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

Percentage Accurate: 96.0% → 98.0%

Time: 8.1s

Alternatives: 15

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: 98.0% 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 98.4%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

Alternative 2: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. fma-define 96.9%

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

3. Simplified 96.9%

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

Alternative 3: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2.55 \cdot 10^{+95}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.12 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-322}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 0.009:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -2.55e+95)
     (+ (* a b) (* c i))
     (if (<= (* c i) -1.12e-113)
       t_1
       (if (<= (* c i) -5e-322)
         (+ (* a b) (* x y))
         (if (<= (* c i) 0.009)
           t_1
           (if (<= (* c i) 1.05e+121)
             (+ (* x y) (* z t))
             (+ (* c i) (* 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) + (z * t);
	double tmp;
	if ((c * i) <= -2.55e+95) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -1.12e-113) {
		tmp = t_1;
	} else if ((c * i) <= -5e-322) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 0.009) {
		tmp = t_1;
	} else if ((c * i) <= 1.05e+121) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-2.55d+95)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-1.12d-113)) then
        tmp = t_1
    else if ((c * i) <= (-5d-322)) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 0.009d0) then
        tmp = t_1
    else if ((c * i) <= 1.05d+121) then
        tmp = (x * y) + (z * t)
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -2.55e+95) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -1.12e-113) {
		tmp = t_1;
	} else if ((c * i) <= -5e-322) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 0.009) {
		tmp = t_1;
	} else if ((c * i) <= 1.05e+121) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -2.55e+95:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -1.12e-113:
		tmp = t_1
	elif (c * i) <= -5e-322:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 0.009:
		tmp = t_1
	elif (c * i) <= 1.05e+121:
		tmp = (x * y) + (z * t)
	else:
		tmp = (c * i) + (z * t)
	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(c * i) <= -2.55e+95)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -1.12e-113)
		tmp = t_1;
	elseif (Float64(c * i) <= -5e-322)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 0.009)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.05e+121)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2.55e+95)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -1.12e-113)
		tmp = t_1;
	elseif ((c * i) <= -5e-322)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 0.009)
		tmp = t_1;
	elseif ((c * i) <= 1.05e+121)
		tmp = (x * y) + (z * t);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.55e+95], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.12e-113], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5e-322], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 0.009], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+121], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -2.55000000000000001e95

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 83.2%

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

   4. Taylor expanded in x around 0 73.5%

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

   if -2.55000000000000001e95 < (*.f64 c i) < -1.1200000000000001e-113 or -4.99006e-322 < (*.f64 c i) < 0.00899999999999999932

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0 95.2%

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

   4. Taylor expanded in x around 0 74.6%

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

   if -1.1200000000000001e-113 < (*.f64 c i) < -4.99006e-322

   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 0 100.0%

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

   4. Taylor expanded in t around 0 90.0%

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

   if 0.00899999999999999932 < (*.f64 c i) < 1.0500000000000001e121

   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 c around 0 88.5%

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

   4. Taylor expanded in a around 0 84.9%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if 1.0500000000000001e121 < (*.f64 c i)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around 0 86.9%

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

   4. Taylor expanded in x around 0 78.6%

      \[\leadsto \color{blue}{c \cdot i + t \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.55 \cdot 10^{+95}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.12 \cdot 10^{-113}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-322}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 0.009:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.4 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-322}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

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 (<= (* c i) -1.45e+97)
     (+ (* a b) (* c i))
     (if (<= (* c i) -7.4e-115)
       t_1
       (if (<= (* c i) -5e-322)
         t_2
         (if (<= (* c i) 7.5e-72)
           t_1
           (if (<= (* c i) 9.2e+35) t_2 (+ (* c i) (* 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) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -1.45e+97) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -7.4e-115) {
		tmp = t_1;
	} else if ((c * i) <= -5e-322) {
		tmp = t_2;
	} else if ((c * i) <= 7.5e-72) {
		tmp = t_1;
	} else if ((c * i) <= 9.2e+35) {
		tmp = t_2;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((c * i) <= (-1.45d+97)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-7.4d-115)) then
        tmp = t_1
    else if ((c * i) <= (-5d-322)) then
        tmp = t_2
    else if ((c * i) <= 7.5d-72) then
        tmp = t_1
    else if ((c * i) <= 9.2d+35) then
        tmp = t_2
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -1.45e+97) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -7.4e-115) {
		tmp = t_1;
	} else if ((c * i) <= -5e-322) {
		tmp = t_2;
	} else if ((c * i) <= 7.5e-72) {
		tmp = t_1;
	} else if ((c * i) <= 9.2e+35) {
		tmp = t_2;
	} else {
		tmp = (c * i) + (z * t);
	}
	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 (c * i) <= -1.45e+97:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -7.4e-115:
		tmp = t_1
	elif (c * i) <= -5e-322:
		tmp = t_2
	elif (c * i) <= 7.5e-72:
		tmp = t_1
	elif (c * i) <= 9.2e+35:
		tmp = t_2
	else:
		tmp = (c * i) + (z * t)
	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(c * i) <= -1.45e+97)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -7.4e-115)
		tmp = t_1;
	elseif (Float64(c * i) <= -5e-322)
		tmp = t_2;
	elseif (Float64(c * i) <= 7.5e-72)
		tmp = t_1;
	elseif (Float64(c * i) <= 9.2e+35)
		tmp = t_2;
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -1.45e+97)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -7.4e-115)
		tmp = t_1;
	elseif ((c * i) <= -5e-322)
		tmp = t_2;
	elseif ((c * i) <= 7.5e-72)
		tmp = t_1;
	elseif ((c * i) <= 9.2e+35)
		tmp = t_2;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.45e+97], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -7.4e-115], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5e-322], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 7.5e-72], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 9.2e+35], t$95$2, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.44999999999999994e97

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 83.2%

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

   4. Taylor expanded in x around 0 73.5%

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

   if -1.44999999999999994e97 < (*.f64 c i) < -7.4e-115 or -4.99006e-322 < (*.f64 c i) < 7.5000000000000004e-72

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0 95.8%

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

   4. Taylor expanded in x around 0 75.8%

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

   if -7.4e-115 < (*.f64 c i) < -4.99006e-322 or 7.5000000000000004e-72 < (*.f64 c i) < 9.1999999999999993e35

   1. Initial program 97.7%

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

   3. Taylor expanded in c around 0 95.6%

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

   4. Taylor expanded in t around 0 87.2%

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

   if 9.1999999999999993e35 < (*.f64 c i)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around 0 88.7%

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

   4. Taylor expanded in x around 0 75.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.4 \cdot 10^{-115}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-322}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{-72}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{+35}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -3.05 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-322}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -3.05e+97)
     t_2
     (if (<= (* c i) -1.8e-113)
       t_1
       (if (<= (* c i) -5e-322)
         (+ (* a b) (* x y))
         (if (<= (* c i) 1.05e+127) 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) + (c * i);
	double tmp;
	if ((c * i) <= -3.05e+97) {
		tmp = t_2;
	} else if ((c * i) <= -1.8e-113) {
		tmp = t_1;
	} else if ((c * i) <= -5e-322) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.05e+127) {
		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) + (c * i)
    if ((c * i) <= (-3.05d+97)) then
        tmp = t_2
    else if ((c * i) <= (-1.8d-113)) then
        tmp = t_1
    else if ((c * i) <= (-5d-322)) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 1.05d+127) 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) + (c * i);
	double tmp;
	if ((c * i) <= -3.05e+97) {
		tmp = t_2;
	} else if ((c * i) <= -1.8e-113) {
		tmp = t_1;
	} else if ((c * i) <= -5e-322) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.05e+127) {
		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) + (c * i)
	tmp = 0
	if (c * i) <= -3.05e+97:
		tmp = t_2
	elif (c * i) <= -1.8e-113:
		tmp = t_1
	elif (c * i) <= -5e-322:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 1.05e+127:
		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(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -3.05e+97)
		tmp = t_2;
	elseif (Float64(c * i) <= -1.8e-113)
		tmp = t_1;
	elseif (Float64(c * i) <= -5e-322)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 1.05e+127)
		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) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -3.05e+97)
		tmp = t_2;
	elseif ((c * i) <= -1.8e-113)
		tmp = t_1;
	elseif ((c * i) <= -5e-322)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 1.05e+127)
		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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.05e+97], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -1.8e-113], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5e-322], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+127], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.05e97 or 1.04999999999999996e127 < (*.f64 c i)

   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 z around 0 83.1%

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

   4. Taylor expanded in x around 0 75.2%

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

   if -3.05e97 < (*.f64 c i) < -1.79999999999999987e-113 or -4.99006e-322 < (*.f64 c i) < 1.04999999999999996e127

   1. Initial program 97.9%

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

   3. Taylor expanded in c around 0 94.0%

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

   4. Taylor expanded in x around 0 70.2%

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

   if -1.79999999999999987e-113 < (*.f64 c i) < -4.99006e-322

   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 0 100.0%

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

   4. Taylor expanded in t around 0 90.0%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.05 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.8 \cdot 10^{-113}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -5 \cdot 10^{-322}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + \left(a \cdot b + t\_1\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) (+ (* a b) t_1))))
   (if (<= t_2 INFINITY) 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 = (x * y) + (z * t);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 = (x * y) + (z * t);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (c * i) + ((a * b) + t_1)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(Float64(a * b) + t_1))
	tmp = 0.0
	if (t_2 <= Inf)
		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 = (x * y) + (z * t);
	t_2 = (c * i) + ((a * b) + t_1);
	tmp = 0.0;
	if (t_2 <= Inf)
		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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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 c around 0 33.3%

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

   4. Taylor expanded in a around 0 45.4%

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

4. Final simplification 98.1%

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

Alternative 7: 42.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.2 \cdot 10^{+96}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 0.24:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+120}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.2e+96)
   (* c i)
   (if (<= (* c i) 0.24)
     (* a b)
     (if (<= (* c i) 9.5e+35)
       (* x y)
       (if (<= (* c i) 9.5e+120) (* 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) <= -2.2e+96) {
		tmp = c * i;
	} else if ((c * i) <= 0.24) {
		tmp = a * b;
	} else if ((c * i) <= 9.5e+35) {
		tmp = x * y;
	} else if ((c * i) <= 9.5e+120) {
		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) <= (-2.2d+96)) then
        tmp = c * i
    else if ((c * i) <= 0.24d0) then
        tmp = a * b
    else if ((c * i) <= 9.5d+35) then
        tmp = x * y
    else if ((c * i) <= 9.5d+120) 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) <= -2.2e+96) {
		tmp = c * i;
	} else if ((c * i) <= 0.24) {
		tmp = a * b;
	} else if ((c * i) <= 9.5e+35) {
		tmp = x * y;
	} else if ((c * i) <= 9.5e+120) {
		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) <= -2.2e+96:
		tmp = c * i
	elif (c * i) <= 0.24:
		tmp = a * b
	elif (c * i) <= 9.5e+35:
		tmp = x * y
	elif (c * i) <= 9.5e+120:
		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) <= -2.2e+96)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 0.24)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 9.5e+35)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 9.5e+120)
		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) <= -2.2e+96)
		tmp = c * i;
	elseif ((c * i) <= 0.24)
		tmp = a * b;
	elseif ((c * i) <= 9.5e+35)
		tmp = x * y;
	elseif ((c * i) <= 9.5e+120)
		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], -2.2e+96], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 0.24], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.5e+35], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.5e+120], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.1999999999999999e96 or 9.5e120 < (*.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 64.6%

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

   if -2.1999999999999999e96 < (*.f64 c i) < 0.23999999999999999

   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 40.7%

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

   if 0.23999999999999999 < (*.f64 c i) < 9.50000000000000062e35

   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 x around inf 70.4%

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

   if 9.50000000000000062e35 < (*.f64 c i) < 9.5e120

   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 65.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.2 \cdot 10^{+96}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 0.24:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+120}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.5 \cdot 10^{+169} \lor \neg \left(c \cdot i \leq 9.6 \cdot 10^{+120}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.5e+169) (not (<= (* c i) 9.6e+120)))
   (+ (* c i) (+ (* a b) (* x y)))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.5e+169) || !((c * i) <= 9.6e+120)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (a * b) + ((x * y) + (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) <= (-2.5d+169)) .or. (.not. ((c * i) <= 9.6d+120))) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.5e+169) || !((c * i) <= 9.6e+120)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2.5e+169) or not ((c * i) <= 9.6e+120):
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2.5e+169) || !(Float64(c * i) <= 9.6e+120))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + 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) <= -2.5e+169) || ~(((c * i) <= 9.6e+120)))
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.5e+169], N[Not[LessEqual[N[(c * i), $MachinePrecision], 9.6e+120]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.50000000000000009e169 or 9.60000000000000004e120 < (*.f64 c i)

   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 84.6%

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

   if -2.50000000000000009e169 < (*.f64 c i) < 9.60000000000000004e120

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 93.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.5 \cdot 10^{+169} \lor \neg \left(c \cdot i \leq 9.6 \cdot 10^{+120}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+169}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -3.3e+169)
     (+ (* c i) (+ (* a b) (* x y)))
     (if (<= (* c i) 1.35e+58) (+ (* a b) t_1) (+ (* c i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -3.3e+169) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((c * i) <= 1.35e+58) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + 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) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-3.3d+169)) then
        tmp = (c * i) + ((a * b) + (x * y))
    else if ((c * i) <= 1.35d+58) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + 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 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -3.3e+169) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else if ((c * i) <= 1.35e+58) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -3.3e+169:
		tmp = (c * i) + ((a * b) + (x * y))
	elif (c * i) <= 1.35e+58:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -3.3e+169)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	elseif (Float64(c * i) <= 1.35e+58)
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -3.3e+169)
		tmp = (c * i) + ((a * b) + (x * y));
	elseif ((c * i) <= 1.35e+58)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.3e+169], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.35e+58], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.2999999999999997e169

   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 z around 0 90.0%

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

   if -3.2999999999999997e169 < (*.f64 c i) < 1.3500000000000001e58

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0 93.9%

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

   if 1.3500000000000001e58 < (*.f64 c i)

   1. Initial program 93.1%

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

   3. Taylor expanded in a around 0 89.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.3 \cdot 10^{+169}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.2 \cdot 10^{+183}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.2e+183)
   (+ (* c i) (* x y))
   (if (<= (* c i) 8.2e+118)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* c i) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.2e+183) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= 8.2e+118) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.2d+183)) then
        tmp = (c * i) + (x * y)
    else if ((c * i) <= 8.2d+118) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.2e+183) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= 8.2e+118) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.2e+183:
		tmp = (c * i) + (x * y)
	elif (c * i) <= 8.2e+118:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.2e+183)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(c * i) <= 8.2e+118)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.2e+183)
		tmp = (c * i) + (x * y);
	elseif ((c * i) <= 8.2e+118)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.2e+183], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.2e+118], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.19999999999999991e183

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 89.3%

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

   4. Taylor expanded in a around 0 82.7%

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

   if -2.19999999999999991e183 < (*.f64 c i) < 8.1999999999999994e118

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 93.3%

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

   if 8.1999999999999994e118 < (*.f64 c i)

   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 a around 0 87.7%

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

   4. Taylor expanded in x around 0 77.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.2 \cdot 10^{+183}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8 \cdot 10^{+97}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5.5 \cdot 10^{+120}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -8e+97)
   (* c i)
   (if (<= (* c i) 1.35e-176)
     (* a b)
     (if (<= (* c i) 5.5e+120) (* 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) <= -8e+97) {
		tmp = c * i;
	} else if ((c * i) <= 1.35e-176) {
		tmp = a * b;
	} else if ((c * i) <= 5.5e+120) {
		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) <= (-8d+97)) then
        tmp = c * i
    else if ((c * i) <= 1.35d-176) then
        tmp = a * b
    else if ((c * i) <= 5.5d+120) 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) <= -8e+97) {
		tmp = c * i;
	} else if ((c * i) <= 1.35e-176) {
		tmp = a * b;
	} else if ((c * i) <= 5.5e+120) {
		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) <= -8e+97:
		tmp = c * i
	elif (c * i) <= 1.35e-176:
		tmp = a * b
	elif (c * i) <= 5.5e+120:
		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) <= -8e+97)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 1.35e-176)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 5.5e+120)
		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) <= -8e+97)
		tmp = c * i;
	elseif ((c * i) <= 1.35e-176)
		tmp = a * b;
	elseif ((c * i) <= 5.5e+120)
		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], -8e+97], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.35e-176], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.5e+120], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -8.0000000000000006e97 or 5.50000000000000003e120 < (*.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 64.6%

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

   if -8.0000000000000006e97 < (*.f64 c i) < 1.3499999999999999e-176

   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 42.1%

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

   if 1.3499999999999999e-176 < (*.f64 c i) < 5.50000000000000003e120

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 42.8%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8 \cdot 10^{+97}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{-176}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5.5 \cdot 10^{+120}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.1 \cdot 10^{+96} \lor \neg \left(c \cdot i \leq 9.5 \cdot 10^{+120}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.1e+96) (not (<= (* c i) 9.5e+120)))
   (+ (* 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) <= -1.1e+96) || !((c * i) <= 9.5e+120)) {
		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) <= (-1.1d+96)) .or. (.not. ((c * i) <= 9.5d+120))) 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) <= -1.1e+96) || !((c * i) <= 9.5e+120)) {
		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) <= -1.1e+96) or not ((c * i) <= 9.5e+120):
		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) <= -1.1e+96) || !(Float64(c * i) <= 9.5e+120))
		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) <= -1.1e+96) || ~(((c * i) <= 9.5e+120)))
		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], -1.1e+96], N[Not[LessEqual[N[(c * i), $MachinePrecision], 9.5e+120]], $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) < -1.0999999999999999e96 or 9.5e120 < (*.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 z around 0 82.1%

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

   4. Taylor expanded in x around 0 74.4%

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

   if -1.0999999999999999e96 < (*.f64 c i) < 9.5e120

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0 95.5%

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

   4. Taylor expanded in x around 0 67.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.1 \cdot 10^{+96} \lor \neg \left(c \cdot i \leq 9.5 \cdot 10^{+120}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+237} \lor \neg \left(x \cdot y \leq 7.8 \cdot 10^{+232}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.15e+237) (not (<= (* x y) 7.8e+232)))
   (* x y)
   (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.15e+237) || !((x * y) <= 7.8e+232)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.15d+237)) .or. (.not. ((x * y) <= 7.8d+232))) then
        tmp = x * y
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.15e+237) || !((x * y) <= 7.8e+232)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.15e+237) or not ((x * y) <= 7.8e+232):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.15e+237) || !(Float64(x * y) <= 7.8e+232))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.15e+237) || ~(((x * y) <= 7.8e+232)))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.15e+237], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.8e+232]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.14999999999999998e237 or 7.7999999999999998e232 < (*.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -1.14999999999999998e237 < (*.f64 x y) < 7.7999999999999998e232

   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 z around 0 71.2%

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

   4. Taylor expanded in x around 0 58.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+237} \lor \neg \left(x \cdot y \leq 7.8 \cdot 10^{+232}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+97} \lor \neg \left(c \cdot i \leq 1.6 \cdot 10^{+58}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -6.8e+97) (not (<= (* c i) 1.6e+58))) (* 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) <= -6.8e+97) || !((c * i) <= 1.6e+58)) {
		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) <= (-6.8d+97)) .or. (.not. ((c * i) <= 1.6d+58))) 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) <= -6.8e+97) || !((c * i) <= 1.6e+58)) {
		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) <= -6.8e+97) or not ((c * i) <= 1.6e+58):
		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) <= -6.8e+97) || !(Float64(c * i) <= 1.6e+58))
		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) <= -6.8e+97) || ~(((c * i) <= 1.6e+58)))
		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], -6.8e+97], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.6e+58]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -6.8000000000000002e97 or 1.60000000000000008e58 < (*.f64 c i)

   1. Initial program 92.9%

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

   3. Taylor expanded in c around inf 58.7%

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

   if -6.8000000000000002e97 < (*.f64 c i) < 1.60000000000000008e58

   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 a around inf 39.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+97} \lor \neg \left(c \cdot i \leq 1.6 \cdot 10^{+58}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.1% 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 29.5%

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

Reproduce

herbie shell --seed 2024137 
(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)))