:
		tmp = (a * b) + (x * y)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2e-26)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(c * i) <= 1e-274)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 2e+51)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2e-26)
		tmp = (c * i) + (x * y);
	elseif ((c * i) <= 1e-274)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 2e+51)
		tmp = (a * b) + (x * y);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2e-26], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e-274], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2e+51], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.0000000000000001e-26

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 94.5%

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

   4. Taylor expanded in t around 0 86.0%

      \[\leadsto \color{blue}{c \cdot i + x \cdot y} \]

   if -2.0000000000000001e-26 < (*.f64 c i) < 9.99999999999999966e-275

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 91.6%

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

   4. Taylor expanded in t around inf 74.1%

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

   5. Taylor expanded in c around 0 70.4%

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

   if 9.99999999999999966e-275 < (*.f64 c i) < 2e51

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 76.3%

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

   4. Taylor expanded in c around 0 68.9%

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

   if 2e51 < (*.f64 c i)

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 90.9%

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

   4. Taylor expanded in x around 0 76.3%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2 \cdot 10^{-26}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 10^{-274}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{+51}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -10000 \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -10000.0) (not (<= (* x y) 2e-14)))
   (+ (* c i) (+ (* x y) (* z t)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -10000.0) || !((x * y) <= 2e-14)) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-10000.0d0)) .or. (.not. ((x * y) <= 2d-14))) then
        tmp = (c * i) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((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 c, double i) {
	double tmp;
	if (((x * y) <= -10000.0) || !((x * y) <= 2e-14)) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -10000.0) or not ((x * y) <= 2e-14):
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -10000.0) || !(Float64(x * y) <= 2e-14))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -10000.0) || ~(((x * y) <= 2e-14)))
		tmp = (c * i) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -10000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e-14]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1e4 or 2e-14 < (*.f64 x y)

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 86.5%

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

   if -1e4 < (*.f64 x y) < 2e-14

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 97.2%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -10000 \lor \neg \left(x \cdot y \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+174}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.32 \cdot 10^{+195}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -6e+174)
   (+ (* a b) (* z t))
   (if (<= (* a b) 1.32e+195)
     (+ (* c i) (+ (* x y) (* z t)))
     (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -6e+174) {
		tmp = (a * b) + (z * t);
	} else if ((a * b) <= 1.32e+195) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-6d+174)) then
        tmp = (a * b) + (z * t)
    else if ((a * b) <= 1.32d+195) then
        tmp = (c * i) + ((x * y) + (z * t))
    else
        tmp = (a * b) + (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 c, double i) {
	double tmp;
	if ((a * b) <= -6e+174) {
		tmp = (a * b) + (z * t);
	} else if ((a * b) <= 1.32e+195) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -6e+174:
		tmp = (a * b) + (z * t)
	elif (a * b) <= 1.32e+195:
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -6e+174)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(a * b) <= 1.32e+195)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -6e+174)
		tmp = (a * b) + (z * t);
	elseif ((a * b) <= 1.32e+195)
		tmp = (c * i) + ((x * y) + (z * t));
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -6e+174], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.32e+195], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6e174

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.8%

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

   4. Taylor expanded in t around inf 92.2%

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

   5. Taylor expanded in c around 0 83.7%

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

   if -6e174 < (*.f64 a b) < 1.31999999999999993e195

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0 90.2%

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

   if 1.31999999999999993e195 < (*.f64 a b)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.6%

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

   4. Taylor expanded in c around 0 91.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+174}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.32 \cdot 10^{+195}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+69)
   (+ (* c i) (+ (* x y) (* z t)))
   (if (<= (* z t) 4e+19)
     (+ (* c i) (+ (* a b) (* x y)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+69) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((z * t) <= 4e+19) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-5d+69)) then
        tmp = (c * i) + ((x * y) + (z * t))
    else if ((z * t) <= 4d+19) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((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 c, double i) {
	double tmp;
	if ((z * t) <= -5e+69) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((z * t) <= 4e+19) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+69:
		tmp = (c * i) + ((x * y) + (z * t))
	elif (z * t) <= 4e+19:
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+69)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(z * t) <= 4e+19)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -5e+69)
		tmp = (c * i) + ((x * y) + (z * t));
	elseif ((z * t) <= 4e+19)
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+69], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+19], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.00000000000000036e69

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0 90.7%

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

   if -5.00000000000000036e69 < (*.f64 z t) < 4e19

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 94.8%

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

   if 4e19 < (*.f64 z t)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i + t \cdot \left(z + x \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+69)
   (+ (* c i) (* t (+ z (* x (/ y t)))))
   (if (<= (* z t) 4e+19)
     (+ (* c i) (+ (* a b) (* x y)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+69) {
		tmp = (c * i) + (t * (z + (x * (y / t))));
	} else if ((z * t) <= 4e+19) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-5d+69)) then
        tmp = (c * i) + (t * (z + (x * (y / t))))
    else if ((z * t) <= 4d+19) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((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 c, double i) {
	double tmp;
	if ((z * t) <= -5e+69) {
		tmp = (c * i) + (t * (z + (x * (y / t))));
	} else if ((z * t) <= 4e+19) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+69:
		tmp = (c * i) + (t * (z + (x * (y / t))))
	elif (z * t) <= 4e+19:
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+69)
		tmp = Float64(Float64(c * i) + Float64(t * Float64(z + Float64(x * Float64(y / t)))));
	elseif (Float64(z * t) <= 4e+19)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -5e+69)
		tmp = (c * i) + (t * (z + (x * (y / t))));
	elseif ((z * t) <= 4e+19)
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+69], N[(N[(c * i), $MachinePrecision] + N[(t * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+19], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.00000000000000036e69

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 98.0%

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

   4. Taylor expanded in a around 0 92.6%

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

   5. Taylor expanded in t around inf 92.6%

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

      1. associate-/l* 90.7%

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

   7. Simplified 90.7%

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

   if -5.00000000000000036e69 < (*.f64 z t) < 4e19

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 94.8%

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

   if 4e19 < (*.f64 z t)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i + t \cdot \left(z + x \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i + z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+69)
   (+ (* c i) (* z (+ t (/ (* x y) z))))
   (if (<= (* z t) 4e+19)
     (+ (* c i) (+ (* a b) (* x y)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+69) {
		tmp = (c * i) + (z * (t + ((x * y) / z)));
	} else if ((z * t) <= 4e+19) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-5d+69)) then
        tmp = (c * i) + (z * (t + ((x * y) / z)))
    else if ((z * t) <= 4d+19) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((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 c, double i) {
	double tmp;
	if ((z * t) <= -5e+69) {
		tmp = (c * i) + (z * (t + ((x * y) / z)));
	} else if ((z * t) <= 4e+19) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+69:
		tmp = (c * i) + (z * (t + ((x * y) / z)))
	elif (z * t) <= 4e+19:
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+69)
		tmp = Float64(Float64(c * i) + Float64(z * Float64(t + Float64(Float64(x * y) / z))));
	elseif (Float64(z * t) <= 4e+19)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -5e+69)
		tmp = (c * i) + (z * (t + ((x * y) / z)));
	elseif ((z * t) <= 4e+19)
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+69], N[(N[(c * i), $MachinePrecision] + N[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+19], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.00000000000000036e69

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 98.0%

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

   4. Taylor expanded in a around 0 92.6%

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

   if -5.00000000000000036e69 < (*.f64 z t) < 4e19

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 94.8%

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

   if 4e19 < (*.f64 z t)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i + z \cdot \left(t + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 4.1 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.5e+85)
   (* c i)
   (if (<= (* c i) 4.1e-308)
     (* z t)
     (if (<= (* c i) 3.8e+64) (* a b) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.5e+85) {
		tmp = c * i;
	} else if ((c * i) <= 4.1e-308) {
		tmp = z * t;
	} else if ((c * i) <= 3.8e+64) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.5d+85)) then
        tmp = c * i
    else if ((c * i) <= 4.1d-308) then
        tmp = z * t
    else if ((c * i) <= 3.8d+64) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.5e+85) {
		tmp = c * i;
	} else if ((c * i) <= 4.1e-308) {
		tmp = z * t;
	} else if ((c * i) <= 3.8e+64) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.5e+85:
		tmp = c * i
	elif (c * i) <= 4.1e-308:
		tmp = z * t
	elif (c * i) <= 3.8e+64:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.5e+85)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 4.1e-308)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 3.8e+64)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.5e+85)
		tmp = c * i;
	elseif ((c * i) <= 4.1e-308)
		tmp = z * t;
	elseif ((c * i) <= 3.8e+64)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.5e+85], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.1e-308], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.8e+64], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.50000000000000005e85 or 3.8000000000000001e64 < (*.f64 c i)

   1. Initial program 98.0%

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

   3. Taylor expanded in c around inf 67.4%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -3.50000000000000005e85 < (*.f64 c i) < 4.09999999999999983e-308

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 36.5%

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

   if 4.09999999999999983e-308 < (*.f64 c i) < 3.8000000000000001e64

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 38.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.5 \cdot 10^{+85}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 4.1 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+126} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+36}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.25e+126) (not (<= (* x y) 3.9e+36)))
   (+ (* a b) (* x y))
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.25e+126) || !((x * y) <= 3.9e+36)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2.25d+126)) .or. (.not. ((x * y) <= 3.9d+36))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (c * i) + (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 c, double i) {
	double tmp;
	if (((x * y) <= -2.25e+126) || !((x * y) <= 3.9e+36)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2.25e+126) or not ((x * y) <= 3.9e+36):
		tmp = (a * b) + (x * y)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2.25e+126) || !(Float64(x * y) <= 3.9e+36))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2.25e+126) || ~(((x * y) <= 3.9e+36)))
		tmp = (a * b) + (x * y);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.25e+126], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.9e+36]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.24999999999999987e126 or 3.90000000000000021e36 < (*.f64 x y)

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in c around 0 76.8%

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

   if -2.24999999999999987e126 < (*.f64 x y) < 3.90000000000000021e36

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 77.3%

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

   4. Taylor expanded in x around 0 69.9%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.25 \cdot 10^{+126} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+36}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.4 \cdot 10^{-28} \lor \neg \left(c \cdot i \leq 3.8 \cdot 10^{+63}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.4e-28) (not (<= (* c i) 3.8e+63))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.4e-28) || !((c * i) <= 3.8e+63)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-2.4d-28)) .or. (.not. ((c * i) <= 3.8d+63))) then
        tmp = c * i
    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 c, double i) {
	double tmp;
	if (((c * i) <= -2.4e-28) || !((c * i) <= 3.8e+63)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2.4e-28) or not ((c * i) <= 3.8e+63):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2.4e-28) || !(Float64(c * i) <= 3.8e+63))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -2.4e-28) || ~(((c * i) <= 3.8e+63)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.4e-28], N[Not[LessEqual[N[(c * i), $MachinePrecision], 3.8e+63]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.4000000000000002e-28 or 3.8000000000000001e63 < (*.f64 c i)

   1. Initial program 98.3%

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

   3. Taylor expanded in c around inf 60.7%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -2.4000000000000002e-28 < (*.f64 c i) < 3.8000000000000001e63

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 35.4%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.4 \cdot 10^{-28} \lor \neg \left(c \cdot i \leq 3.8 \cdot 10^{+63}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 17: 27.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in a around inf 21.9%

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

4. Final simplification 21.9%

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

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))