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

Percentage Accurate: 95.6% → 97.8%

Time: 9.7s

Alternatives: 16

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: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% 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 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-define 98.0%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

Alternative 2: 97.8% 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 96.9%

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

   3. +-commutative 96.9%

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

   4. fma-define 97.3%

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

   5. fma-define 97.6%

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

3. Simplified 97.6%

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

Alternative 3: 95.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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 4: 42.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+226}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.15 \cdot 10^{-164}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -6.5 \cdot 10^{-299}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.2 \cdot 10^{-194}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{-35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.7e+226)
   (* a b)
   (if (<= (* a b) -1.15e-164)
     (* z t)
     (if (<= (* a b) -6.5e-299)
       (* c i)
       (if (<= (* a b) 8.2e-194)
         (* z t)
         (if (<= (* a b) 1.16e-35)
           (* x y)
           (if (<= (* a b) 2.1e+63) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.7e+226) {
		tmp = a * b;
	} else if ((a * b) <= -1.15e-164) {
		tmp = z * t;
	} else if ((a * b) <= -6.5e-299) {
		tmp = c * i;
	} else if ((a * b) <= 8.2e-194) {
		tmp = z * t;
	} else if ((a * b) <= 1.16e-35) {
		tmp = x * y;
	} else if ((a * b) <= 2.1e+63) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.7d+226)) then
        tmp = a * b
    else if ((a * b) <= (-1.15d-164)) then
        tmp = z * t
    else if ((a * b) <= (-6.5d-299)) then
        tmp = c * i
    else if ((a * b) <= 8.2d-194) then
        tmp = z * t
    else if ((a * b) <= 1.16d-35) then
        tmp = x * y
    else if ((a * b) <= 2.1d+63) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.7e+226) {
		tmp = a * b;
	} else if ((a * b) <= -1.15e-164) {
		tmp = z * t;
	} else if ((a * b) <= -6.5e-299) {
		tmp = c * i;
	} else if ((a * b) <= 8.2e-194) {
		tmp = z * t;
	} else if ((a * b) <= 1.16e-35) {
		tmp = x * y;
	} else if ((a * b) <= 2.1e+63) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.7e+226:
		tmp = a * b
	elif (a * b) <= -1.15e-164:
		tmp = z * t
	elif (a * b) <= -6.5e-299:
		tmp = c * i
	elif (a * b) <= 8.2e-194:
		tmp = z * t
	elif (a * b) <= 1.16e-35:
		tmp = x * y
	elif (a * b) <= 2.1e+63:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.7e+226)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.15e-164)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -6.5e-299)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 8.2e-194)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.16e-35)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.1e+63)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.7e+226)
		tmp = a * b;
	elseif ((a * b) <= -1.15e-164)
		tmp = z * t;
	elseif ((a * b) <= -6.5e-299)
		tmp = c * i;
	elseif ((a * b) <= 8.2e-194)
		tmp = z * t;
	elseif ((a * b) <= 1.16e-35)
		tmp = x * y;
	elseif ((a * b) <= 2.1e+63)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.7e+226], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.15e-164], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -6.5e-299], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.2e-194], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.16e-35], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.1e+63], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.69999999999999989e226 or 2.1000000000000002e63 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 77.6%

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

   if -1.69999999999999989e226 < (*.f64 a b) < -1.14999999999999993e-164 or -6.4999999999999997e-299 < (*.f64 a b) < 8.2000000000000005e-194 or 1.16000000000000005e-35 < (*.f64 a b) < 2.1000000000000002e63

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 43.4%

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

   if -1.14999999999999993e-164 < (*.f64 a b) < -6.4999999999999997e-299

   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 58.9%

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

   if 8.2000000000000005e-194 < (*.f64 a b) < 1.16000000000000005e-35

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf 49.9%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{+226}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.15 \cdot 10^{-164}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -6.5 \cdot 10^{-299}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.2 \cdot 10^{-194}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{-35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+215}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-166}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -4.7 \cdot 10^{-302}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{-254}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 0.225:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3e+215)
   (* a b)
   (if (<= (* a b) -8.2e-166)
     (* z t)
     (if (<= (* a b) -4.7e-302)
       (* c i)
       (if (<= (* a b) 4.6e-254)
         (* z t)
         (if (<= (* a b) 0.225)
           (* c i)
           (if (<= (* a b) 8.5e+63) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3e+215) {
		tmp = a * b;
	} else if ((a * b) <= -8.2e-166) {
		tmp = z * t;
	} else if ((a * b) <= -4.7e-302) {
		tmp = c * i;
	} else if ((a * b) <= 4.6e-254) {
		tmp = z * t;
	} else if ((a * b) <= 0.225) {
		tmp = c * i;
	} else if ((a * b) <= 8.5e+63) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-3d+215)) then
        tmp = a * b
    else if ((a * b) <= (-8.2d-166)) then
        tmp = z * t
    else if ((a * b) <= (-4.7d-302)) then
        tmp = c * i
    else if ((a * b) <= 4.6d-254) then
        tmp = z * t
    else if ((a * b) <= 0.225d0) then
        tmp = c * i
    else if ((a * b) <= 8.5d+63) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3e+215) {
		tmp = a * b;
	} else if ((a * b) <= -8.2e-166) {
		tmp = z * t;
	} else if ((a * b) <= -4.7e-302) {
		tmp = c * i;
	} else if ((a * b) <= 4.6e-254) {
		tmp = z * t;
	} else if ((a * b) <= 0.225) {
		tmp = c * i;
	} else if ((a * b) <= 8.5e+63) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -3e+215:
		tmp = a * b
	elif (a * b) <= -8.2e-166:
		tmp = z * t
	elif (a * b) <= -4.7e-302:
		tmp = c * i
	elif (a * b) <= 4.6e-254:
		tmp = z * t
	elif (a * b) <= 0.225:
		tmp = c * i
	elif (a * b) <= 8.5e+63:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -3e+215)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -8.2e-166)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -4.7e-302)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 4.6e-254)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 0.225)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 8.5e+63)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -3e+215)
		tmp = a * b;
	elseif ((a * b) <= -8.2e-166)
		tmp = z * t;
	elseif ((a * b) <= -4.7e-302)
		tmp = c * i;
	elseif ((a * b) <= 4.6e-254)
		tmp = z * t;
	elseif ((a * b) <= 0.225)
		tmp = c * i;
	elseif ((a * b) <= 8.5e+63)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -3e+215], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -8.2e-166], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4.7e-302], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.6e-254], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.225], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.5e+63], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.9999999999999999e215 or 8.5000000000000004e63 < (*.f64 a b)

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 77.6%

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

   if -2.9999999999999999e215 < (*.f64 a b) < -8.1999999999999995e-166 or -4.7000000000000005e-302 < (*.f64 a b) < 4.5999999999999997e-254 or 0.225000000000000006 < (*.f64 a b) < 8.5000000000000004e63

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 44.1%

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

   if -8.1999999999999995e-166 < (*.f64 a b) < -4.7000000000000005e-302 or 4.5999999999999997e-254 < (*.f64 a b) < 0.225000000000000006

   1. Initial program 96.1%

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

   3. Taylor expanded in c around inf 45.5%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3 \cdot 10^{+215}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-166}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -4.7 \cdot 10^{-302}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{-254}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 0.225:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -7.6 \cdot 10^{+140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{+35}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 4.2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) -7.6e+140)
     t_2
     (if (<= (* c i) 6.5e-247)
       t_1
       (if (<= (* c i) 1.35e+35)
         (+ (* a b) (* x y))
         (if (<= (* c i) 3e+177)
           t_1
           (if (<= (* c i) 4.2e+196) (* x y) 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) <= -7.6e+140) {
		tmp = t_2;
	} else if ((c * i) <= 6.5e-247) {
		tmp = t_1;
	} else if ((c * i) <= 1.35e+35) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 3e+177) {
		tmp = t_1;
	} else if ((c * i) <= 4.2e+196) {
		tmp = x * y;
	} 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) <= (-7.6d+140)) then
        tmp = t_2
    else if ((c * i) <= 6.5d-247) then
        tmp = t_1
    else if ((c * i) <= 1.35d+35) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 3d+177) then
        tmp = t_1
    else if ((c * i) <= 4.2d+196) then
        tmp = x * y
    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) <= -7.6e+140) {
		tmp = t_2;
	} else if ((c * i) <= 6.5e-247) {
		tmp = t_1;
	} else if ((c * i) <= 1.35e+35) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 3e+177) {
		tmp = t_1;
	} else if ((c * i) <= 4.2e+196) {
		tmp = x * y;
	} 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) <= -7.6e+140:
		tmp = t_2
	elif (c * i) <= 6.5e-247:
		tmp = t_1
	elif (c * i) <= 1.35e+35:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 3e+177:
		tmp = t_1
	elif (c * i) <= 4.2e+196:
		tmp = x * y
	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) <= -7.6e+140)
		tmp = t_2;
	elseif (Float64(c * i) <= 6.5e-247)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.35e+35)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 3e+177)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.2e+196)
		tmp = Float64(x * y);
	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) <= -7.6e+140)
		tmp = t_2;
	elseif ((c * i) <= 6.5e-247)
		tmp = t_1;
	elseif ((c * i) <= 1.35e+35)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 3e+177)
		tmp = t_1;
	elseif ((c * i) <= 4.2e+196)
		tmp = x * y;
	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], -7.6e+140], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 6.5e-247], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.35e+35], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3e+177], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.2e+196], N[(x * y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -7.6000000000000002e140 or 4.20000000000000029e196 < (*.f64 c i)

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in t around 0 80.5%

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

   if -7.6000000000000002e140 < (*.f64 c i) < 6.4999999999999996e-247 or 1.35000000000000001e35 < (*.f64 c i) < 3e177

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 80.4%

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

   4. Taylor expanded in c around 0 72.2%

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

   if 6.4999999999999996e-247 < (*.f64 c i) < 1.35000000000000001e35

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 78.1%

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

   4. Taylor expanded in c around 0 74.0%

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

   if 3e177 < (*.f64 c i) < 4.20000000000000029e196

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.6 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{+35}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+177}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -2.05 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 6.6 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) -2.05e+137)
     t_2
     (if (<= (* c i) 2.5e-143)
       t_1
       (if (<= (* c i) 6.6e-85) (* x y) (if (<= (* c i) 2.1e+162) 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) <= -2.05e+137) {
		tmp = t_2;
	} else if ((c * i) <= 2.5e-143) {
		tmp = t_1;
	} else if ((c * i) <= 6.6e-85) {
		tmp = x * y;
	} else if ((c * i) <= 2.1e+162) {
		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) <= (-2.05d+137)) then
        tmp = t_2
    else if ((c * i) <= 2.5d-143) then
        tmp = t_1
    else if ((c * i) <= 6.6d-85) then
        tmp = x * y
    else if ((c * i) <= 2.1d+162) 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) <= -2.05e+137) {
		tmp = t_2;
	} else if ((c * i) <= 2.5e-143) {
		tmp = t_1;
	} else if ((c * i) <= 6.6e-85) {
		tmp = x * y;
	} else if ((c * i) <= 2.1e+162) {
		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) <= -2.05e+137:
		tmp = t_2
	elif (c * i) <= 2.5e-143:
		tmp = t_1
	elif (c * i) <= 6.6e-85:
		tmp = x * y
	elif (c * i) <= 2.1e+162:
		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) <= -2.05e+137)
		tmp = t_2;
	elseif (Float64(c * i) <= 2.5e-143)
		tmp = t_1;
	elseif (Float64(c * i) <= 6.6e-85)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 2.1e+162)
		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) <= -2.05e+137)
		tmp = t_2;
	elseif ((c * i) <= 2.5e-143)
		tmp = t_1;
	elseif ((c * i) <= 6.6e-85)
		tmp = x * y;
	elseif ((c * i) <= 2.1e+162)
		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], -2.05e+137], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2.5e-143], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 6.6e-85], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.1e+162], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.04999999999999998e137 or 2.1e162 < (*.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 x around 0 80.5%

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

   4. Taylor expanded in t around 0 76.6%

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

   if -2.04999999999999998e137 < (*.f64 c i) < 2.5000000000000001e-143 or 6.59999999999999945e-85 < (*.f64 c i) < 2.1e162

   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 x around 0 76.3%

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

   4. Taylor expanded in c around 0 70.5%

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

   if 2.5000000000000001e-143 < (*.f64 c i) < 6.59999999999999945e-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 x around inf 75.5%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.05 \cdot 10^{+137}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-143}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 6.6 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+162}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(c + N[(N[(z * t), $MachinePrecision] / i), $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 i around inf 11.1%

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

   4. Taylor expanded in a around 0 33.3%

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

   5. Taylor expanded in x around 0 45.0%

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

4. Final simplification 98.0%

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

Alternative 9: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-255}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4e+142)
   (* i (+ c (/ (* z t) i)))
   (if (<= (* c i) 5e-255)
     (+ (* a b) (* z t))
     (if (<= (* c i) 5e+94) (+ (* a b) (* x y)) (+ (* c i) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4e+142) {
		tmp = i * (c + ((z * t) / i));
	} else if ((c * i) <= 5e-255) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 5e+94) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (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 ((c * i) <= (-4d+142)) then
        tmp = i * (c + ((z * t) / i))
    else if ((c * i) <= 5d-255) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 5d+94) then
        tmp = (a * b) + (x * y)
    else
        tmp = (c * i) + (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 ((c * i) <= -4e+142) {
		tmp = i * (c + ((z * t) / i));
	} else if ((c * i) <= 5e-255) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 5e+94) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4e+142:
		tmp = i * (c + ((z * t) / i))
	elif (c * i) <= 5e-255:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 5e+94:
		tmp = (a * b) + (x * y)
	else:
		tmp = (c * i) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4e+142)
		tmp = Float64(i * Float64(c + Float64(Float64(z * t) / i)));
	elseif (Float64(c * i) <= 5e-255)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 5e+94)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(c * i) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4e+142)
		tmp = i * (c + ((z * t) / i));
	elseif ((c * i) <= 5e-255)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 5e+94)
		tmp = (a * b) + (x * y);
	else
		tmp = (c * i) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4e+142], N[(i * N[(c + N[(N[(z * t), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e-255], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+94], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.0000000000000002e142

   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 i around inf 90.6%

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

   4. Taylor expanded in a around 0 84.5%

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

   5. Taylor expanded in x around 0 72.2%

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

   if -4.0000000000000002e142 < (*.f64 c i) < 4.9999999999999996e-255

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in c around 0 76.0%

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

   if 4.9999999999999996e-255 < (*.f64 c i) < 5.0000000000000001e94

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 75.2%

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

   4. Taylor expanded in c around 0 70.1%

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

   if 5.0000000000000001e94 < (*.f64 c i)

   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 z around 0 88.1%

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

   4. Taylor expanded in a around 0 82.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(c + \frac{z \cdot t}{i}\right)\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-255}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -9.6 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 4.75 \cdot 10^{-253}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* x y))))
   (if (<= (* c i) -9.6e+139)
     t_1
     (if (<= (* c i) 4.75e-253)
       (+ (* a b) (* z t))
       (if (<= (* c i) 4.4e+94) (+ (* a b) (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double tmp;
	if ((c * i) <= -9.6e+139) {
		tmp = t_1;
	} else if ((c * i) <= 4.75e-253) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 4.4e+94) {
		tmp = (a * b) + (x * y);
	} 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) :: tmp
    t_1 = (c * i) + (x * y)
    if ((c * i) <= (-9.6d+139)) then
        tmp = t_1
    else if ((c * i) <= 4.75d-253) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 4.4d+94) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double tmp;
	if ((c * i) <= -9.6e+139) {
		tmp = t_1;
	} else if ((c * i) <= 4.75e-253) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 4.4e+94) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (x * y)
	tmp = 0
	if (c * i) <= -9.6e+139:
		tmp = t_1
	elif (c * i) <= 4.75e-253:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 4.4e+94:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -9.6e+139)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.75e-253)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 4.4e+94)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -9.6e+139)
		tmp = t_1;
	elseif ((c * i) <= 4.75e-253)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 4.4e+94)
		tmp = (a * b) + (x * y);
	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[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -9.6e+139], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.75e-253], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.4e+94], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -9.60000000000000032e139 or 4.40000000000000024e94 < (*.f64 c i)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 84.6%

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

   4. Taylor expanded in a around 0 79.1%

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

   if -9.60000000000000032e139 < (*.f64 c i) < 4.75e-253

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in c around 0 76.0%

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

   if 4.75e-253 < (*.f64 c i) < 4.40000000000000024e94

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 75.2%

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

   4. Taylor expanded in c around 0 70.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9.6 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.75 \cdot 10^{-253}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 4.75 \cdot 10^{-253}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* c i) -3e+138)
     t_1
     (if (<= (* c i) 4.75e-253)
       (+ (* a b) (* z t))
       (if (<= (* c i) 5.5e+105) (+ (* a b) (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3e+138) {
		tmp = t_1;
	} else if ((c * i) <= 4.75e-253) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 5.5e+105) {
		tmp = (a * b) + (x * y);
	} 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) :: tmp
    t_1 = (c * i) + (z * t)
    if ((c * i) <= (-3d+138)) then
        tmp = t_1
    else if ((c * i) <= 4.75d-253) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 5.5d+105) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3e+138) {
		tmp = t_1;
	} else if ((c * i) <= 4.75e-253) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 5.5e+105) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -3e+138:
		tmp = t_1
	elif (c * i) <= 4.75e-253:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 5.5e+105:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -3e+138)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.75e-253)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 5.5e+105)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -3e+138)
		tmp = t_1;
	elseif ((c * i) <= 4.75e-253)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 5.5e+105)
		tmp = (a * b) + (x * y);
	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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3e+138], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.75e-253], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.5e+105], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.0000000000000001e138 or 5.49999999999999979e105 < (*.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 x around 0 81.2%

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

   4. Taylor expanded in a around 0 74.5%

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

   if -3.0000000000000001e138 < (*.f64 c i) < 4.75e-253

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in c around 0 76.0%

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

   if 4.75e-253 < (*.f64 c i) < 5.49999999999999979e105

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 76.8%

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

   4. Taylor expanded in c around 0 70.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.75 \cdot 10^{-253}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 9.5 \cdot 10^{+65}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.05e+102) (not (<= (* x y) 9.5e+65)))
   (+ (* c i) (+ (* a b) (* x y)))
   (+ (* a b) (+ (* c i) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.05e+102) || !((x * y) <= 9.5e+65)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.05d+102)) .or. (.not. ((x * y) <= 9.5d+65))) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (a * b) + ((c * i) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.05e+102) || !((x * y) <= 9.5e+65)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.05e+102) or not ((x * y) <= 9.5e+65):
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (a * b) + ((c * i) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.05e+102) || !(Float64(x * y) <= 9.5e+65))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.05e+102) || ~(((x * y) <= 9.5e+65)))
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (a * b) + ((c * i) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.05e+102], N[Not[LessEqual[N[(x * y), $MachinePrecision], 9.5e+65]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.05000000000000001e102 or 9.5000000000000005e65 < (*.f64 x y)

   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 z around 0 85.1%

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

   if -1.05000000000000001e102 < (*.f64 x y) < 9.5000000000000005e65

   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 x around 0 94.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+102} \lor \neg \left(x \cdot y \leq 9.5 \cdot 10^{+65}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+175}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+160}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2.05e+175)
   (+ (* c i) (* x y))
   (if (<= (* x y) 4.2e+160)
     (+ (* a b) (+ (* c i) (* 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) <= -2.05e+175) {
		tmp = (c * i) + (x * y);
	} else if ((x * y) <= 4.2e+160) {
		tmp = (a * b) + ((c * i) + (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) <= (-2.05d+175)) then
        tmp = (c * i) + (x * y)
    else if ((x * y) <= 4.2d+160) then
        tmp = (a * b) + ((c * i) + (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) <= -2.05e+175) {
		tmp = (c * i) + (x * y);
	} else if ((x * y) <= 4.2e+160) {
		tmp = (a * b) + ((c * i) + (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) <= -2.05e+175:
		tmp = (c * i) + (x * y)
	elif (x * y) <= 4.2e+160:
		tmp = (a * b) + ((c * i) + (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) <= -2.05e+175)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(x * y) <= 4.2e+160)
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + 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) <= -2.05e+175)
		tmp = (c * i) + (x * y);
	elseif ((x * y) <= 4.2e+160)
		tmp = (a * b) + ((c * i) + (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], -2.05e+175], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.2e+160], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $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) < -2.04999999999999989e175

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 87.2%

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

   4. Taylor expanded in a around 0 87.2%

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

   if -2.04999999999999989e175 < (*.f64 x y) < 4.19999999999999993e160

   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 91.1%

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

   if 4.19999999999999993e160 < (*.f64 x y)

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 87.6%

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

   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 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.05 \cdot 10^{+175}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+160}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.6 \cdot 10^{+173} \lor \neg \left(x \cdot y \leq 3.2 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -5.6e+173) (not (<= (* x y) 3.2e+158)))
   (* 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) <= -5.6e+173) || !((x * y) <= 3.2e+158)) {
		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) <= (-5.6d+173)) .or. (.not. ((x * y) <= 3.2d+158))) 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) <= -5.6e+173) || !((x * y) <= 3.2e+158)) {
		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) <= -5.6e+173) or not ((x * y) <= 3.2e+158):
		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) <= -5.6e+173) || !(Float64(x * y) <= 3.2e+158))
		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) <= -5.6e+173) || ~(((x * y) <= 3.2e+158)))
		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], -5.6e+173], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.2e+158]], $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) < -5.59999999999999964e173 or 3.19999999999999995e158 < (*.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 78.0%

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

   if -5.59999999999999964e173 < (*.f64 x y) < 3.19999999999999995e158

   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 91.1%

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

   4. Taylor expanded in t around 0 63.4%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.6 \cdot 10^{+173} \lor \neg \left(x \cdot y \leq 3.2 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.1 \cdot 10^{+139} \lor \neg \left(c \cdot i \leq 4 \cdot 10^{+94}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.1e+139) (not (<= (* c i) 4e+94))) (* 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) <= -3.1e+139) || !((c * i) <= 4e+94)) {
		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) <= (-3.1d+139)) .or. (.not. ((c * i) <= 4d+94))) 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) <= -3.1e+139) || !((c * i) <= 4e+94)) {
		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) <= -3.1e+139) or not ((c * i) <= 4e+94):
		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) <= -3.1e+139) || !(Float64(c * i) <= 4e+94))
		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) <= -3.1e+139) || ~(((c * i) <= 4e+94)))
		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], -3.1e+139], N[Not[LessEqual[N[(c * i), $MachinePrecision], 4e+94]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.1e139 or 4.0000000000000001e94 < (*.f64 c i)

   1. Initial program 93.2%

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

   3. Taylor expanded in c around inf 62.6%

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

   if -3.1e139 < (*.f64 c i) < 4.0000000000000001e94

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 38.6%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.1 \cdot 10^{+139} \lor \neg \left(c \cdot i \leq 4 \cdot 10^{+94}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 30.1%

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

Reproduce

herbie shell --seed 2024101 
(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)))