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

Percentage Accurate: 95.8% → 97.7%

Time: 10.3s

Alternatives: 14

Speedup: 0.4×

• 40.9% 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: 97.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) 5e+257)
   (fma c i (fma a b (fma x y (* z t))))
   (fma x y (fma 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 ((c * i) <= 5e+257) {
		tmp = fma(c, i, fma(a, b, fma(x, y, (z * t))));
	} else {
		tmp = fma(x, y, fma(a, b, (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= 5e+257)
		tmp = fma(c, i, fma(a, b, fma(x, y, Float64(z * t))));
	else
		tmp = fma(x, y, fma(a, b, Float64(c * i)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], 5e+257], N[(c * i + N[(a * b + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y + N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < 5.00000000000000028e257

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. fma-def 99.1%

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

      3. +-commutative 99.1%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

   if 5.00000000000000028e257 < (*.f64 c i)

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-+r+ 73.1%

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

      2. fma-udef 84.6%

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

      3. +-commutative 84.6%

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

      4. fma-def 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, c \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \left(a \cdot b + x \cdot y\right) + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) 5e+257)
   (fma c i (+ (+ (* a b) (* x y)) (* z t)))
   (fma x y (fma 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 ((c * i) <= 5e+257) {
		tmp = fma(c, i, (((a * b) + (x * y)) + (z * t)));
	} else {
		tmp = fma(x, y, fma(a, b, (c * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= 5e+257)
		tmp = fma(c, i, Float64(Float64(Float64(a * b) + Float64(x * y)) + Float64(z * t)));
	else
		tmp = fma(x, y, fma(a, b, Float64(c * i)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], 5e+257], N[(c * i + N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y + N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < 5.00000000000000028e257

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. fma-def 99.1%

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

      3. +-commutative 99.1%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-def 100.0%

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

      2. fma-udef 99.1%

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

      3. associate-+r+ 99.1%

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

   6. Applied egg-rr 99.1%

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

   if 5.00000000000000028e257 < (*.f64 c i)

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-+r+ 73.1%

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

      2. fma-udef 84.6%

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

      3. +-commutative 84.6%

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

      4. fma-def 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, c \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \left(a \cdot b + x \cdot y\right) + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(a, b, c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \left(a \cdot b + x \cdot y\right) + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) 5e+307) (fma c i (+ (+ (* a b) (* x y)) (* 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) <= 5e+307) {
		tmp = fma(c, i, (((a * b) + (x * y)) + (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) <= 5e+307)
		tmp = fma(c, i, Float64(Float64(Float64(a * b) + Float64(x * y)) + Float64(z * t)));
	else
		tmp = Float64(c * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], 5e+307], N[(c * i + N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < 5e307

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. fma-def 99.1%

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

      3. +-commutative 99.1%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-def 100.0%

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

      2. fma-udef 99.1%

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

      3. associate-+r+ 99.1%

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

   6. Applied egg-rr 99.1%

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

   if 5e307 < (*.f64 c i)

   1. Initial program 61.9%

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

   3. Taylor expanded in c around inf 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \left(a \cdot b + x \cdot y\right) + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.1 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.55 \cdot 10^{+116} \lor \neg \left(c \cdot i \leq 1.18 \cdot 10^{+138}\right) \land c \cdot i \leq 1.2 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -1.25e+185)
     (* c i)
     (if (<= (* c i) -3.1e+66)
       t_1
       (if (<= (* c i) -8e-10)
         (* x y)
         (if (or (<= (* c i) 2.55e+116)
                 (and (not (<= (* c i) 1.18e+138)) (<= (* c i) 1.2e+193)))
           t_1
           (* 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) + (z * t);
	double tmp;
	if ((c * i) <= -1.25e+185) {
		tmp = c * i;
	} else if ((c * i) <= -3.1e+66) {
		tmp = t_1;
	} else if ((c * i) <= -8e-10) {
		tmp = x * y;
	} else if (((c * i) <= 2.55e+116) || (!((c * i) <= 1.18e+138) && ((c * i) <= 1.2e+193))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-1.25d+185)) then
        tmp = c * i
    else if ((c * i) <= (-3.1d+66)) then
        tmp = t_1
    else if ((c * i) <= (-8d-10)) then
        tmp = x * y
    else if (((c * i) <= 2.55d+116) .or. (.not. ((c * i) <= 1.18d+138)) .and. ((c * i) <= 1.2d+193)) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.25e+185) {
		tmp = c * i;
	} else if ((c * i) <= -3.1e+66) {
		tmp = t_1;
	} else if ((c * i) <= -8e-10) {
		tmp = x * y;
	} else if (((c * i) <= 2.55e+116) || (!((c * i) <= 1.18e+138) && ((c * i) <= 1.2e+193))) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -1.25e+185:
		tmp = c * i
	elif (c * i) <= -3.1e+66:
		tmp = t_1
	elif (c * i) <= -8e-10:
		tmp = x * y
	elif ((c * i) <= 2.55e+116) or (not ((c * i) <= 1.18e+138) and ((c * i) <= 1.2e+193)):
		tmp = t_1
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.25e+185)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -3.1e+66)
		tmp = t_1;
	elseif (Float64(c * i) <= -8e-10)
		tmp = Float64(x * y);
	elseif ((Float64(c * i) <= 2.55e+116) || (!(Float64(c * i) <= 1.18e+138) && (Float64(c * i) <= 1.2e+193)))
		tmp = t_1;
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.25e+185)
		tmp = c * i;
	elseif ((c * i) <= -3.1e+66)
		tmp = t_1;
	elseif ((c * i) <= -8e-10)
		tmp = x * y;
	elseif (((c * i) <= 2.55e+116) || (~(((c * i) <= 1.18e+138)) && ((c * i) <= 1.2e+193)))
		tmp = t_1;
	else
		tmp = 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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.25e+185], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -3.1e+66], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -8e-10], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], 2.55e+116], And[N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.18e+138]], $MachinePrecision], LessEqual[N[(c * i), $MachinePrecision], 1.2e+193]]], t$95$1, N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.24999999999999997e185 or 2.55e116 < (*.f64 c i) < 1.18000000000000007e138 or 1.2e193 < (*.f64 c i)

   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 c around inf 84.6%

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

   if -1.24999999999999997e185 < (*.f64 c i) < -3.10000000000000019e66 or -8.00000000000000029e-10 < (*.f64 c i) < 2.55e116 or 1.18000000000000007e138 < (*.f64 c i) < 1.2e193

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 72.7%

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

   4. Taylor expanded in c around 0 66.7%

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

   if -3.10000000000000019e66 < (*.f64 c i) < -8.00000000000000029e-10

   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 58.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.1 \cdot 10^{+66}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.55 \cdot 10^{+116} \lor \neg \left(c \cdot i \leq 1.18 \cdot 10^{+138}\right) \land c \cdot i \leq 1.2 \cdot 10^{+193}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.2 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.1 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -2.4 \cdot 10^{-135}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-313}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{-274}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -8.2e+185)
   (* c i)
   (if (<= (* c i) -1.1e-12)
     (* x y)
     (if (<= (* c i) -2.4e-135)
       (* z t)
       (if (<= (* c i) -2e-313)
         (* a b)
         (if (<= (* c i) 4.4e-274)
           (* z t)
           (if (<= (* c i) 1.55e+68) (* 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 ((c * i) <= -8.2e+185) {
		tmp = c * i;
	} else if ((c * i) <= -1.1e-12) {
		tmp = x * y;
	} else if ((c * i) <= -2.4e-135) {
		tmp = z * t;
	} else if ((c * i) <= -2e-313) {
		tmp = a * b;
	} else if ((c * i) <= 4.4e-274) {
		tmp = z * t;
	} else if ((c * i) <= 1.55e+68) {
		tmp = a * b;
	} 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) <= (-8.2d+185)) then
        tmp = c * i
    else if ((c * i) <= (-1.1d-12)) then
        tmp = x * y
    else if ((c * i) <= (-2.4d-135)) then
        tmp = z * t
    else if ((c * i) <= (-2d-313)) then
        tmp = a * b
    else if ((c * i) <= 4.4d-274) then
        tmp = z * t
    else if ((c * i) <= 1.55d+68) then
        tmp = a * b
    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) <= -8.2e+185) {
		tmp = c * i;
	} else if ((c * i) <= -1.1e-12) {
		tmp = x * y;
	} else if ((c * i) <= -2.4e-135) {
		tmp = z * t;
	} else if ((c * i) <= -2e-313) {
		tmp = a * b;
	} else if ((c * i) <= 4.4e-274) {
		tmp = z * t;
	} else if ((c * i) <= 1.55e+68) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -8.2e+185:
		tmp = c * i
	elif (c * i) <= -1.1e-12:
		tmp = x * y
	elif (c * i) <= -2.4e-135:
		tmp = z * t
	elif (c * i) <= -2e-313:
		tmp = a * b
	elif (c * i) <= 4.4e-274:
		tmp = z * t
	elif (c * i) <= 1.55e+68:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -8.2e+185)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.1e-12)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -2.4e-135)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -2e-313)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.4e-274)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.55e+68)
		tmp = Float64(a * b);
	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) <= -8.2e+185)
		tmp = c * i;
	elseif ((c * i) <= -1.1e-12)
		tmp = x * y;
	elseif ((c * i) <= -2.4e-135)
		tmp = z * t;
	elseif ((c * i) <= -2e-313)
		tmp = a * b;
	elseif ((c * i) <= 4.4e-274)
		tmp = z * t;
	elseif ((c * i) <= 1.55e+68)
		tmp = a * b;
	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], -8.2e+185], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.1e-12], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.4e-135], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2e-313], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.4e-274], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.55e+68], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -8.2e185 or 1.5499999999999999e68 < (*.f64 c i)

   1. Initial program 88.4%

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

   3. Taylor expanded in c around inf 73.0%

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

   if -8.2e185 < (*.f64 c i) < -1.09999999999999996e-12

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 46.9%

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

   if -1.09999999999999996e-12 < (*.f64 c i) < -2.3999999999999999e-135 or -1.99999999998e-313 < (*.f64 c i) < 4.3999999999999999e-274

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 50.9%

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

   if -2.3999999999999999e-135 < (*.f64 c i) < -1.99999999998e-313 or 4.3999999999999999e-274 < (*.f64 c i) < 1.5499999999999999e68

   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 43.1%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.2 \cdot 10^{+185}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.1 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -2.4 \cdot 10^{-135}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2 \cdot 10^{-313}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{-274}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.3 \cdot 10^{+190}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.45 \cdot 10^{+69} \lor \neg \left(c \cdot i \leq 2.45 \cdot 10^{+134}\right) \land c \cdot i \leq 1.3 \cdot 10^{+195}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6.3e+190)
   (+ (* c i) (* x y))
   (if (or (<= (* c i) 1.45e+69)
           (and (not (<= (* c i) 2.45e+134)) (<= (* c i) 1.3e+195)))
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* c i) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.3e+190) {
		tmp = (c * i) + (x * y);
	} else if (((c * i) <= 1.45e+69) || (!((c * i) <= 2.45e+134) && ((c * i) <= 1.3e+195))) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-6.3d+190)) then
        tmp = (c * i) + (x * y)
    else if (((c * i) <= 1.45d+69) .or. (.not. ((c * i) <= 2.45d+134)) .and. ((c * i) <= 1.3d+195)) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.3e+190) {
		tmp = (c * i) + (x * y);
	} else if (((c * i) <= 1.45e+69) || (!((c * i) <= 2.45e+134) && ((c * i) <= 1.3e+195))) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -6.3e+190:
		tmp = (c * i) + (x * y)
	elif ((c * i) <= 1.45e+69) or (not ((c * i) <= 2.45e+134) and ((c * i) <= 1.3e+195)):
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -6.3e+190)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif ((Float64(c * i) <= 1.45e+69) || (!(Float64(c * i) <= 2.45e+134) && (Float64(c * i) <= 1.3e+195)))
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -6.3e+190)
		tmp = (c * i) + (x * y);
	elseif (((c * i) <= 1.45e+69) || (~(((c * i) <= 2.45e+134)) && ((c * i) <= 1.3e+195)))
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -6.3e+190], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], 1.45e+69], And[N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.45e+134]], $MachinePrecision], LessEqual[N[(c * i), $MachinePrecision], 1.3e+195]]], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.3000000000000002e190

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 91.7%

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

   4. Taylor expanded in t around 0 88.9%

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

   if -6.3000000000000002e190 < (*.f64 c i) < 1.4499999999999999e69 or 2.44999999999999998e134 < (*.f64 c i) < 1.30000000000000001e195

   1. Initial program 99.4%

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

   3. Taylor expanded in c around 0 92.8%

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

   if 1.4499999999999999e69 < (*.f64 c i) < 2.44999999999999998e134 or 1.30000000000000001e195 < (*.f64 c i)

   1. Initial program 81.3%

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

   3. Taylor expanded in a around 0 85.6%

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

   4. Taylor expanded in x around 0 90.2%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.3 \cdot 10^{+190}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.45 \cdot 10^{+69} \lor \neg \left(c \cdot i \leq 2.45 \cdot 10^{+134}\right) \land c \cdot i \leq 1.3 \cdot 10^{+195}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+270}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.55 \cdot 10^{+159} \lor \neg \left(x \cdot y \leq -5 \cdot 10^{+74}\right) \land x \cdot y \leq 2.1 \cdot 10^{-168}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4.5e+270)
   (* x y)
   (if (or (<= (* x y) -1.55e+159)
           (and (not (<= (* x y) -5e+74)) (<= (* x y) 2.1e-168)))
     (+ (* 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) <= -4.5e+270) {
		tmp = x * y;
	} else if (((x * y) <= -1.55e+159) || (!((x * y) <= -5e+74) && ((x * y) <= 2.1e-168))) {
		tmp = (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) <= (-4.5d+270)) then
        tmp = x * y
    else if (((x * y) <= (-1.55d+159)) .or. (.not. ((x * y) <= (-5d+74))) .and. ((x * y) <= 2.1d-168)) then
        tmp = (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) <= -4.5e+270) {
		tmp = x * y;
	} else if (((x * y) <= -1.55e+159) || (!((x * y) <= -5e+74) && ((x * y) <= 2.1e-168))) {
		tmp = (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) <= -4.5e+270:
		tmp = x * y
	elif ((x * y) <= -1.55e+159) or (not ((x * y) <= -5e+74) and ((x * y) <= 2.1e-168)):
		tmp = (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) <= -4.5e+270)
		tmp = Float64(x * y);
	elseif ((Float64(x * y) <= -1.55e+159) || (!(Float64(x * y) <= -5e+74) && (Float64(x * y) <= 2.1e-168)))
		tmp = 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) <= -4.5e+270)
		tmp = x * y;
	elseif (((x * y) <= -1.55e+159) || (~(((x * y) <= -5e+74)) && ((x * y) <= 2.1e-168)))
		tmp = (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], -4.5e+270], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.55e+159], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], -5e+74]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 2.1e-168]]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.5000000000000004e270

   1. Initial program 78.3%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -4.5000000000000004e270 < (*.f64 x y) < -1.5499999999999999e159 or -4.99999999999999963e74 < (*.f64 x y) < 2.09999999999999994e-168

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 80.9%

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

   4. Taylor expanded in x around 0 75.8%

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

   if -1.5499999999999999e159 < (*.f64 x y) < -4.99999999999999963e74 or 2.09999999999999994e-168 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 88.6%

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

      1. associate-+r+ 88.6%

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

      2. fma-udef 90.4%

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

      3. +-commutative 90.4%

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

      4. fma-def 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in c around 0 73.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+270}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.55 \cdot 10^{+159} \lor \neg \left(x \cdot y \leq -5 \cdot 10^{+74}\right) \land x \cdot y \leq 2.1 \cdot 10^{-168}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.0% accurate, 0.4× speedup

Math

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

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 (* 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 = 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 = 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 = 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(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 = 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[(c * i), $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 c around inf 67.4%

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

4. Final simplification 98.5%

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

Alternative 9: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;i \leq -1.66 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= i -1.66e-9)
     (* c i)
     (if (<= i 3e-302)
       t_1
       (if (<= i 4.8e+70)
         (+ (* a b) (* x y))
         (if (<= i 7.6e+192) t_1 (* 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) + (z * t);
	double tmp;
	if (i <= -1.66e-9) {
		tmp = c * i;
	} else if (i <= 3e-302) {
		tmp = t_1;
	} else if (i <= 4.8e+70) {
		tmp = (a * b) + (x * y);
	} else if (i <= 7.6e+192) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if (i <= (-1.66d-9)) then
        tmp = c * i
    else if (i <= 3d-302) then
        tmp = t_1
    else if (i <= 4.8d+70) then
        tmp = (a * b) + (x * y)
    else if (i <= 7.6d+192) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double tmp;
	if (i <= -1.66e-9) {
		tmp = c * i;
	} else if (i <= 3e-302) {
		tmp = t_1;
	} else if (i <= 4.8e+70) {
		tmp = (a * b) + (x * y);
	} else if (i <= 7.6e+192) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if i <= -1.66e-9:
		tmp = c * i
	elif i <= 3e-302:
		tmp = t_1
	elif i <= 4.8e+70:
		tmp = (a * b) + (x * y)
	elif i <= 7.6e+192:
		tmp = t_1
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (i <= -1.66e-9)
		tmp = Float64(c * i);
	elseif (i <= 3e-302)
		tmp = t_1;
	elseif (i <= 4.8e+70)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (i <= 7.6e+192)
		tmp = t_1;
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if (i <= -1.66e-9)
		tmp = c * i;
	elseif (i <= 3e-302)
		tmp = t_1;
	elseif (i <= 4.8e+70)
		tmp = (a * b) + (x * y);
	elseif (i <= 7.6e+192)
		tmp = t_1;
	else
		tmp = 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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.66e-9], N[(c * i), $MachinePrecision], If[LessEqual[i, 3e-302], t$95$1, If[LessEqual[i, 4.8e+70], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.6e+192], t$95$1, N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.6600000000000001e-9 or 7.5999999999999999e192 < i

   1. Initial program 90.9%

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

   3. Taylor expanded in c around inf 55.2%

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

   if -1.6600000000000001e-9 < i < 2.99999999999999989e-302 or 4.79999999999999974e70 < i < 7.5999999999999999e192

   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 76.6%

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

   4. Taylor expanded in c around 0 61.3%

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

   if 2.99999999999999989e-302 < i < 4.79999999999999974e70

   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 z around 0 78.0%

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

      1. associate-+r+ 78.0%

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

      2. fma-udef 79.3%

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

      3. +-commutative 79.3%

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

      4. fma-def 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in c around 0 58.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.66 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-302}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{+192}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+186}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.18 \cdot 10^{+57}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5.5e+186)
   (+ (* c i) (* x y))
   (if (<= (* c i) 1.18e+57)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5.5e+186) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= 1.18e+57) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-5.5d+186)) then
        tmp = (c * i) + (x * y)
    else if ((c * i) <= 1.18d+57) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -5.5e+186) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= 1.18e+57) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5.5e+186:
		tmp = (c * i) + (x * y)
	elif (c * i) <= 1.18e+57:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -5.5e+186)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(c * i) <= 1.18e+57)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -5.5e+186)
		tmp = (c * i) + (x * y);
	elseif ((c * i) <= 1.18e+57)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5.5e+186], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.18e+57], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.4999999999999996e186

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 91.7%

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

   4. Taylor expanded in t around 0 88.9%

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

   if -5.4999999999999996e186 < (*.f64 c i) < 1.18e57

   1. Initial program 99.3%

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

   3. Taylor expanded in c around 0 93.1%

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

   if 1.18e57 < (*.f64 c i)

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 82.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+186}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.18 \cdot 10^{+57}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1.75 \cdot 10^{-5}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 4.1 \cdot 10^{+49}:\\ \;\;\;\;c \cdot i + t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* a b) -1.75e-5)
     (+ (* c i) (+ (* a b) (* z t)))
     (if (<= (* a b) 4.1e+49) (+ (* c i) t_1) (+ (* a b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -1.75e-5) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((a * b) <= 4.1e+49) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((a * b) <= (-1.75d-5)) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((a * b) <= 4.1d+49) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((a * b) <= -1.75e-5) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((a * b) <= 4.1e+49) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (a * b) <= -1.75e-5:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (a * b) <= 4.1e+49:
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -1.75e-5)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(a * b) <= 4.1e+49)
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -1.75e-5)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((a * b) <= 4.1e+49)
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.75e-5], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.1e+49], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.7499999999999998e-5

   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 x around 0 82.9%

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

   if -1.7499999999999998e-5 < (*.f64 a b) < 4.1e49

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0 95.8%

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

   if 4.1e49 < (*.f64 a b)

   1. Initial program 91.7%

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

   3. Taylor expanded in c around 0 90.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.75 \cdot 10^{-5}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 4.1 \cdot 10^{+49}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+165}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+99} \lor \neg \left(x \leq 2.25 \cdot 10^{-95}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.25e+165)
   (+ (* c i) (* x y))
   (if (or (<= x -7.5e+99) (not (<= x 2.25e-95)))
     (+ (* a b) (* x y))
     (+ (* 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 <= -2.25e+165) {
		tmp = (c * i) + (x * y);
	} else if ((x <= -7.5e+99) || !(x <= 2.25e-95)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-2.25d+165)) then
        tmp = (c * i) + (x * y)
    else if ((x <= (-7.5d+99)) .or. (.not. (x <= 2.25d-95))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.25e+165) {
		tmp = (c * i) + (x * y);
	} else if ((x <= -7.5e+99) || !(x <= 2.25e-95)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -2.25e+165:
		tmp = (c * i) + (x * y)
	elif (x <= -7.5e+99) or not (x <= 2.25e-95):
		tmp = (a * b) + (x * y)
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.25e+165)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif ((x <= -7.5e+99) || !(x <= 2.25e-95))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -2.25e+165)
		tmp = (c * i) + (x * y);
	elseif ((x <= -7.5e+99) || ~((x <= 2.25e-95)))
		tmp = (a * b) + (x * y);
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.25e+165], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7.5e+99], N[Not[LessEqual[x, 2.25e-95]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2499999999999998e165

   1. Initial program 96.7%

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

   3. Taylor expanded in a around 0 77.0%

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

   4. Taylor expanded in t around 0 67.2%

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

   if -2.2499999999999998e165 < x < -7.49999999999999963e99 or 2.25e-95 < x

   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 77.2%

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

      1. associate-+r+ 77.2%

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

      2. fma-udef 79.2%

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

      3. +-commutative 79.2%

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

      4. fma-def 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in c around 0 66.2%

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

   if -7.49999999999999963e99 < x < 2.25e-95

   1. Initial program 97.6%

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

   3. Taylor expanded in a around 0 73.2%

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

   4. Taylor expanded in x around 0 66.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+165}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+99} \lor \neg \left(x \leq 2.25 \cdot 10^{-95}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+184} \lor \neg \left(c \cdot i \leq 1.9 \cdot 10^{+68}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -8.5e+184) (not (<= (* c i) 1.9e+68))) (* 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) <= -8.5e+184) || !((c * i) <= 1.9e+68)) {
		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) <= (-8.5d+184)) .or. (.not. ((c * i) <= 1.9d+68))) 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) <= -8.5e+184) || !((c * i) <= 1.9e+68)) {
		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) <= -8.5e+184) or not ((c * i) <= 1.9e+68):
		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) <= -8.5e+184) || !(Float64(c * i) <= 1.9e+68))
		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) <= -8.5e+184) || ~(((c * i) <= 1.9e+68)))
		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], -8.5e+184], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.9e+68]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -8.50000000000000043e184 or 1.9e68 < (*.f64 c i)

   1. Initial program 88.5%

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

   3. Taylor expanded in c around inf 72.3%

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

   if -8.50000000000000043e184 < (*.f64 c i) < 1.9e68

   1. Initial program 99.4%

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

   3. Taylor expanded in a around inf 35.8%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+184} \lor \neg \left(c \cdot i \leq 1.9 \cdot 10^{+68}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.2% 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 95.3%

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

3. Taylor expanded in a around inf 27.5%

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

4. Final simplification 27.5%

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

Reproduce

herbie shell --seed 2024017 
(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)))