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

Percentage Accurate: 95.4% → 97.5%

Time: 12.3s

Alternatives: 15

Speedup: 0.4×

• 41.3% 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: 95.4% 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: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(c * i), $MachinePrecision] + N[(y * x + N[(z * t + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(a * b), $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
   3. Step-by-step derivation

      1. associate-+l+ 100.0%

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

      2. fma-udef 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   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 18.2%

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

      1. +-commutative 18.2%

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

      2. *-commutative 18.2%

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

      3. fma-def 27.3%

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

   5. Applied egg-rr 27.3%

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

   6. Taylor expanded in c around 0 73.0%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   7. Step-by-step derivation

      1. +-commutative 18.2%

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

      2. *-commutative 18.2%

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

      3. fma-def 27.3%

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

   8. Applied egg-rr 82.1%

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

4. Final simplification 99.2%

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

Alternative 2: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. +-commutative 95.7%

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

   2. fma-def 98.0%

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

   3. associate-+l+ 98.0%

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

   4. fma-def 98.4%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

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 = fma(y, x, (a * b));
	}
	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 = fma(y, x, Float64(a * b));
	end
	return 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[(y * x + N[(a * b), $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 18.2%

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

      1. +-commutative 18.2%

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

      2. *-commutative 18.2%

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

      3. fma-def 27.3%

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

   5. Applied egg-rr 27.3%

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

   6. Taylor expanded in c around 0 73.0%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
   7. Step-by-step derivation

      1. +-commutative 18.2%

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

      2. *-commutative 18.2%

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

      3. fma-def 27.3%

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

   8. Applied egg-rr 82.1%

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

4. Final simplification 99.2%

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

Alternative 4: 65.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := c \cdot i + z \cdot t\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{+156}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -7.8 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -1.45 \cdot 10^{-296}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 240:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+97}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y)))
        (t_2 (+ (* c i) (* z t)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.55e+185)
     t_1
     (if (<= (* x y) -2.3e+156)
       t_2
       (if (<= (* x y) -5e+19)
         t_1
         (if (<= (* x y) -7.8e-164)
           t_2
           (if (<= (* x y) -1.45e-296)
             t_3
             (if (<= (* x y) 240.0)
               t_2
               (if (<= (* x y) 1.9e+97) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (c * i) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.55e+185) {
		tmp = t_1;
	} else if ((x * y) <= -2.3e+156) {
		tmp = t_2;
	} else if ((x * y) <= -5e+19) {
		tmp = t_1;
	} else if ((x * y) <= -7.8e-164) {
		tmp = t_2;
	} else if ((x * y) <= -1.45e-296) {
		tmp = t_3;
	} else if ((x * y) <= 240.0) {
		tmp = t_2;
	} else if ((x * y) <= 1.9e+97) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (c * i) + (z * t)
    t_3 = (a * b) + (c * i)
    if ((x * y) <= (-1.55d+185)) then
        tmp = t_1
    else if ((x * y) <= (-2.3d+156)) then
        tmp = t_2
    else if ((x * y) <= (-5d+19)) then
        tmp = t_1
    else if ((x * y) <= (-7.8d-164)) then
        tmp = t_2
    else if ((x * y) <= (-1.45d-296)) then
        tmp = t_3
    else if ((x * y) <= 240.0d0) then
        tmp = t_2
    else if ((x * y) <= 1.9d+97) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (c * i) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -1.55e+185) {
		tmp = t_1;
	} else if ((x * y) <= -2.3e+156) {
		tmp = t_2;
	} else if ((x * y) <= -5e+19) {
		tmp = t_1;
	} else if ((x * y) <= -7.8e-164) {
		tmp = t_2;
	} else if ((x * y) <= -1.45e-296) {
		tmp = t_3;
	} else if ((x * y) <= 240.0) {
		tmp = t_2;
	} else if ((x * y) <= 1.9e+97) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (c * i) + (z * t)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -1.55e+185:
		tmp = t_1
	elif (x * y) <= -2.3e+156:
		tmp = t_2
	elif (x * y) <= -5e+19:
		tmp = t_1
	elif (x * y) <= -7.8e-164:
		tmp = t_2
	elif (x * y) <= -1.45e-296:
		tmp = t_3
	elif (x * y) <= 240.0:
		tmp = t_2
	elif (x * y) <= 1.9e+97:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -1.55e+185)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.3e+156)
		tmp = t_2;
	elseif (Float64(x * y) <= -5e+19)
		tmp = t_1;
	elseif (Float64(x * y) <= -7.8e-164)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.45e-296)
		tmp = t_3;
	elseif (Float64(x * y) <= 240.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.9e+97)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (c * i) + (z * t);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -1.55e+185)
		tmp = t_1;
	elseif ((x * y) <= -2.3e+156)
		tmp = t_2;
	elseif ((x * y) <= -5e+19)
		tmp = t_1;
	elseif ((x * y) <= -7.8e-164)
		tmp = t_2;
	elseif ((x * y) <= -1.45e-296)
		tmp = t_3;
	elseif ((x * y) <= 240.0)
		tmp = t_2;
	elseif ((x * y) <= 1.9e+97)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.55e+185], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e+156], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5e+19], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -7.8e-164], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.45e-296], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 240.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.9e+97], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.55e185 or -2.2999999999999999e156 < (*.f64 x y) < -5e19 or 1.90000000000000018e97 < (*.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 84.8%

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

      1. +-commutative 84.8%

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

      2. *-commutative 84.8%

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

      3. fma-def 85.9%

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

   5. Applied egg-rr 85.9%

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

   6. Taylor expanded in c around 0 83.9%

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

   if -1.55e185 < (*.f64 x y) < -2.2999999999999999e156 or -5e19 < (*.f64 x y) < -7.7999999999999997e-164 or -1.44999999999999991e-296 < (*.f64 x y) < 240

   1. Initial program 96.9%

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

      1. associate-+l+ 96.9%

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

      2. fma-udef 96.9%

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

      3. *-commutative 96.9%

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

      4. fma-def 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in a around 0 76.4%

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

   6. Taylor expanded in x around 0 72.5%

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

   if -7.7999999999999997e-164 < (*.f64 x y) < -1.44999999999999991e-296 or 240 < (*.f64 x y) < 1.90000000000000018e97

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 91.9%

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

   4. Taylor expanded in x around 0 84.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+185}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{+156}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+19}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7.8 \cdot 10^{-164}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.45 \cdot 10^{-296}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 240:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+97}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+185}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.18 \cdot 10^{-147}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -1.55e+185)
     (* x y)
     (if (<= (* x y) -1.75e+149)
       t_1
       (if (<= (* x y) -5.8e+128)
         (* x y)
         (if (<= (* x y) -2.2e-118)
           t_1
           (if (<= (* x y) -1.18e-147)
             (* z t)
             (if (<= (* x y) 4.4e+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) <= -1.55e+185) {
		tmp = x * y;
	} else if ((x * y) <= -1.75e+149) {
		tmp = t_1;
	} else if ((x * y) <= -5.8e+128) {
		tmp = x * y;
	} else if ((x * y) <= -2.2e-118) {
		tmp = t_1;
	} else if ((x * y) <= -1.18e-147) {
		tmp = z * t;
	} else if ((x * y) <= 4.4e+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) <= (-1.55d+185)) then
        tmp = x * y
    else if ((x * y) <= (-1.75d+149)) then
        tmp = t_1
    else if ((x * y) <= (-5.8d+128)) then
        tmp = x * y
    else if ((x * y) <= (-2.2d-118)) then
        tmp = t_1
    else if ((x * y) <= (-1.18d-147)) then
        tmp = z * t
    else if ((x * y) <= 4.4d+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) <= -1.55e+185) {
		tmp = x * y;
	} else if ((x * y) <= -1.75e+149) {
		tmp = t_1;
	} else if ((x * y) <= -5.8e+128) {
		tmp = x * y;
	} else if ((x * y) <= -2.2e-118) {
		tmp = t_1;
	} else if ((x * y) <= -1.18e-147) {
		tmp = z * t;
	} else if ((x * y) <= 4.4e+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) <= -1.55e+185:
		tmp = x * y
	elif (x * y) <= -1.75e+149:
		tmp = t_1
	elif (x * y) <= -5.8e+128:
		tmp = x * y
	elif (x * y) <= -2.2e-118:
		tmp = t_1
	elif (x * y) <= -1.18e-147:
		tmp = z * t
	elif (x * y) <= 4.4e+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) <= -1.55e+185)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.75e+149)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.8e+128)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.2e-118)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.18e-147)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 4.4e+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) <= -1.55e+185)
		tmp = x * y;
	elseif ((x * y) <= -1.75e+149)
		tmp = t_1;
	elseif ((x * y) <= -5.8e+128)
		tmp = x * y;
	elseif ((x * y) <= -2.2e-118)
		tmp = t_1;
	elseif ((x * y) <= -1.18e-147)
		tmp = z * t;
	elseif ((x * y) <= 4.4e+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], -1.55e+185], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.75e+149], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.8e+128], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.2e-118], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.18e-147], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.4e+158], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.55e185 or -1.75000000000000006e149 < (*.f64 x y) < -5.8000000000000001e128 or 4.4000000000000002e158 < (*.f64 x y)

   1. Initial program 90.3%

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

   3. Taylor expanded in x around inf 82.7%

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

   if -1.55e185 < (*.f64 x y) < -1.75000000000000006e149 or -5.8000000000000001e128 < (*.f64 x y) < -2.19999999999999984e-118 or -1.18000000000000003e-147 < (*.f64 x y) < 4.4000000000000002e158

   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 z around 0 73.1%

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

   4. Taylor expanded in x around 0 65.1%

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

   if -2.19999999999999984e-118 < (*.f64 x y) < -1.18000000000000003e-147

   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 97.9%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.55 \cdot 10^{+185}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.18 \cdot 10^{-147}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+158}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -1.95 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 9.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{+32} \lor \neg \left(a \cdot b \leq 1.9 \cdot 10^{+146}\right) \land a \cdot b \leq 5.2 \cdot 10^{+172}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* a b) -1.95e+98)
     t_1
     (if (<= (* a b) 9.5e-253)
       (+ (* x y) (* c i))
       (if (or (<= (* a b) 4.2e+32)
               (and (not (<= (* a b) 1.9e+146)) (<= (* a b) 5.2e+172)))
         (+ (* c i) (* z t))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -1.95e+98) {
		tmp = t_1;
	} else if ((a * b) <= 9.5e-253) {
		tmp = (x * y) + (c * i);
	} else if (((a * b) <= 4.2e+32) || (!((a * b) <= 1.9e+146) && ((a * b) <= 5.2e+172))) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((a * b) <= (-1.95d+98)) then
        tmp = t_1
    else if ((a * b) <= 9.5d-253) then
        tmp = (x * y) + (c * i)
    else if (((a * b) <= 4.2d+32) .or. (.not. ((a * b) <= 1.9d+146)) .and. ((a * b) <= 5.2d+172)) then
        tmp = (c * i) + (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -1.95e+98) {
		tmp = t_1;
	} else if ((a * b) <= 9.5e-253) {
		tmp = (x * y) + (c * i);
	} else if (((a * b) <= 4.2e+32) || (!((a * b) <= 1.9e+146) && ((a * b) <= 5.2e+172))) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (a * b) <= -1.95e+98:
		tmp = t_1
	elif (a * b) <= 9.5e-253:
		tmp = (x * y) + (c * i)
	elif ((a * b) <= 4.2e+32) or (not ((a * b) <= 1.9e+146) and ((a * b) <= 5.2e+172)):
		tmp = (c * i) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -1.95e+98)
		tmp = t_1;
	elseif (Float64(a * b) <= 9.5e-253)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif ((Float64(a * b) <= 4.2e+32) || (!(Float64(a * b) <= 1.9e+146) && (Float64(a * b) <= 5.2e+172)))
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -1.95e+98)
		tmp = t_1;
	elseif ((a * b) <= 9.5e-253)
		tmp = (x * y) + (c * i);
	elseif (((a * b) <= 4.2e+32) || (~(((a * b) <= 1.9e+146)) && ((a * b) <= 5.2e+172)))
		tmp = (c * i) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.95e+98], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 9.5e-253], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 4.2e+32], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.9e+146]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 5.2e+172]]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.95e98 or 4.2000000000000001e32 < (*.f64 a b) < 1.8999999999999999e146 or 5.2e172 < (*.f64 a b)

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. *-commutative 82.0%

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

      3. fma-def 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in c around 0 81.0%

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

   if -1.95e98 < (*.f64 a b) < 9.5e-253

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 76.1%

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

   4. Taylor expanded in a around 0 71.9%

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

   if 9.5e-253 < (*.f64 a b) < 4.2000000000000001e32 or 1.8999999999999999e146 < (*.f64 a b) < 5.2e172

   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. Step-by-step derivation

      1. associate-+l+ 100.0%

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

      2. fma-udef 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 96.4%

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

   6. Taylor expanded in x around 0 81.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.95 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 9.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{+32} \lor \neg \left(a \cdot b \leq 1.9 \cdot 10^{+146}\right) \land a \cdot b \leq 5.2 \cdot 10^{+172}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + \left(x \cdot y + z \cdot t\right)\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 3250000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 3.9 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -5.2e+118)
     t_2
     (if (<= (* c i) 1.9e-16)
       t_1
       (if (<= (* c i) 3250000.0)
         t_2
         (if (<= (* c i) 3.9e+140) t_1 (+ (* c i) (* z t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -5.2e+118) {
		tmp = t_2;
	} else if ((c * i) <= 1.9e-16) {
		tmp = t_1;
	} else if ((c * i) <= 3250000.0) {
		tmp = t_2;
	} else if ((c * i) <= 3.9e+140) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + ((x * y) + (z * t))
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-5.2d+118)) then
        tmp = t_2
    else if ((c * i) <= 1.9d-16) then
        tmp = t_1
    else if ((c * i) <= 3250000.0d0) then
        tmp = t_2
    else if ((c * i) <= 3.9d+140) then
        tmp = t_1
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -5.2e+118) {
		tmp = t_2;
	} else if ((c * i) <= 1.9e-16) {
		tmp = t_1;
	} else if ((c * i) <= 3250000.0) {
		tmp = t_2;
	} else if ((c * i) <= 3.9e+140) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + ((x * y) + (z * t))
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -5.2e+118:
		tmp = t_2
	elif (c * i) <= 1.9e-16:
		tmp = t_1
	elif (c * i) <= 3250000.0:
		tmp = t_2
	elif (c * i) <= 3.9e+140:
		tmp = t_1
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -5.2e+118)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.9e-16)
		tmp = t_1;
	elseif (Float64(c * i) <= 3250000.0)
		tmp = t_2;
	elseif (Float64(c * i) <= 3.9e+140)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + ((x * y) + (z * t));
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -5.2e+118)
		tmp = t_2;
	elseif ((c * i) <= 1.9e-16)
		tmp = t_1;
	elseif ((c * i) <= 3250000.0)
		tmp = t_2;
	elseif ((c * i) <= 3.9e+140)
		tmp = t_1;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -5.2e+118], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.9e-16], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3250000.0], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 3.9e+140], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.20000000000000032e118 or 1.90000000000000006e-16 < (*.f64 c i) < 3.25e6

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 88.5%

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

   4. Taylor expanded in x around 0 84.7%

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

   if -5.20000000000000032e118 < (*.f64 c i) < 1.90000000000000006e-16 or 3.25e6 < (*.f64 c i) < 3.89999999999999974e140

   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 93.8%

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

   if 3.89999999999999974e140 < (*.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. Step-by-step derivation

      1. associate-+l+ 84.2%

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

      2. fma-udef 84.2%

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

      3. *-commutative 84.2%

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

      4. fma-def 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in a around 0 86.8%

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

   6. Taylor expanded in x around 0 79.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{-16}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 3250000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3.9 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.85 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 6.1 \cdot 10^{-227}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-15}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.85e+98)
   (* a b)
   (if (<= (* a b) -5.5e-275)
     (* c i)
     (if (<= (* a b) 6.1e-227)
       (* x y)
       (if (<= (* a b) 7.2e-15)
         (* z t)
         (if (<= (* a b) 2.9e+133) (* x y) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.85e+98) {
		tmp = a * b;
	} else if ((a * b) <= -5.5e-275) {
		tmp = c * i;
	} else if ((a * b) <= 6.1e-227) {
		tmp = x * y;
	} else if ((a * b) <= 7.2e-15) {
		tmp = z * t;
	} else if ((a * b) <= 2.9e+133) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.85d+98)) then
        tmp = a * b
    else if ((a * b) <= (-5.5d-275)) then
        tmp = c * i
    else if ((a * b) <= 6.1d-227) then
        tmp = x * y
    else if ((a * b) <= 7.2d-15) then
        tmp = z * t
    else if ((a * b) <= 2.9d+133) then
        tmp = x * y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.85e+98) {
		tmp = a * b;
	} else if ((a * b) <= -5.5e-275) {
		tmp = c * i;
	} else if ((a * b) <= 6.1e-227) {
		tmp = x * y;
	} else if ((a * b) <= 7.2e-15) {
		tmp = z * t;
	} else if ((a * b) <= 2.9e+133) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.85e+98:
		tmp = a * b
	elif (a * b) <= -5.5e-275:
		tmp = c * i
	elif (a * b) <= 6.1e-227:
		tmp = x * y
	elif (a * b) <= 7.2e-15:
		tmp = z * t
	elif (a * b) <= 2.9e+133:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.85e+98)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -5.5e-275)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 6.1e-227)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 7.2e-15)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.9e+133)
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.85e+98)
		tmp = a * b;
	elseif ((a * b) <= -5.5e-275)
		tmp = c * i;
	elseif ((a * b) <= 6.1e-227)
		tmp = x * y;
	elseif ((a * b) <= 7.2e-15)
		tmp = z * t;
	elseif ((a * b) <= 2.9e+133)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.85e+98], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5.5e-275], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.1e-227], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.2e-15], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.9e+133], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.8499999999999999e98 or 2.9000000000000001e133 < (*.f64 a b)

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 71.4%

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

   if -1.8499999999999999e98 < (*.f64 a b) < -5.49999999999999988e-275

   1. Initial program 97.0%

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

   3. Taylor expanded in c around inf 39.4%

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

   if -5.49999999999999988e-275 < (*.f64 a b) < 6.1000000000000002e-227 or 7.2000000000000002e-15 < (*.f64 a b) < 2.9000000000000001e133

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 51.1%

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

   if 6.1000000000000002e-227 < (*.f64 a b) < 7.2000000000000002e-15

   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 52.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.85 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5.5 \cdot 10^{-275}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 6.1 \cdot 10^{-227}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-15}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (x * y);
	}
	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 = (a * b) + (x * y);
	}
	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 = (a * b) + (x * y)
	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(a * b) + Float64(x * y));
	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 = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(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[(a * b), $MachinePrecision] + N[(x * y), $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 18.2%

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

      1. +-commutative 18.2%

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

      2. *-commutative 18.2%

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

      3. fma-def 27.3%

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

   5. Applied egg-rr 27.3%

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

   6. Taylor expanded in c around 0 73.0%

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

4. Final simplification 98.8%

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

Alternative 10: 41.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.95 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.3 \cdot 10^{-150}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{-23}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.95e+98)
   (* a b)
   (if (<= (* a b) 4.3e-150)
     (* c i)
     (if (<= (* a b) 3.4e-23)
       (* z t)
       (if (<= (* a b) 5.8e+80) (* 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 ((a * b) <= -1.95e+98) {
		tmp = a * b;
	} else if ((a * b) <= 4.3e-150) {
		tmp = c * i;
	} else if ((a * b) <= 3.4e-23) {
		tmp = z * t;
	} else if ((a * b) <= 5.8e+80) {
		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 ((a * b) <= (-1.95d+98)) then
        tmp = a * b
    else if ((a * b) <= 4.3d-150) then
        tmp = c * i
    else if ((a * b) <= 3.4d-23) then
        tmp = z * t
    else if ((a * b) <= 5.8d+80) 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 ((a * b) <= -1.95e+98) {
		tmp = a * b;
	} else if ((a * b) <= 4.3e-150) {
		tmp = c * i;
	} else if ((a * b) <= 3.4e-23) {
		tmp = z * t;
	} else if ((a * b) <= 5.8e+80) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.95e+98:
		tmp = a * b
	elif (a * b) <= 4.3e-150:
		tmp = c * i
	elif (a * b) <= 3.4e-23:
		tmp = z * t
	elif (a * b) <= 5.8e+80:
		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(a * b) <= -1.95e+98)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 4.3e-150)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 3.4e-23)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.8e+80)
		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 ((a * b) <= -1.95e+98)
		tmp = a * b;
	elseif ((a * b) <= 4.3e-150)
		tmp = c * i;
	elseif ((a * b) <= 3.4e-23)
		tmp = z * t;
	elseif ((a * b) <= 5.8e+80)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.95e+98], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.3e-150], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.4e-23], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.8e+80], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.95e98 or 5.79999999999999971e80 < (*.f64 a b)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 68.0%

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

   if -1.95e98 < (*.f64 a b) < 4.30000000000000004e-150 or 3.4000000000000001e-23 < (*.f64 a b) < 5.79999999999999971e80

   1. Initial program 96.4%

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

   3. Taylor expanded in c around inf 38.2%

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

   if 4.30000000000000004e-150 < (*.f64 a b) < 3.4000000000000001e-23

   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 61.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.95 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 4.3 \cdot 10^{-150}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.4 \cdot 10^{-23}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -48000000000 \lor \neg \left(x \cdot y \leq 1.02 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -48000000000.0) (not (<= (* x y) 1.02e+95)))
   (+ (* 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 (((x * y) <= -48000000000.0) || !((x * y) <= 1.02e+95)) {
		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 (((x * y) <= (-48000000000.0d0)) .or. (.not. ((x * y) <= 1.02d+95))) 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 (((x * y) <= -48000000000.0) || !((x * y) <= 1.02e+95)) {
		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 ((x * y) <= -48000000000.0) or not ((x * y) <= 1.02e+95):
		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(x * y) <= -48000000000.0) || !(Float64(x * y) <= 1.02e+95))
		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 (((x * y) <= -48000000000.0) || ~(((x * y) <= 1.02e+95)))
		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[Or[LessEqual[N[(x * y), $MachinePrecision], -48000000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.02e+95]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 x y) < -4.8e10 or 1.0200000000000001e95 < (*.f64 x y)

   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 91.4%

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

   if -4.8e10 < (*.f64 x y) < 1.0200000000000001e95

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 92.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -48000000000 \lor \neg \left(x \cdot y \leq 1.02 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+99} \lor \neg \left(a \cdot b \leq 7.8 \cdot 10^{+31}\right):\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* a b) -4.2e+99) (not (<= (* a b) 7.8e+31)))
     (+ (* a b) t_1)
     (+ (* c i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((a * b) <= -4.2e+99) || !((a * b) <= 7.8e+31)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (((a * b) <= (-4.2d+99)) .or. (.not. ((a * b) <= 7.8d+31))) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((a * b) <= -4.2e+99) || !((a * b) <= 7.8e+31)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((a * b) <= -4.2e+99) or not ((a * b) <= 7.8e+31):
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -4.2e+99) || !(Float64(a * b) <= 7.8e+31))
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((a * b) <= -4.2e+99) || ~(((a * b) <= 7.8e+31)))
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -4.2e+99], N[Not[LessEqual[N[(a * b), $MachinePrecision], 7.8e+31]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.2000000000000002e99 or 7.79999999999999999e31 < (*.f64 a b)

   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 c around 0 88.0%

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

   if -4.2000000000000002e99 < (*.f64 a b) < 7.79999999999999999e31

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. fma-udef 98.1%

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

      3. *-commutative 98.1%

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

      4. fma-def 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in a around 0 94.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+99} \lor \neg \left(a \cdot b \leq 7.8 \cdot 10^{+31}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -35000000000 \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+94}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -35000000000.0) (not (<= (* x y) 3.8e+94)))
   (+ (* a b) (* x y))
   (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -35000000000.0) || !((x * y) <= 3.8e+94)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-35000000000.0d0)) .or. (.not. ((x * y) <= 3.8d+94))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -35000000000.0) || !((x * y) <= 3.8e+94)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -35000000000.0) or not ((x * y) <= 3.8e+94):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -35000000000.0) || !(Float64(x * y) <= 3.8e+94))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -35000000000.0) || ~(((x * y) <= 3.8e+94)))
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -35000000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.8e+94]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.5e10 or 3.7999999999999996e94 < (*.f64 x y)

   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 z around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. *-commutative 80.0%

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

      3. fma-def 81.0%

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

   5. Applied egg-rr 81.0%

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

   6. Taylor expanded in c around 0 77.3%

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

   if -3.5e10 < (*.f64 x y) < 3.7999999999999996e94

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 70.8%

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

   4. Taylor expanded in x around 0 66.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -35000000000 \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+94}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.85 \cdot 10^{+98} \lor \neg \left(a \cdot b \leq 2.05 \cdot 10^{+85}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.85e+98) (not (<= (* a b) 2.05e+85))) (* 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 (((a * b) <= -1.85e+98) || !((a * b) <= 2.05e+85)) {
		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 (((a * b) <= (-1.85d+98)) .or. (.not. ((a * b) <= 2.05d+85))) 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 (((a * b) <= -1.85e+98) || !((a * b) <= 2.05e+85)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.85e+98) or not ((a * b) <= 2.05e+85):
		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(a * b) <= -1.85e+98) || !(Float64(a * b) <= 2.05e+85))
		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 (((a * b) <= -1.85e+98) || ~(((a * b) <= 2.05e+85)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.85e+98], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.05e+85]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.8499999999999999e98 or 2.04999999999999989e85 < (*.f64 a b)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 68.0%

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

   if -1.8499999999999999e98 < (*.f64 a b) < 2.04999999999999989e85

   1. Initial program 97.0%

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

   3. Taylor expanded in c around inf 36.3%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.85 \cdot 10^{+98} \lor \neg \left(a \cdot b \leq 2.05 \cdot 10^{+85}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.8% 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 95.7%

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

3. Taylor expanded in a around inf 27.9%

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

4. Final simplification 27.9%

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

Reproduce

herbie shell --seed 2024026 
(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)))