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

Percentage Accurate: 95.8% → 97.9%

Time: 12.5s

Alternatives: 13

Speedup: 0.4×

• 42.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.0× speedup

Math

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

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 93.4%

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

   1. +-commutative 93.4%

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

   2. fma-define 94.9%

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

   3. +-commutative 94.9%

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

   4. fma-define 96.5%

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

   5. fma-define 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 2: 65.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.06 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 2.3 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{-40}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6000000000000 \lor \neg \left(x \cdot y \leq 1.28 \cdot 10^{+92}\right) \land x \cdot y \leq 2.4 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* x y) (* c i))))
   (if (<= (* x y) -1.06e+102)
     t_2
     (if (<= (* x y) 2.3e-217)
       t_1
       (if (<= (* x y) 7e-40)
         (+ (* a b) (* c i))
         (if (or (<= (* x y) 6000000000000.0)
                 (and (not (<= (* x y) 1.28e+92)) (<= (* x y) 2.4e+156)))
           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 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -1.06e+102) {
		tmp = t_2;
	} else if ((x * y) <= 2.3e-217) {
		tmp = t_1;
	} else if ((x * y) <= 7e-40) {
		tmp = (a * b) + (c * i);
	} else if (((x * y) <= 6000000000000.0) || (!((x * y) <= 1.28e+92) && ((x * y) <= 2.4e+156))) {
		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 = (x * y) + (c * i)
    if ((x * y) <= (-1.06d+102)) then
        tmp = t_2
    else if ((x * y) <= 2.3d-217) then
        tmp = t_1
    else if ((x * y) <= 7d-40) then
        tmp = (a * b) + (c * i)
    else if (((x * y) <= 6000000000000.0d0) .or. (.not. ((x * y) <= 1.28d+92)) .and. ((x * y) <= 2.4d+156)) 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 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -1.06e+102) {
		tmp = t_2;
	} else if ((x * y) <= 2.3e-217) {
		tmp = t_1;
	} else if ((x * y) <= 7e-40) {
		tmp = (a * b) + (c * i);
	} else if (((x * y) <= 6000000000000.0) || (!((x * y) <= 1.28e+92) && ((x * y) <= 2.4e+156))) {
		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 = (x * y) + (c * i)
	tmp = 0
	if (x * y) <= -1.06e+102:
		tmp = t_2
	elif (x * y) <= 2.3e-217:
		tmp = t_1
	elif (x * y) <= 7e-40:
		tmp = (a * b) + (c * i)
	elif ((x * y) <= 6000000000000.0) or (not ((x * y) <= 1.28e+92) and ((x * y) <= 2.4e+156)):
		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(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -1.06e+102)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.3e-217)
		tmp = t_1;
	elseif (Float64(x * y) <= 7e-40)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif ((Float64(x * y) <= 6000000000000.0) || (!(Float64(x * y) <= 1.28e+92) && (Float64(x * y) <= 2.4e+156)))
		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 = (x * y) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -1.06e+102)
		tmp = t_2;
	elseif ((x * y) <= 2.3e-217)
		tmp = t_1;
	elseif ((x * y) <= 7e-40)
		tmp = (a * b) + (c * i);
	elseif (((x * y) <= 6000000000000.0) || (~(((x * y) <= 1.28e+92)) && ((x * y) <= 2.4e+156)))
		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[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.06e+102], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.3e-217], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7e-40], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 6000000000000.0], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.28e+92]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 2.4e+156]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.06000000000000001e102 or 6e12 < (*.f64 x y) < 1.27999999999999996e92 or 2.4000000000000001e156 < (*.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 86.1%

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

   4. Taylor expanded in a around 0 81.4%

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

   if -1.06000000000000001e102 < (*.f64 x y) < 2.30000000000000005e-217 or 7.0000000000000003e-40 < (*.f64 x y) < 6e12 or 1.27999999999999996e92 < (*.f64 x y) < 2.4000000000000001e156

   1. Initial program 94.9%

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

   3. Taylor expanded in c around 0 78.7%

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

   4. Taylor expanded in x around 0 75.2%

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

   if 2.30000000000000005e-217 < (*.f64 x y) < 7.0000000000000003e-40

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 94.2%

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

   4. Taylor expanded in t around 0 80.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.06 \cdot 10^{+102}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.3 \cdot 10^{-217}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{-40}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6000000000000 \lor \neg \left(x \cdot y \leq 1.28 \cdot 10^{+92}\right) \land x \cdot y \leq 2.4 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.12 \cdot 10^{-43}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9.2 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 11000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -2.9e+190)
     (* x y)
     (if (<= (* x y) -1.7e+17)
       t_1
       (if (<= (* x y) -1.12e-43)
         (* z t)
         (if (<= (* x y) 9.2e-40)
           t_1
           (if (<= (* x y) 11000000000000.0)
             (* z t)
             (if (<= (* x y) 4.6e+158) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -2.9e+190) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e+17) {
		tmp = t_1;
	} else if ((x * y) <= -1.12e-43) {
		tmp = z * t;
	} else if ((x * y) <= 9.2e-40) {
		tmp = t_1;
	} else if ((x * y) <= 11000000000000.0) {
		tmp = z * t;
	} else if ((x * y) <= 4.6e+158) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-2.9d+190)) then
        tmp = x * y
    else if ((x * y) <= (-1.7d+17)) then
        tmp = t_1
    else if ((x * y) <= (-1.12d-43)) then
        tmp = z * t
    else if ((x * y) <= 9.2d-40) then
        tmp = t_1
    else if ((x * y) <= 11000000000000.0d0) then
        tmp = z * t
    else if ((x * y) <= 4.6d+158) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -2.9e+190) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e+17) {
		tmp = t_1;
	} else if ((x * y) <= -1.12e-43) {
		tmp = z * t;
	} else if ((x * y) <= 9.2e-40) {
		tmp = t_1;
	} else if ((x * y) <= 11000000000000.0) {
		tmp = z * t;
	} else if ((x * y) <= 4.6e+158) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -2.9e+190:
		tmp = x * y
	elif (x * y) <= -1.7e+17:
		tmp = t_1
	elif (x * y) <= -1.12e-43:
		tmp = z * t
	elif (x * y) <= 9.2e-40:
		tmp = t_1
	elif (x * y) <= 11000000000000.0:
		tmp = z * t
	elif (x * y) <= 4.6e+158:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -2.9e+190)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.7e+17)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.12e-43)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 9.2e-40)
		tmp = t_1;
	elseif (Float64(x * y) <= 11000000000000.0)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 4.6e+158)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -2.9e+190)
		tmp = x * y;
	elseif ((x * y) <= -1.7e+17)
		tmp = t_1;
	elseif ((x * y) <= -1.12e-43)
		tmp = z * t;
	elseif ((x * y) <= 9.2e-40)
		tmp = t_1;
	elseif ((x * y) <= 11000000000000.0)
		tmp = z * t;
	elseif ((x * y) <= 4.6e+158)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.9e+190], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.7e+17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.12e-43], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.2e-40], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 11000000000000.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.6e+158], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.89999999999999989e190 or 4.59999999999999971e158 < (*.f64 x y)

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 79.3%

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

   if -2.89999999999999989e190 < (*.f64 x y) < -1.7e17 or -1.12e-43 < (*.f64 x y) < 9.2e-40 or 1.1e13 < (*.f64 x y) < 4.59999999999999971e158

   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 x around 0 88.1%

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

   4. Taylor expanded in t around 0 63.8%

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

   if -1.7e17 < (*.f64 x y) < -1.12e-43 or 9.2e-40 < (*.f64 x y) < 1.1e13

   1. Initial program 87.5%

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

   3. Taylor expanded in z around inf 68.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{+190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{+17}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.12 \cdot 10^{-43}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 11000000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{+158}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ t_3 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+66}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t)))
        (t_2 (+ (* a b) (* c i)))
        (t_3 (+ (* x y) (* a b))))
   (if (<= (* x y) -2.8e+66)
     t_3
     (if (<= (* x y) 3.6e-216)
       t_1
       (if (<= (* x y) 6.4e-40)
         t_2
         (if (<= (* x y) 5500000000000.0)
           t_1
           (if (<= (* x y) 2e+81) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -2.8e+66) {
		tmp = t_3;
	} else if ((x * y) <= 3.6e-216) {
		tmp = t_1;
	} else if ((x * y) <= 6.4e-40) {
		tmp = t_2;
	} else if ((x * y) <= 5500000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e+81) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (c * i)
    t_3 = (x * y) + (a * b)
    if ((x * y) <= (-2.8d+66)) then
        tmp = t_3
    else if ((x * y) <= 3.6d-216) then
        tmp = t_1
    else if ((x * y) <= 6.4d-40) then
        tmp = t_2
    else if ((x * y) <= 5500000000000.0d0) then
        tmp = t_1
    else if ((x * y) <= 2d+81) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -2.8e+66) {
		tmp = t_3;
	} else if ((x * y) <= 3.6e-216) {
		tmp = t_1;
	} else if ((x * y) <= 6.4e-40) {
		tmp = t_2;
	} else if ((x * y) <= 5500000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2e+81) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (c * i)
	t_3 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -2.8e+66:
		tmp = t_3
	elif (x * y) <= 3.6e-216:
		tmp = t_1
	elif (x * y) <= 6.4e-40:
		tmp = t_2
	elif (x * y) <= 5500000000000.0:
		tmp = t_1
	elif (x * y) <= 2e+81:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	t_3 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -2.8e+66)
		tmp = t_3;
	elseif (Float64(x * y) <= 3.6e-216)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.4e-40)
		tmp = t_2;
	elseif (Float64(x * y) <= 5500000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+81)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (c * i);
	t_3 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -2.8e+66)
		tmp = t_3;
	elseif ((x * y) <= 3.6e-216)
		tmp = t_1;
	elseif ((x * y) <= 6.4e-40)
		tmp = t_2;
	elseif ((x * y) <= 5500000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 2e+81)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.8e+66], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 3.6e-216], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.4e-40], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5500000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+81], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.8000000000000001e66 or 1.99999999999999984e81 < (*.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in c around 0 80.9%

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

   4. Taylor expanded in t around 0 70.0%

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

   if -2.8000000000000001e66 < (*.f64 x y) < 3.5999999999999999e-216 or 6.40000000000000004e-40 < (*.f64 x y) < 5.5e12

   1. Initial program 94.1%

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

   3. Taylor expanded in c around 0 77.2%

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

   4. Taylor expanded in x around 0 75.5%

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

   if 3.5999999999999999e-216 < (*.f64 x y) < 6.40000000000000004e-40 or 5.5e12 < (*.f64 x y) < 1.99999999999999984e81

   1. Initial program 95.8%

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

   3. Taylor expanded in x around 0 89.3%

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

   4. Taylor expanded in t around 0 77.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+66}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-216}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 5500000000000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+81}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+127}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.05 \cdot 10^{+63}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -2.05 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.7 \cdot 10^{-151}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+152}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.25e+127)
   (* c i)
   (if (<= (* c i) -2.05e+63)
     (* a b)
     (if (<= (* c i) -2.05e-8)
       (* x y)
       (if (<= (* c i) -4.7e-151)
         (* a b)
         (if (<= (* c i) 5e+152) (* 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) <= -1.25e+127) {
		tmp = c * i;
	} else if ((c * i) <= -2.05e+63) {
		tmp = a * b;
	} else if ((c * i) <= -2.05e-8) {
		tmp = x * y;
	} else if ((c * i) <= -4.7e-151) {
		tmp = a * b;
	} else if ((c * i) <= 5e+152) {
		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) <= (-1.25d+127)) then
        tmp = c * i
    else if ((c * i) <= (-2.05d+63)) then
        tmp = a * b
    else if ((c * i) <= (-2.05d-8)) then
        tmp = x * y
    else if ((c * i) <= (-4.7d-151)) then
        tmp = a * b
    else if ((c * i) <= 5d+152) 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) <= -1.25e+127) {
		tmp = c * i;
	} else if ((c * i) <= -2.05e+63) {
		tmp = a * b;
	} else if ((c * i) <= -2.05e-8) {
		tmp = x * y;
	} else if ((c * i) <= -4.7e-151) {
		tmp = a * b;
	} else if ((c * i) <= 5e+152) {
		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) <= -1.25e+127:
		tmp = c * i
	elif (c * i) <= -2.05e+63:
		tmp = a * b
	elif (c * i) <= -2.05e-8:
		tmp = x * y
	elif (c * i) <= -4.7e-151:
		tmp = a * b
	elif (c * i) <= 5e+152:
		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) <= -1.25e+127)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.05e+63)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= -2.05e-8)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -4.7e-151)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 5e+152)
		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) <= -1.25e+127)
		tmp = c * i;
	elseif ((c * i) <= -2.05e+63)
		tmp = a * b;
	elseif ((c * i) <= -2.05e-8)
		tmp = x * y;
	elseif ((c * i) <= -4.7e-151)
		tmp = a * b;
	elseif ((c * i) <= 5e+152)
		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], -1.25e+127], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.05e+63], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.05e-8], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4.7e-151], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+152], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.2500000000000001e127 or 5e152 < (*.f64 c i)

   1. Initial program 84.2%

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

   3. Taylor expanded in c around inf 66.1%

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

   if -1.2500000000000001e127 < (*.f64 c i) < -2.04999999999999996e63 or -2.05000000000000016e-8 < (*.f64 c i) < -4.70000000000000029e-151

   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 65.8%

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

   if -2.04999999999999996e63 < (*.f64 c i) < -2.05000000000000016e-8

   1. Initial program 85.7%

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

   3. Taylor expanded in x around inf 51.4%

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

   if -4.70000000000000029e-151 < (*.f64 c i) < 5e152

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 43.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+127}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.05 \cdot 10^{+63}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -2.05 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.7 \cdot 10^{-151}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+152}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * 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 = (x * y) + (c * 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 = (x * y) + (c * 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(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(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[(N[(x * y), $MachinePrecision] + N[(c * i), $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 z around 0 17.6%

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

   4. Taylor expanded in a around 0 47.4%

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

4. Final simplification 96.5%

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

Alternative 7: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))))
   (if (<= (* x y) -4e+142)
     t_1
     (if (<= (* x y) 1.2e+77)
       (+ (* c i) (+ (* a b) (* z t)))
       (if (<= (* x y) 3.4e+217) t_1 (+ (* x y) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if ((x * y) <= -4e+142) {
		tmp = t_1;
	} else if ((x * y) <= 1.2e+77) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((x * y) <= 3.4e+217) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + ((x * y) + (z * t))
    if ((x * y) <= (-4d+142)) then
        tmp = t_1
    else if ((x * y) <= 1.2d+77) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((x * y) <= 3.4d+217) then
        tmp = t_1
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double tmp;
	if ((x * y) <= -4e+142) {
		tmp = t_1;
	} else if ((x * y) <= 1.2e+77) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((x * y) <= 3.4e+217) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + ((x * y) + (z * t))
	tmp = 0
	if (x * y) <= -4e+142:
		tmp = t_1
	elif (x * y) <= 1.2e+77:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (x * y) <= 3.4e+217:
		tmp = t_1
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -4e+142)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.2e+77)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(x * y) <= 3.4e+217)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + ((x * y) + (z * t));
	tmp = 0.0;
	if ((x * y) <= -4e+142)
		tmp = t_1;
	elseif ((x * y) <= 1.2e+77)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((x * y) <= 3.4e+217)
		tmp = t_1;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4e+142], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.2e+77], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.4e+217], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000002e142 or 1.1999999999999999e77 < (*.f64 x y) < 3.3999999999999999e217

   1. Initial program 95.4%

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

   3. Taylor expanded in c around 0 87.6%

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

   if -4.0000000000000002e142 < (*.f64 x y) < 1.1999999999999999e77

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 90.5%

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

   if 3.3999999999999999e217 < (*.f64 x y)

   1. Initial program 75.0%

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

   3. Taylor expanded in z around 0 80.0%

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

   4. Taylor expanded in a around 0 90.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+142}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+77}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+217}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5.2 \cdot 10^{+173}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.12e+195)
   (* c i)
   (if (<= (* c i) 5.2e+173)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.12e+195) {
		tmp = c * i;
	} else if ((c * i) <= 5.2e+173) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.12d+195)) then
        tmp = c * i
    else if ((c * i) <= 5.2d+173) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.12e+195) {
		tmp = c * i;
	} else if ((c * i) <= 5.2e+173) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.12e+195:
		tmp = c * i
	elif (c * i) <= 5.2e+173:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.12e+195)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 5.2e+173)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.12e+195)
		tmp = c * i;
	elseif ((c * i) <= 5.2e+173)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.12e+195], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.2e+173], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.12000000000000004e195

   1. Initial program 86.2%

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

   3. Taylor expanded in c around inf 85.0%

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

   if -1.12000000000000004e195 < (*.f64 c i) < 5.1999999999999997e173

   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 c around 0 88.7%

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

   if 5.1999999999999997e173 < (*.f64 c i)

   1. Initial program 74.2%

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

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in a around 0 84.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.12 \cdot 10^{+195}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 5.2 \cdot 10^{+173}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{+52}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.6e+52)
   (+ (* c i) (+ (* x y) (* a b)))
   (if (<= (* c i) 5.8e+174)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.6e+52) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((c * i) <= 5.8e+174) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.6d+52)) then
        tmp = (c * i) + ((x * y) + (a * b))
    else if ((c * i) <= 5.8d+174) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.6e+52) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else if ((c * i) <= 5.8e+174) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.6e+52:
		tmp = (c * i) + ((x * y) + (a * b))
	elif (c * i) <= 5.8e+174:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.6e+52)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	elseif (Float64(c * i) <= 5.8e+174)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.6e+52)
		tmp = (c * i) + ((x * y) + (a * b));
	elseif ((c * i) <= 5.8e+174)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.6e+52], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.8e+174], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.6e52

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 84.3%

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

   if -3.6e52 < (*.f64 c i) < 5.7999999999999999e174

   1. Initial program 97.5%

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

   3. Taylor expanded in c around 0 91.2%

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

   if 5.7999999999999999e174 < (*.f64 c i)

   1. Initial program 74.2%

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

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in a around 0 84.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{+52}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+126}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.65 \cdot 10^{-147}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 10^{+151}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.9e+126)
   (* c i)
   (if (<= (* c i) -1.65e-147)
     (* a b)
     (if (<= (* c i) 1e+151) (* 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) <= -3.9e+126) {
		tmp = c * i;
	} else if ((c * i) <= -1.65e-147) {
		tmp = a * b;
	} else if ((c * i) <= 1e+151) {
		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) <= (-3.9d+126)) then
        tmp = c * i
    else if ((c * i) <= (-1.65d-147)) then
        tmp = a * b
    else if ((c * i) <= 1d+151) 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) <= -3.9e+126) {
		tmp = c * i;
	} else if ((c * i) <= -1.65e-147) {
		tmp = a * b;
	} else if ((c * i) <= 1e+151) {
		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) <= -3.9e+126:
		tmp = c * i
	elif (c * i) <= -1.65e-147:
		tmp = a * b
	elif (c * i) <= 1e+151:
		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) <= -3.9e+126)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.65e-147)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1e+151)
		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) <= -3.9e+126)
		tmp = c * i;
	elseif ((c * i) <= -1.65e-147)
		tmp = a * b;
	elseif ((c * i) <= 1e+151)
		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], -3.9e+126], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.65e-147], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+151], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.89999999999999993e126 or 1.00000000000000002e151 < (*.f64 c i)

   1. Initial program 84.2%

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

   3. Taylor expanded in c around inf 66.1%

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

   if -3.89999999999999993e126 < (*.f64 c i) < -1.64999999999999994e-147

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 52.4%

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

   if -1.64999999999999994e-147 < (*.f64 c i) < 1.00000000000000002e151

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 43.1%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.9 \cdot 10^{+126}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.65 \cdot 10^{-147}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 10^{+151}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+177}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.75e+53)
   (+ (* a b) (* c i))
   (if (<= (* c i) 3e+177) (+ (* a b) (* 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) <= -1.75e+53) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 3e+177) {
		tmp = (a * b) + (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) <= (-1.75d+53)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 3d+177) then
        tmp = (a * b) + (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) <= -1.75e+53) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 3e+177) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.75e+53:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 3e+177:
		tmp = (a * b) + (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) <= -1.75e+53)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 3e+177)
		tmp = Float64(Float64(a * b) + 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) <= -1.75e+53)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 3e+177)
		tmp = (a * b) + (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], -1.75e+53], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3e+177], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.75000000000000009e53

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 78.2%

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

   4. Taylor expanded in t around 0 67.7%

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

   if -1.75000000000000009e53 < (*.f64 c i) < 3e177

   1. Initial program 97.5%

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

   3. Taylor expanded in c around 0 91.2%

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

   4. Taylor expanded in x around 0 67.3%

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

   if 3e177 < (*.f64 c i)

   1. Initial program 74.2%

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

   3. Taylor expanded in c around inf 68.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{+53}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+177}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7 \cdot 10^{+128} \lor \neg \left(c \cdot i \leq 10^{+173}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -7e+128) (not (<= (* c i) 1e+173))) (* 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) <= -7e+128) || !((c * i) <= 1e+173)) {
		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) <= (-7d+128)) .or. (.not. ((c * i) <= 1d+173))) 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) <= -7e+128) || !((c * i) <= 1e+173)) {
		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) <= -7e+128) or not ((c * i) <= 1e+173):
		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) <= -7e+128) || !(Float64(c * i) <= 1e+173))
		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) <= -7e+128) || ~(((c * i) <= 1e+173)))
		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], -7e+128], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1e+173]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -6.99999999999999937e128 or 1e173 < (*.f64 c i)

   1. Initial program 83.5%

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

   3. Taylor expanded in c around inf 68.5%

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

   if -6.99999999999999937e128 < (*.f64 c i) < 1e173

   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 a around inf 34.6%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7 \cdot 10^{+128} \lor \neg \left(c \cdot i \leq 10^{+173}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.6% 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 93.4%

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

3. Taylor expanded in a around inf 27.4%

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

4. Final simplification 27.4%

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

Reproduce

herbie shell --seed 2024080 
(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)))