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

Percentage Accurate: 96.0% → 98.1%

Time: 11.3s

Alternatives: 13

Speedup: 0.4×

• 40.6% 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: 96.0% 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: 98.1% 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 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.7%

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

   3. associate-+l+ 97.7%

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

   4. fma-define 98.8%

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

   5. fma-define 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.7%

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

   3. +-commutative 97.7%

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

   4. fma-define 98.0%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ t_3 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -6.2 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -3 \cdot 10^{-194}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 1.22 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t)))
        (t_2 (+ (* a b) (* x y)))
        (t_3 (+ (* a b) (* z t))))
   (if (<= (* x y) -9e+101)
     t_2
     (if (<= (* x y) -6.2e-39)
       t_1
       (if (<= (* x y) -3e-194)
         t_3
         (if (<= (* x y) -4e-290)
           t_1
           (if (<= (* x y) 7.6e-39)
             t_3
             (if (<= (* x y) 1.22e+150) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double t_3 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -9e+101) {
		tmp = t_2;
	} else if ((x * y) <= -6.2e-39) {
		tmp = t_1;
	} else if ((x * y) <= -3e-194) {
		tmp = t_3;
	} else if ((x * y) <= -4e-290) {
		tmp = t_1;
	} else if ((x * y) <= 7.6e-39) {
		tmp = t_3;
	} else if ((x * y) <= 1.22e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    t_3 = (a * b) + (z * t)
    if ((x * y) <= (-9d+101)) then
        tmp = t_2
    else if ((x * y) <= (-6.2d-39)) then
        tmp = t_1
    else if ((x * y) <= (-3d-194)) then
        tmp = t_3
    else if ((x * y) <= (-4d-290)) then
        tmp = t_1
    else if ((x * y) <= 7.6d-39) then
        tmp = t_3
    else if ((x * y) <= 1.22d+150) then
        tmp = t_1
    else
        tmp = t_2
    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 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double t_3 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -9e+101) {
		tmp = t_2;
	} else if ((x * y) <= -6.2e-39) {
		tmp = t_1;
	} else if ((x * y) <= -3e-194) {
		tmp = t_3;
	} else if ((x * y) <= -4e-290) {
		tmp = t_1;
	} else if ((x * y) <= 7.6e-39) {
		tmp = t_3;
	} else if ((x * y) <= 1.22e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	t_3 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -9e+101:
		tmp = t_2
	elif (x * y) <= -6.2e-39:
		tmp = t_1
	elif (x * y) <= -3e-194:
		tmp = t_3
	elif (x * y) <= -4e-290:
		tmp = t_1
	elif (x * y) <= 7.6e-39:
		tmp = t_3
	elif (x * y) <= 1.22e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	t_3 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -9e+101)
		tmp = t_2;
	elseif (Float64(x * y) <= -6.2e-39)
		tmp = t_1;
	elseif (Float64(x * y) <= -3e-194)
		tmp = t_3;
	elseif (Float64(x * y) <= -4e-290)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.6e-39)
		tmp = t_3;
	elseif (Float64(x * y) <= 1.22e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	t_3 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -9e+101)
		tmp = t_2;
	elseif ((x * y) <= -6.2e-39)
		tmp = t_1;
	elseif ((x * y) <= -3e-194)
		tmp = t_3;
	elseif ((x * y) <= -4e-290)
		tmp = t_1;
	elseif ((x * y) <= 7.6e-39)
		tmp = t_3;
	elseif ((x * y) <= 1.22e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9e+101], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -6.2e-39], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3e-194], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -4e-290], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.6e-39], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1.22e+150], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.0000000000000004e101 or 1.22e150 < (*.f64 x y)

   1. Initial program 91.7%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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 79.9%

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

   if -9.0000000000000004e101 < (*.f64 x y) < -6.1999999999999994e-39 or -3e-194 < (*.f64 x y) < -4.0000000000000003e-290 or 7.6000000000000004e-39 < (*.f64 x y) < 1.22e150

   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 76.0%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -6.1999999999999994e-39 < (*.f64 x y) < -3e-194 or -4.0000000000000003e-290 < (*.f64 x y) < 7.6000000000000004e-39

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0 96.5%

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

   4. Taylor expanded in c around 0 79.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+101}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -6.2 \cdot 10^{-39}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3 \cdot 10^{-194}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-290}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-39}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.22 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ t_3 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -4.2 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.35 \cdot 10^{-244}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t)))
        (t_2 (+ (* a b) (* c i)))
        (t_3 (+ (* a b) (* x y))))
   (if (<= (* x y) -4.2e+103)
     t_3
     (if (<= (* x y) -4e-172)
       t_1
       (if (<= (* x y) -1.35e-244)
         t_2
         (if (<= (* x y) 6e+47) t_1 (if (<= (* x y) 4.2e+114) t_2 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) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -4.2e+103) {
		tmp = t_3;
	} else if ((x * y) <= -4e-172) {
		tmp = t_1;
	} else if ((x * y) <= -1.35e-244) {
		tmp = t_2;
	} else if ((x * y) <= 6e+47) {
		tmp = t_1;
	} else if ((x * y) <= 4.2e+114) {
		tmp = t_2;
	} 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) + (z * t)
    t_2 = (a * b) + (c * i)
    t_3 = (a * b) + (x * y)
    if ((x * y) <= (-4.2d+103)) then
        tmp = t_3
    else if ((x * y) <= (-4d-172)) then
        tmp = t_1
    else if ((x * y) <= (-1.35d-244)) then
        tmp = t_2
    else if ((x * y) <= 6d+47) then
        tmp = t_1
    else if ((x * y) <= 4.2d+114) then
        tmp = t_2
    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) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -4.2e+103) {
		tmp = t_3;
	} else if ((x * y) <= -4e-172) {
		tmp = t_1;
	} else if ((x * y) <= -1.35e-244) {
		tmp = t_2;
	} else if ((x * y) <= 6e+47) {
		tmp = t_1;
	} else if ((x * y) <= 4.2e+114) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (c * i)
	t_3 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -4.2e+103:
		tmp = t_3
	elif (x * y) <= -4e-172:
		tmp = t_1
	elif (x * y) <= -1.35e-244:
		tmp = t_2
	elif (x * y) <= 6e+47:
		tmp = t_1
	elif (x * y) <= 4.2e+114:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	t_3 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -4.2e+103)
		tmp = t_3;
	elseif (Float64(x * y) <= -4e-172)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.35e-244)
		tmp = t_2;
	elseif (Float64(x * y) <= 6e+47)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.2e+114)
		tmp = t_2;
	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) + (z * t);
	t_2 = (a * b) + (c * i);
	t_3 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -4.2e+103)
		tmp = t_3;
	elseif ((x * y) <= -4e-172)
		tmp = t_1;
	elseif ((x * y) <= -1.35e-244)
		tmp = t_2;
	elseif ((x * y) <= 6e+47)
		tmp = t_1;
	elseif ((x * y) <= 4.2e+114)
		tmp = t_2;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.2e+103], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -4e-172], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.35e-244], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 6e+47], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.2e+114], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.2000000000000003e103 or 4.2000000000000001e114 < (*.f64 x y)

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 85.5%

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

   4. Taylor expanded in c around 0 79.1%

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

   if -4.2000000000000003e103 < (*.f64 x y) < -4.0000000000000002e-172 or -1.35e-244 < (*.f64 x y) < 6.0000000000000003e47

   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 x around 0 94.6%

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

   4. Taylor expanded in c around 0 72.5%

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

   if -4.0000000000000002e-172 < (*.f64 x y) < -1.35e-244 or 6.0000000000000003e47 < (*.f64 x y) < 4.2000000000000001e114

   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 a around inf 78.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.2 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-172}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.35 \cdot 10^{-244}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4.3 \cdot 10^{-194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -4.3 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* x y) -9.5e+101)
     (+ (* a b) (* x y))
     (if (<= (* x y) -9.5e-39)
       t_1
       (if (<= (* x y) -4.3e-194)
         t_2
         (if (<= (* x y) -4.3e-290)
           t_1
           (if (<= (* x y) 7.5e+49) t_2 (+ (* x y) (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -9.5e+101) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= -9.5e-39) {
		tmp = t_1;
	} else if ((x * y) <= -4.3e-194) {
		tmp = t_2;
	} else if ((x * y) <= -4.3e-290) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+49) {
		tmp = t_2;
	} else {
		tmp = (x * y) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (z * t)
    if ((x * y) <= (-9.5d+101)) then
        tmp = (a * b) + (x * y)
    else if ((x * y) <= (-9.5d-39)) then
        tmp = t_1
    else if ((x * y) <= (-4.3d-194)) then
        tmp = t_2
    else if ((x * y) <= (-4.3d-290)) then
        tmp = t_1
    else if ((x * y) <= 7.5d+49) then
        tmp = t_2
    else
        tmp = (x * y) + (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 t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -9.5e+101) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= -9.5e-39) {
		tmp = t_1;
	} else if ((x * y) <= -4.3e-194) {
		tmp = t_2;
	} else if ((x * y) <= -4.3e-290) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+49) {
		tmp = t_2;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -9.5e+101:
		tmp = (a * b) + (x * y)
	elif (x * y) <= -9.5e-39:
		tmp = t_1
	elif (x * y) <= -4.3e-194:
		tmp = t_2
	elif (x * y) <= -4.3e-290:
		tmp = t_1
	elif (x * y) <= 7.5e+49:
		tmp = t_2
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -9.5e+101)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(x * y) <= -9.5e-39)
		tmp = t_1;
	elseif (Float64(x * y) <= -4.3e-194)
		tmp = t_2;
	elseif (Float64(x * y) <= -4.3e-290)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.5e+49)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -9.5e+101)
		tmp = (a * b) + (x * y);
	elseif ((x * y) <= -9.5e-39)
		tmp = t_1;
	elseif ((x * y) <= -4.3e-194)
		tmp = t_2;
	elseif ((x * y) <= -4.3e-290)
		tmp = t_1;
	elseif ((x * y) <= 7.5e+49)
		tmp = t_2;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9.5e+101], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -9.5e-39], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4.3e-194], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -4.3e-290], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+49], t$95$2, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.49999999999999947e101

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0 84.7%

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

   4. Taylor expanded in c around 0 80.5%

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

   if -9.49999999999999947e101 < (*.f64 x y) < -9.4999999999999999e-39 or -4.30000000000000006e-194 < (*.f64 x y) < -4.3000000000000002e-290

   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 76.5%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -9.4999999999999999e-39 < (*.f64 x y) < -4.30000000000000006e-194 or -4.3000000000000002e-290 < (*.f64 x y) < 7.4999999999999995e49

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 96.3%

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

   4. Taylor expanded in c around 0 77.5%

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

   if 7.4999999999999995e49 < (*.f64 x y)

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 82.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.3 \cdot 10^{-194}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.3 \cdot 10^{-290}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (* a b) (+ (* x y) (* z t))) (* c i))))
   (if (<= t_1 INFINITY) 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) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

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) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		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) + ((x * y) + (z * t))) + (c * i)
	tmp = 0
	if t_1 <= math.inf:
		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(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t))) + Float64(c * i))
	tmp = 0.0
	if (t_1 <= Inf)
		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) + ((x * y) + (z * t))) + (c * i);
	tmp = 0.0;
	if (t_1 <= Inf)
		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[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 33.3%

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

   4. Taylor expanded in c around 0 66.7%

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

4. Final simplification 98.8%

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

Alternative 7: 42.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+20}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.2e+84)
   (* a b)
   (if (<= (* a b) -7.5e-50)
     (* c i)
     (if (<= (* a b) 5.4e+20)
       (* z t)
       (if (<= (* a b) 1.5e+183) (* 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 ((a * b) <= -4.2e+84) {
		tmp = a * b;
	} else if ((a * b) <= -7.5e-50) {
		tmp = c * i;
	} else if ((a * b) <= 5.4e+20) {
		tmp = z * t;
	} else if ((a * b) <= 1.5e+183) {
		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 ((a * b) <= (-4.2d+84)) then
        tmp = a * b
    else if ((a * b) <= (-7.5d-50)) then
        tmp = c * i
    else if ((a * b) <= 5.4d+20) then
        tmp = z * t
    else if ((a * b) <= 1.5d+183) 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 ((a * b) <= -4.2e+84) {
		tmp = a * b;
	} else if ((a * b) <= -7.5e-50) {
		tmp = c * i;
	} else if ((a * b) <= 5.4e+20) {
		tmp = z * t;
	} else if ((a * b) <= 1.5e+183) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4.2e+84:
		tmp = a * b
	elif (a * b) <= -7.5e-50:
		tmp = c * i
	elif (a * b) <= 5.4e+20:
		tmp = z * t
	elif (a * b) <= 1.5e+183:
		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(a * b) <= -4.2e+84)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -7.5e-50)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 5.4e+20)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.5e+183)
		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 ((a * b) <= -4.2e+84)
		tmp = a * b;
	elseif ((a * b) <= -7.5e-50)
		tmp = c * i;
	elseif ((a * b) <= 5.4e+20)
		tmp = z * t;
	elseif ((a * b) <= 1.5e+183)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -4.2e+84], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -7.5e-50], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.4e+20], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.5e+183], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.20000000000000037e84 or 1.49999999999999998e183 < (*.f64 a b)

   1. Initial program 91.8%

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

   3. Taylor expanded in i around inf 73.3%

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

   4. Taylor expanded in a around inf 73.1%

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

   if -4.20000000000000037e84 < (*.f64 a b) < -7.5e-50 or 5.4e20 < (*.f64 a b) < 1.49999999999999998e183

   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 47.7%

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

   if -7.5e-50 < (*.f64 a b) < 5.4e20

   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 i around inf 86.6%

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

   4. Taylor expanded in t around inf 45.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+20}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.5 \cdot 10^{+183}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+103} \lor \neg \left(x \cdot y \leq 5.6 \cdot 10^{+44}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5.2e+103) (not (<= (* x y) 5.6e+44)))
   (+ (* 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 (((x * y) <= -5.2e+103) || !((x * y) <= 5.6e+44)) {
		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 (((x * y) <= (-5.2d+103)) .or. (.not. ((x * y) <= 5.6d+44))) 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 (((x * y) <= -5.2e+103) || !((x * y) <= 5.6e+44)) {
		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 ((x * y) <= -5.2e+103) or not ((x * y) <= 5.6e+44):
		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(x * y) <= -5.2e+103) || !(Float64(x * y) <= 5.6e+44))
		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 (((x * y) <= -5.2e+103) || ~(((x * y) <= 5.6e+44)))
		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[Or[LessEqual[N[(x * y), $MachinePrecision], -5.2e+103], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.6e+44]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 x y) < -5.2000000000000003e103 or 5.6000000000000002e44 < (*.f64 x y)

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 86.9%

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

   if -5.2000000000000003e103 < (*.f64 x y) < 5.6000000000000002e44

   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 x around 0 95.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+103} \lor \neg \left(x \cdot y \leq 5.6 \cdot 10^{+44}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.8 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+65}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5.8e+103)
   (+ (* a b) (* x y))
   (if (<= (* x y) 6e+65)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* x y) (* 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) <= -5.8e+103) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 6e+65) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (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) <= (-5.8d+103)) then
        tmp = (a * b) + (x * y)
    else if ((x * y) <= 6d+65) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (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) <= -5.8e+103) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 6e+65) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5.8e+103:
		tmp = (a * b) + (x * y)
	elif (x * y) <= 6e+65:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5.8e+103)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(x * y) <= 6e+65)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + 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) <= -5.8e+103)
		tmp = (a * b) + (x * y);
	elseif ((x * y) <= 6e+65)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.8e+103], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e+65], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.7999999999999997e103

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0 84.7%

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

   4. Taylor expanded in c around 0 80.5%

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

   if -5.7999999999999997e103 < (*.f64 x y) < 6.0000000000000004e65

   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 x around 0 94.7%

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

   if 6.0000000000000004e65 < (*.f64 x y)

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 83.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.8 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+65}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+93} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -2e+93) (not (<= (* z t) 2e+123)))
   (* 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) {
	double tmp;
	if (((z * t) <= -2e+93) || !((z * t) <= 2e+123)) {
		tmp = z * t;
	} 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 (((z * t) <= (-2d+93)) .or. (.not. ((z * t) <= 2d+123))) then
        tmp = z * t
    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 (((z * t) <= -2e+93) || !((z * t) <= 2e+123)) {
		tmp = z * t;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -2e+93) or not ((z * t) <= 2e+123):
		tmp = z * t
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+93) || !(Float64(z * t) <= 2e+123))
		tmp = Float64(z * t);
	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 (((z * t) <= -2e+93) || ~(((z * t) <= 2e+123)))
		tmp = z * t;
	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[(z * t), $MachinePrecision], -2e+93], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+123]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000009e93 or 1.99999999999999996e123 < (*.f64 z t)

   1. Initial program 92.8%

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

   3. Taylor expanded in i around inf 71.2%

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

   4. Taylor expanded in t around inf 75.7%

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

   if -2.00000000000000009e93 < (*.f64 z t) < 1.99999999999999996e123

   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 65.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+93} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+123}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+93} \lor \neg \left(z \cdot t \leq 10^{+113}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -2e+93) (not (<= (* z t) 1e+113)))
   (+ (* a b) (* 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) {
	double tmp;
	if (((z * t) <= -2e+93) || !((z * t) <= 1e+113)) {
		tmp = (a * b) + (z * t);
	} 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 (((z * t) <= (-2d+93)) .or. (.not. ((z * t) <= 1d+113))) then
        tmp = (a * b) + (z * t)
    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 (((z * t) <= -2e+93) || !((z * t) <= 1e+113)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -2e+93) or not ((z * t) <= 1e+113):
		tmp = (a * b) + (z * t)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+93) || !(Float64(z * t) <= 1e+113))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	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 (((z * t) <= -2e+93) || ~(((z * t) <= 1e+113)))
		tmp = (a * b) + (z * t);
	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[(z * t), $MachinePrecision], -2e+93], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+113]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000009e93 or 1e113 < (*.f64 z t)

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 86.2%

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

   4. Taylor expanded in c around 0 81.8%

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

   if -2.00000000000000009e93 < (*.f64 z t) < 1e113

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 65.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+93} \lor \neg \left(z \cdot t \leq 10^{+113}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+110} \lor \neg \left(c \leq 5 \cdot 10^{-152}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.4e+110) (not (<= c 5e-152))) (* 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 <= -2.4e+110) || !(c <= 5e-152)) {
		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 <= (-2.4d+110)) .or. (.not. (c <= 5d-152))) 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 <= -2.4e+110) || !(c <= 5e-152)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.4e+110) or not (c <= 5e-152):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.4e+110) || !(c <= 5e-152))
		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 <= -2.4e+110) || ~((c <= 5e-152)))
		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[c, -2.4e+110], N[Not[LessEqual[c, 5e-152]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.40000000000000012e110 or 4.9999999999999997e-152 < c

   1. Initial program 95.1%

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

   3. Taylor expanded in c around inf 36.7%

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

   if -2.40000000000000012e110 < c < 4.9999999999999997e-152

   1. Initial program 98.2%

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

   3. Taylor expanded in i around inf 82.7%

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

   4. Taylor expanded in a around inf 37.2%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+110} \lor \neg \left(c \leq 5 \cdot 10^{-152}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.4% 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 96.5%

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

3. Taylor expanded in i around inf 83.4%

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

4. Taylor expanded in a around inf 28.5%

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

5. Final simplification 28.5%

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

Reproduce

herbie shell --seed 2024067 
(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)))