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

Percentage Accurate: 95.8% → 97.9%

Time: 12.0s

Alternatives: 15

Speedup: 0.4×

• 41.6% 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: 95.8% 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 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 98.0%

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

   3. associate-+l+ 98.0%

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

   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 99.2%

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

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: 97.7% 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 98.0%

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

   3. +-commutative 98.0%

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

   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: 43.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+181}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-154}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -8.5e+181)
   (* x y)
   (if (<= (* x y) -5.6e-34)
     (* c i)
     (if (<= (* x y) -1.05e-55)
       (* z t)
       (if (<= (* x y) -2.8e-85)
         (* c i)
         (if (<= (* x y) -1.9e-154)
           (* a b)
           (if (<= (* x y) -3.5e-241)
             (* z t)
             (if (<= (* x y) 5.5e+128) (* 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 ((x * y) <= -8.5e+181) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e-34) {
		tmp = c * i;
	} else if ((x * y) <= -1.05e-55) {
		tmp = z * t;
	} else if ((x * y) <= -2.8e-85) {
		tmp = c * i;
	} else if ((x * y) <= -1.9e-154) {
		tmp = a * b;
	} else if ((x * y) <= -3.5e-241) {
		tmp = z * t;
	} else if ((x * y) <= 5.5e+128) {
		tmp = a * b;
	} 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) <= (-8.5d+181)) then
        tmp = x * y
    else if ((x * y) <= (-5.6d-34)) then
        tmp = c * i
    else if ((x * y) <= (-1.05d-55)) then
        tmp = z * t
    else if ((x * y) <= (-2.8d-85)) then
        tmp = c * i
    else if ((x * y) <= (-1.9d-154)) then
        tmp = a * b
    else if ((x * y) <= (-3.5d-241)) then
        tmp = z * t
    else if ((x * y) <= 5.5d+128) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -8.5e+181) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e-34) {
		tmp = c * i;
	} else if ((x * y) <= -1.05e-55) {
		tmp = z * t;
	} else if ((x * y) <= -2.8e-85) {
		tmp = c * i;
	} else if ((x * y) <= -1.9e-154) {
		tmp = a * b;
	} else if ((x * y) <= -3.5e-241) {
		tmp = z * t;
	} else if ((x * y) <= 5.5e+128) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -8.5e+181:
		tmp = x * y
	elif (x * y) <= -5.6e-34:
		tmp = c * i
	elif (x * y) <= -1.05e-55:
		tmp = z * t
	elif (x * y) <= -2.8e-85:
		tmp = c * i
	elif (x * y) <= -1.9e-154:
		tmp = a * b
	elif (x * y) <= -3.5e-241:
		tmp = z * t
	elif (x * y) <= 5.5e+128:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -8.5e+181)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.6e-34)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= -1.05e-55)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -2.8e-85)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= -1.9e-154)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -3.5e-241)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 5.5e+128)
		tmp = Float64(a * b);
	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) <= -8.5e+181)
		tmp = x * y;
	elseif ((x * y) <= -5.6e-34)
		tmp = c * i;
	elseif ((x * y) <= -1.05e-55)
		tmp = z * t;
	elseif ((x * y) <= -2.8e-85)
		tmp = c * i;
	elseif ((x * y) <= -1.9e-154)
		tmp = a * b;
	elseif ((x * y) <= -3.5e-241)
		tmp = z * t;
	elseif ((x * y) <= 5.5e+128)
		tmp = a * b;
	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], -8.5e+181], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.6e-34], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.05e-55], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.8e-85], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.9e-154], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.5e-241], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.5e+128], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -8.49999999999999966e181 or 5.4999999999999998e128 < (*.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 76.6%

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

   if -8.49999999999999966e181 < (*.f64 x y) < -5.59999999999999994e-34 or -1.0500000000000001e-55 < (*.f64 x y) < -2.80000000000000017e-85

   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 44.9%

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

   if -5.59999999999999994e-34 < (*.f64 x y) < -1.0500000000000001e-55 or -1.90000000000000005e-154 < (*.f64 x y) < -3.4999999999999999e-241

   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 73.4%

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

   if -2.80000000000000017e-85 < (*.f64 x y) < -1.90000000000000005e-154 or -3.4999999999999999e-241 < (*.f64 x y) < 5.4999999999999998e128

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+181}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-154}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.15e+182)
     (* x y)
     (if (<= (* x y) -3.5e-36)
       t_1
       (if (<= (* x y) -1.9e-55)
         (* z t)
         (if (<= (* x y) -1.05e-170)
           t_1
           (if (<= (* x y) -5e-241)
             (* z t)
             (if (<= (* x y) 6.5e+140) t_1 (* x y)))))))))

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 ((x * y) <= -1.15e+182) {
		tmp = x * y;
	} else if ((x * y) <= -3.5e-36) {
		tmp = t_1;
	} else if ((x * y) <= -1.9e-55) {
		tmp = z * t;
	} else if ((x * y) <= -1.05e-170) {
		tmp = t_1;
	} else if ((x * y) <= -5e-241) {
		tmp = z * t;
	} else if ((x * y) <= 6.5e+140) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-1.15d+182)) then
        tmp = x * y
    else if ((x * y) <= (-3.5d-36)) then
        tmp = t_1
    else if ((x * y) <= (-1.9d-55)) then
        tmp = z * t
    else if ((x * y) <= (-1.05d-170)) then
        tmp = t_1
    else if ((x * y) <= (-5d-241)) then
        tmp = z * t
    else if ((x * y) <= 6.5d+140) then
        tmp = t_1
    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 t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.15e+182) {
		tmp = x * y;
	} else if ((x * y) <= -3.5e-36) {
		tmp = t_1;
	} else if ((x * y) <= -1.9e-55) {
		tmp = z * t;
	} else if ((x * y) <= -1.05e-170) {
		tmp = t_1;
	} else if ((x * y) <= -5e-241) {
		tmp = z * t;
	} else if ((x * y) <= 6.5e+140) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -1.15e+182:
		tmp = x * y
	elif (x * y) <= -3.5e-36:
		tmp = t_1
	elif (x * y) <= -1.9e-55:
		tmp = z * t
	elif (x * y) <= -1.05e-170:
		tmp = t_1
	elif (x * y) <= -5e-241:
		tmp = z * t
	elif (x * y) <= 6.5e+140:
		tmp = t_1
	else:
		tmp = x * y
	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(x * y) <= -1.15e+182)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.5e-36)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.9e-55)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -1.05e-170)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e-241)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 6.5e+140)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	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 ((x * y) <= -1.15e+182)
		tmp = x * y;
	elseif ((x * y) <= -3.5e-36)
		tmp = t_1;
	elseif ((x * y) <= -1.9e-55)
		tmp = z * t;
	elseif ((x * y) <= -1.05e-170)
		tmp = t_1;
	elseif ((x * y) <= -5e-241)
		tmp = z * t;
	elseif ((x * y) <= 6.5e+140)
		tmp = t_1;
	else
		tmp = x * y;
	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[(x * y), $MachinePrecision], -1.15e+182], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.5e-36], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.9e-55], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.05e-170], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e-241], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.5e+140], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.15e182 or 6.4999999999999999e140 < (*.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 76.6%

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

   if -1.15e182 < (*.f64 x y) < -3.5e-36 or -1.8999999999999998e-55 < (*.f64 x y) < -1.05e-170 or -4.9999999999999998e-241 < (*.f64 x y) < 6.4999999999999999e140

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. associate-/l* 81.0%

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

      2. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in a around inf 65.9%

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

   if -3.5e-36 < (*.f64 x y) < -1.8999999999999998e-55 or -1.05e-170 < (*.f64 x y) < -4.9999999999999998e-241

   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 88.4%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.5 \cdot 10^{-36}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{-170}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 200000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* x y) -8.5e+182)
     t_1
     (if (<= (* x y) -2.45e-85)
       (+ (* c i) (* z t))
       (if (<= (* x y) 1.4e-176)
         t_2
         (if (<= (* x y) 1.7e-114)
           (+ (* a b) (* c i))
           (if (<= (* x y) 200000.0) t_2 t_1)))))))

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);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -8.5e+182) {
		tmp = t_1;
	} else if ((x * y) <= -2.45e-85) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1.4e-176) {
		tmp = t_2;
	} else if ((x * y) <= 1.7e-114) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 200000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 = (a * b) + (x * y)
    t_2 = (a * b) + (z * t)
    if ((x * y) <= (-8.5d+182)) then
        tmp = t_1
    else if ((x * y) <= (-2.45d-85)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 1.4d-176) then
        tmp = t_2
    else if ((x * y) <= 1.7d-114) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 200000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -8.5e+182) {
		tmp = t_1;
	} else if ((x * y) <= -2.45e-85) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1.4e-176) {
		tmp = t_2;
	} else if ((x * y) <= 1.7e-114) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 200000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -8.5e+182:
		tmp = t_1
	elif (x * y) <= -2.45e-85:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 1.4e-176:
		tmp = t_2
	elif (x * y) <= 1.7e-114:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 200000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -8.5e+182)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.45e-85)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 1.4e-176)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.7e-114)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 200000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -8.5e+182)
		tmp = t_1;
	elseif ((x * y) <= -2.45e-85)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 1.4e-176)
		tmp = t_2;
	elseif ((x * y) <= 1.7e-114)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 200000.0)
		tmp = t_2;
	else
		tmp = t_1;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.5e+182], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.45e-85], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.4e-176], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.7e-114], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 200000.0], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -8.5e182 or 2e5 < (*.f64 x y)

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 86.8%

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

   4. Taylor expanded in c around 0 78.0%

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

   if -8.5e182 < (*.f64 x y) < -2.45000000000000007e-85

   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 y around inf 96.6%

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

      1. associate-/l* 96.6%

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

      2. associate-/l* 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in t around inf 71.2%

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

   if -2.45000000000000007e-85 < (*.f64 x y) < 1.4000000000000001e-176 or 1.69999999999999991e-114 < (*.f64 x y) < 2e5

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 92.8%

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

   4. Taylor expanded in c around 0 74.2%

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

   if 1.4000000000000001e-176 < (*.f64 x y) < 1.69999999999999991e-114

   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 y around inf 89.1%

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

      1. associate-/l* 78.0%

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

      2. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in a around inf 100.0%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+182}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.45 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 200000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-115}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 200:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* x y) -5e+185)
     (* y (+ x (/ (* a b) y)))
     (if (<= (* x y) -5e-85)
       (+ (* c i) (* z t))
       (if (<= (* x y) 1e-176)
         t_1
         (if (<= (* x y) 4e-115)
           (+ (* a b) (* c i))
           (if (<= (* x y) 200.0) t_1 (+ (* a b) (* x y)))))))))

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 tmp;
	if ((x * y) <= -5e+185) {
		tmp = y * (x + ((a * b) / y));
	} else if ((x * y) <= -5e-85) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1e-176) {
		tmp = t_1;
	} else if ((x * y) <= 4e-115) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 200.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((x * y) <= (-5d+185)) then
        tmp = y * (x + ((a * b) / y))
    else if ((x * y) <= (-5d-85)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 1d-176) then
        tmp = t_1
    else if ((x * y) <= 4d-115) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 200.0d0) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -5e+185) {
		tmp = y * (x + ((a * b) / y));
	} else if ((x * y) <= -5e-85) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1e-176) {
		tmp = t_1;
	} else if ((x * y) <= 4e-115) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 200.0) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -5e+185:
		tmp = y * (x + ((a * b) / y))
	elif (x * y) <= -5e-85:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 1e-176:
		tmp = t_1
	elif (x * y) <= 4e-115:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 200.0:
		tmp = t_1
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -5e+185)
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	elseif (Float64(x * y) <= -5e-85)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 1e-176)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-115)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 200.0)
		tmp = t_1;
	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)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -5e+185)
		tmp = y * (x + ((a * b) / y));
	elseif ((x * y) <= -5e-85)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 1e-176)
		tmp = t_1;
	elseif ((x * y) <= 4e-115)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 200.0)
		tmp = t_1;
	else
		tmp = (a * b) + (x * y);
	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]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+185], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-85], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-176], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-115], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 200.0], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.9999999999999999e185

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 79.5%

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

   4. Taylor expanded in c around 0 83.7%

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

   5. Taylor expanded in y around inf 84.0%

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

   if -4.9999999999999999e185 < (*.f64 x y) < -5.0000000000000002e-85

   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 y around inf 96.6%

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

      1. associate-/l* 96.6%

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

      2. associate-/l* 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in t around inf 71.2%

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

   if -5.0000000000000002e-85 < (*.f64 x y) < 1e-176 or 4.0000000000000002e-115 < (*.f64 x y) < 200

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 92.8%

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

   4. Taylor expanded in c around 0 74.2%

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

   if 1e-176 < (*.f64 x y) < 4.0000000000000002e-115

   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 y around inf 89.1%

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

      1. associate-/l* 78.0%

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

      2. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in a around inf 100.0%

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

   if 200 < (*.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 89.3%

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

   4. Taylor expanded in c around 0 76.1%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 10^{-176}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-115}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 200:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2100000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* x y) -9e+52)
     t_2
     (if (<= (* x y) 5.8e-173)
       t_1
       (if (<= (* x y) 2.7e-114)
         (+ (* a b) (* c i))
         (if (<= (* x y) 2100000.0) 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 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -9e+52) {
		tmp = t_2;
	} else if ((x * y) <= 5.8e-173) {
		tmp = t_1;
	} else if ((x * y) <= 2.7e-114) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2100000.0) {
		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) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((x * y) <= (-9d+52)) then
        tmp = t_2
    else if ((x * y) <= 5.8d-173) then
        tmp = t_1
    else if ((x * y) <= 2.7d-114) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 2100000.0d0) 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 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -9e+52) {
		tmp = t_2;
	} else if ((x * y) <= 5.8e-173) {
		tmp = t_1;
	} else if ((x * y) <= 2.7e-114) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2100000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -9e+52:
		tmp = t_2
	elif (x * y) <= 5.8e-173:
		tmp = t_1
	elif (x * y) <= 2.7e-114:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 2100000.0:
		tmp = t_1
	else:
		tmp = t_2
	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(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -9e+52)
		tmp = t_2;
	elseif (Float64(x * y) <= 5.8e-173)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.7e-114)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 2100000.0)
		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 = (a * b) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -9e+52)
		tmp = t_2;
	elseif ((x * y) <= 5.8e-173)
		tmp = t_1;
	elseif ((x * y) <= 2.7e-114)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 2100000.0)
		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[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9e+52], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5.8e-173], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.7e-114], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2100000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.9999999999999999e52 or 2.1e6 < (*.f64 x y)

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 86.9%

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

   4. Taylor expanded in c around 0 73.3%

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

   if -8.9999999999999999e52 < (*.f64 x y) < 5.7999999999999997e-173 or 2.7e-114 < (*.f64 x y) < 2.1e6

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 94.2%

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

   4. Taylor expanded in c around 0 72.0%

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

   if 5.7999999999999997e-173 < (*.f64 x y) < 2.7e-114

   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 y around inf 89.1%

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

      1. associate-/l* 78.0%

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

      2. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in a around inf 100.0%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9 \cdot 10^{+52}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{-173}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{-114}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2100000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.4× speedup

Math

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

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 (* z (+ t (/ (* a b) z))))))

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 = z * (t + ((a * b) / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double 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 = z * (t + ((a * b) / z));
	}
	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 = z * (t + ((a * b) / z))
	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(z * Float64(t + Float64(Float64(a * b) / z)));
	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 = z * (t + ((a * b) / z));
	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[(z * N[(t + N[(N[(a * b), $MachinePrecision] / z), $MachinePrecision]), $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 z around inf 44.4%

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

   5. Taylor expanded in c around 0 67.1%

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

4. Final simplification 98.8%

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

Alternative 9: 42.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6 \cdot 10^{+152}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 6.6 \cdot 10^{-224}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6e+152)
   (* c i)
   (if (<= (* c i) -5.8e+29)
     (* z t)
     (if (<= (* c i) 6.6e-224)
       (* a b)
       (if (<= (* c i) 2.4e+97) (* z t) (* 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) <= -6e+152) {
		tmp = c * i;
	} else if ((c * i) <= -5.8e+29) {
		tmp = z * t;
	} else if ((c * i) <= 6.6e-224) {
		tmp = a * b;
	} else if ((c * i) <= 2.4e+97) {
		tmp = z * t;
	} 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) <= (-6d+152)) then
        tmp = c * i
    else if ((c * i) <= (-5.8d+29)) then
        tmp = z * t
    else if ((c * i) <= 6.6d-224) then
        tmp = a * b
    else if ((c * i) <= 2.4d+97) then
        tmp = z * t
    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) <= -6e+152) {
		tmp = c * i;
	} else if ((c * i) <= -5.8e+29) {
		tmp = z * t;
	} else if ((c * i) <= 6.6e-224) {
		tmp = a * b;
	} else if ((c * i) <= 2.4e+97) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -6e+152:
		tmp = c * i
	elif (c * i) <= -5.8e+29:
		tmp = z * t
	elif (c * i) <= 6.6e-224:
		tmp = a * b
	elif (c * i) <= 2.4e+97:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -6e+152)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -5.8e+29)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 6.6e-224)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.4e+97)
		tmp = Float64(z * t);
	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) <= -6e+152)
		tmp = c * i;
	elseif ((c * i) <= -5.8e+29)
		tmp = z * t;
	elseif ((c * i) <= 6.6e-224)
		tmp = a * b;
	elseif ((c * i) <= 2.4e+97)
		tmp = z * t;
	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], -6e+152], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5.8e+29], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.6e-224], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.4e+97], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.99999999999999981e152 or 2.4e97 < (*.f64 c i)

   1. Initial program 90.0%

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

   3. Taylor expanded in c around inf 67.0%

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

   if -5.99999999999999981e152 < (*.f64 c i) < -5.7999999999999999e29 or 6.6000000000000003e-224 < (*.f64 c i) < 2.4e97

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 39.9%

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

   if -5.7999999999999999e29 < (*.f64 c i) < 6.6000000000000003e-224

   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 46.3%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6 \cdot 10^{+152}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 6.6 \cdot 10^{-224}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 200\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5e+62) (not (<= (* x y) 200.0)))
   (+ (* 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) <= -5e+62) || !((x * y) <= 200.0)) {
		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) <= (-5d+62)) .or. (.not. ((x * y) <= 200.0d0))) 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) <= -5e+62) || !((x * y) <= 200.0)) {
		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) <= -5e+62) or not ((x * y) <= 200.0):
		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) <= -5e+62) || !(Float64(x * y) <= 200.0))
		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) <= -5e+62) || ~(((x * y) <= 200.0)))
		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], -5e+62], N[Not[LessEqual[N[(x * y), $MachinePrecision], 200.0]], $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) < -5.00000000000000029e62 or 200 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 86.8%

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

   if -5.00000000000000029e62 < (*.f64 x y) < 200

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 94.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+62} \lor \neg \left(x \cdot y \leq 200\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+185)
   (* y (+ x (/ (* a b) y)))
   (if (<= (* x y) 2e+121)
     (+ (* c i) (+ (* a b) (* 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 ((x * y) <= -5e+185) {
		tmp = y * (x + ((a * b) / y));
	} else if ((x * y) <= 2e+121) {
		tmp = (c * i) + ((a * b) + (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 ((x * y) <= (-5d+185)) then
        tmp = y * (x + ((a * b) / y))
    else if ((x * y) <= 2d+121) then
        tmp = (c * i) + ((a * b) + (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 ((x * y) <= -5e+185) {
		tmp = y * (x + ((a * b) / y));
	} else if ((x * y) <= 2e+121) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+185:
		tmp = y * (x + ((a * b) / y))
	elif (x * y) <= 2e+121:
		tmp = (c * i) + ((a * b) + (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(x * y) <= -5e+185)
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	elseif (Float64(x * y) <= 2e+121)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + 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 ((x * y) <= -5e+185)
		tmp = y * (x + ((a * b) / y));
	elseif ((x * y) <= 2e+121)
		tmp = (c * i) + ((a * b) + (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[(x * y), $MachinePrecision], -5e+185], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+121], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $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 x y) < -4.9999999999999999e185

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 79.5%

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

   4. Taylor expanded in c around 0 83.7%

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

   5. Taylor expanded in y around inf 84.0%

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

   if -4.9999999999999999e185 < (*.f64 x y) < 2.00000000000000007e121

   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 90.4%

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

   if 2.00000000000000007e121 < (*.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 93.8%

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

   4. Taylor expanded in c around 0 85.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+62}:\\ \;\;\;\;c \cdot i + y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 200:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5e+62)
   (+ (* c i) (* y (+ x (/ (* a b) y))))
   (if (<= (* x y) 200.0)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* 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 ((x * y) <= -5e+62) {
		tmp = (c * i) + (y * (x + ((a * b) / y)));
	} else if ((x * y) <= 200.0) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((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 ((x * y) <= (-5d+62)) then
        tmp = (c * i) + (y * (x + ((a * b) / y)))
    else if ((x * y) <= 200.0d0) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((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 ((x * y) <= -5e+62) {
		tmp = (c * i) + (y * (x + ((a * b) / y)));
	} else if ((x * y) <= 200.0) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5e+62:
		tmp = (c * i) + (y * (x + ((a * b) / y)))
	elif (x * y) <= 200.0:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5e+62)
		tmp = Float64(Float64(c * i) + Float64(y * Float64(x + Float64(Float64(a * b) / y))));
	elseif (Float64(x * y) <= 200.0)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + 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 ((x * y) <= -5e+62)
		tmp = (c * i) + (y * (x + ((a * b) / y)));
	elseif ((x * y) <= 200.0)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+62], N[(N[(c * i), $MachinePrecision] + N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 200.0], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000029e62

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 95.1%

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

      1. associate-/l* 95.1%

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

      2. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in t around 0 82.5%

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

   if -5.00000000000000029e62 < (*.f64 x y) < 200

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 94.6%

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

   if 200 < (*.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 89.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+62}:\\ \;\;\;\;c \cdot i + y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;x \cdot y \leq 200:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.4 \cdot 10^{+153} \lor \neg \left(c \cdot i \leq 1.2 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.4e+153) (not (<= (* c i) 1.2e+95)))
   (+ (* a b) (* 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 (((c * i) <= -1.4e+153) || !((c * i) <= 1.2e+95)) {
		tmp = (a * b) + (c * i);
	} 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) :: tmp
    if (((c * i) <= (-1.4d+153)) .or. (.not. ((c * i) <= 1.2d+95))) then
        tmp = (a * b) + (c * i)
    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 tmp;
	if (((c * i) <= -1.4e+153) || !((c * i) <= 1.2e+95)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.4e+153) or not ((c * i) <= 1.2e+95):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.4e+153) || !(Float64(c * i) <= 1.2e+95))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	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)
	tmp = 0.0;
	if (((c * i) <= -1.4e+153) || ~(((c * i) <= 1.2e+95)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.4e+153], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.2e+95]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.39999999999999993e153 or 1.2e95 < (*.f64 c i)

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 82.9%

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

      1. associate-/l* 80.4%

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

      2. associate-/l* 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in a around inf 75.6%

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

   if -1.39999999999999993e153 < (*.f64 c i) < 1.2e95

   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 x around 0 69.8%

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

   4. Taylor expanded in c around 0 65.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.4 \cdot 10^{+153} \lor \neg \left(c \cdot i \leq 1.2 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+39} \lor \neg \left(c \cdot i \leq 1.58 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1e+39) (not (<= (* c i) 1.58e+118))) (* 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) <= -1e+39) || !((c * i) <= 1.58e+118)) {
		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) <= (-1d+39)) .or. (.not. ((c * i) <= 1.58d+118))) 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) <= -1e+39) || !((c * i) <= 1.58e+118)) {
		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) <= -1e+39) or not ((c * i) <= 1.58e+118):
		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) <= -1e+39) || !(Float64(c * i) <= 1.58e+118))
		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) <= -1e+39) || ~(((c * i) <= 1.58e+118)))
		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], -1e+39], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.58e+118]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.9999999999999994e38 or 1.58000000000000002e118 < (*.f64 c i)

   1. Initial program 92.0%

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

   3. Taylor expanded in c around inf 58.1%

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

   if -9.9999999999999994e38 < (*.f64 c i) < 1.58000000000000002e118

   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 a around inf 39.4%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+39} \lor \neg \left(c \cdot i \leq 1.58 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 a around inf 30.6%

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

4. Final simplification 30.6%

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

Reproduce

herbie shell --seed 2024078 
(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)))