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

Percentage Accurate: 95.7% → 97.7%

Time: 12.6s

Alternatives: 15

Speedup: 0.4×

• 41.7% 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: 95.7% 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

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) < +inf.0

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. fma-define 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-define 99.6%

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

      5. fma-define 99.6%

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

   3. Simplified 99.6%

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

   if +inf.0 < (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))

   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 a around inf 78.4%

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

   4. Taylor expanded in i around inf 88.9%

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

4. Final simplification 99.2%

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

Alternative 2: 97.9% 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-define 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-define 96.9%

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

   5. fma-define 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + \left(a \cdot b + c \cdot i\right)} \]
   4. 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 a around inf 64.1%

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

   4. Taylor expanded in i around inf 81.8%

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

4. Final simplification 99.2%

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

Alternative 4: 42.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+139}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{+83}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -9 \cdot 10^{-173}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.1 \cdot 10^{-117}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -8e+139)
   (* a b)
   (if (<= (* a b) -1.3e+83)
     (* z t)
     (if (<= (* a b) -8.2e+17)
       (* x y)
       (if (<= (* a b) -9e-173)
         (* c i)
         (if (<= (* a b) 4.4e-308)
           (* z t)
           (if (<= (* a b) 1.1e-117)
             (* x y)
             (if (<= (* a b) 8.5e-9) (* 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) <= -8e+139) {
		tmp = a * b;
	} else if ((a * b) <= -1.3e+83) {
		tmp = z * t;
	} else if ((a * b) <= -8.2e+17) {
		tmp = x * y;
	} else if ((a * b) <= -9e-173) {
		tmp = c * i;
	} else if ((a * b) <= 4.4e-308) {
		tmp = z * t;
	} else if ((a * b) <= 1.1e-117) {
		tmp = x * y;
	} else if ((a * b) <= 8.5e-9) {
		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) <= (-8d+139)) then
        tmp = a * b
    else if ((a * b) <= (-1.3d+83)) then
        tmp = z * t
    else if ((a * b) <= (-8.2d+17)) then
        tmp = x * y
    else if ((a * b) <= (-9d-173)) then
        tmp = c * i
    else if ((a * b) <= 4.4d-308) then
        tmp = z * t
    else if ((a * b) <= 1.1d-117) then
        tmp = x * y
    else if ((a * b) <= 8.5d-9) 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) <= -8e+139) {
		tmp = a * b;
	} else if ((a * b) <= -1.3e+83) {
		tmp = z * t;
	} else if ((a * b) <= -8.2e+17) {
		tmp = x * y;
	} else if ((a * b) <= -9e-173) {
		tmp = c * i;
	} else if ((a * b) <= 4.4e-308) {
		tmp = z * t;
	} else if ((a * b) <= 1.1e-117) {
		tmp = x * y;
	} else if ((a * b) <= 8.5e-9) {
		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) <= -8e+139:
		tmp = a * b
	elif (a * b) <= -1.3e+83:
		tmp = z * t
	elif (a * b) <= -8.2e+17:
		tmp = x * y
	elif (a * b) <= -9e-173:
		tmp = c * i
	elif (a * b) <= 4.4e-308:
		tmp = z * t
	elif (a * b) <= 1.1e-117:
		tmp = x * y
	elif (a * b) <= 8.5e-9:
		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) <= -8e+139)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.3e+83)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -8.2e+17)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -9e-173)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 4.4e-308)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.1e-117)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 8.5e-9)
		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) <= -8e+139)
		tmp = a * b;
	elseif ((a * b) <= -1.3e+83)
		tmp = z * t;
	elseif ((a * b) <= -8.2e+17)
		tmp = x * y;
	elseif ((a * b) <= -9e-173)
		tmp = c * i;
	elseif ((a * b) <= 4.4e-308)
		tmp = z * t;
	elseif ((a * b) <= 1.1e-117)
		tmp = x * y;
	elseif ((a * b) <= 8.5e-9)
		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], -8e+139], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.3e+83], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -8.2e+17], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -9e-173], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.4e-308], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.1e-117], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.5e-9], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -8.00000000000000026e139 or 8.5e-9 < (*.f64 a b)

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 86.5%

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

   4. Taylor expanded in y around inf 78.1%

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

   5. Taylor expanded in a around inf 64.7%

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

   if -8.00000000000000026e139 < (*.f64 a b) < -1.3000000000000001e83 or -9.00000000000000037e-173 < (*.f64 a b) < 4.3999999999999999e-308

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 96.7%

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

   4. Taylor expanded in y around inf 88.6%

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

   5. Taylor expanded in t around inf 49.5%

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

   if -1.3000000000000001e83 < (*.f64 a b) < -8.2e17 or 4.3999999999999999e-308 < (*.f64 a b) < 1.1000000000000001e-117

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in y around inf 89.6%

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

   5. Taylor expanded in y around inf 54.0%

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

   if -8.2e17 < (*.f64 a b) < -9.00000000000000037e-173 or 1.1000000000000001e-117 < (*.f64 a b) < 8.5e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 48.9%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+139}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{+83}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -9 \cdot 10^{-173}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.1 \cdot 10^{-117}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-64}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-65}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* x y) (* z t))))
   (if (<= (* x y) -2.1e+90)
     t_2
     (if (<= (* x y) -6e-64)
       (+ (* c i) (* z t))
       (if (<= (* x y) -4.1e-129)
         t_1
         (if (<= (* x y) 3e-65)
           (+ (* a b) (* c i))
           (if (<= (* x y) 6.4e+88) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -2.1e+90) {
		tmp = t_2;
	} else if ((x * y) <= -6e-64) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= -4.1e-129) {
		tmp = t_1;
	} else if ((x * y) <= 3e-65) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 6.4e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (x * y) + (z * t)
    if ((x * y) <= (-2.1d+90)) then
        tmp = t_2
    else if ((x * y) <= (-6d-64)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= (-4.1d-129)) then
        tmp = t_1
    else if ((x * y) <= 3d-65) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 6.4d+88) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -2.1e+90) {
		tmp = t_2;
	} else if ((x * y) <= -6e-64) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= -4.1e-129) {
		tmp = t_1;
	} else if ((x * y) <= 3e-65) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 6.4e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (x * y) <= -2.1e+90:
		tmp = t_2
	elif (x * y) <= -6e-64:
		tmp = (c * i) + (z * t)
	elif (x * y) <= -4.1e-129:
		tmp = t_1
	elif (x * y) <= 3e-65:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 6.4e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+90)
		tmp = t_2;
	elseif (Float64(x * y) <= -6e-64)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= -4.1e-129)
		tmp = t_1;
	elseif (Float64(x * y) <= 3e-65)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 6.4e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -2.1e+90)
		tmp = t_2;
	elseif ((x * y) <= -6e-64)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= -4.1e-129)
		tmp = t_1;
	elseif ((x * y) <= 3e-65)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 6.4e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+90], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -6e-64], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.1e-129], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3e-65], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.4e+88], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.09999999999999981e90 or 6.3999999999999997e88 < (*.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 a around 0 86.6%

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

   4. Taylor expanded in c around 0 76.7%

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

   if -2.09999999999999981e90 < (*.f64 x y) < -6.0000000000000001e-64

   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 inf 77.1%

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

   if -6.0000000000000001e-64 < (*.f64 x y) < -4.1e-129 or 2.99999999999999998e-65 < (*.f64 x y) < 6.3999999999999997e88

   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 0 92.7%

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

   4. Taylor expanded in z around inf 83.3%

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

   5. Taylor expanded in c around 0 73.6%

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

   6. Taylor expanded in z around 0 82.9%

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

   if -4.1e-129 < (*.f64 x y) < 2.99999999999999998e-65

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 73.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -6 \cdot 10^{-64}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.1 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-65}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{+88}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-62}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* x y) -1e+96)
     (+ (* x y) (* z t))
     (if (<= (* x y) -2e-62)
       (+ (* c i) (* z t))
       (if (<= (* x y) -2e-128)
         t_1
         (if (<= (* x y) 2e-67)
           (+ (* a b) (* c i))
           (if (<= (* x y) 5e+88) t_1 (+ (* x y) (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -1e+96) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= -2e-62) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= -2e-128) {
		tmp = t_1;
	} else if ((x * y) <= 2e-67) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 5e+88) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((x * y) <= (-1d+96)) then
        tmp = (x * y) + (z * t)
    else if ((x * y) <= (-2d-62)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= (-2d-128)) then
        tmp = t_1
    else if ((x * y) <= 2d-67) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 5d+88) then
        tmp = t_1
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((x * y) <= -1e+96) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= -2e-62) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= -2e-128) {
		tmp = t_1;
	} else if ((x * y) <= 2e-67) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 5e+88) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -1e+96:
		tmp = (x * y) + (z * t)
	elif (x * y) <= -2e-62:
		tmp = (c * i) + (z * t)
	elif (x * y) <= -2e-128:
		tmp = t_1
	elif (x * y) <= 2e-67:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 5e+88:
		tmp = t_1
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -1e+96)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(x * y) <= -2e-62)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= -2e-128)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-67)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 5e+88)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -1e+96)
		tmp = (x * y) + (z * t);
	elseif ((x * y) <= -2e-62)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= -2e-128)
		tmp = t_1;
	elseif ((x * y) <= 2e-67)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 5e+88)
		tmp = t_1;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+96], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-62], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-128], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-67], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+88], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.00000000000000005e96

   1. Initial program 91.5%

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

   3. Taylor expanded in a around 0 87.4%

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

   4. Taylor expanded in c around 0 79.1%

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

   if -1.00000000000000005e96 < (*.f64 x y) < -2.0000000000000001e-62

   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 inf 77.1%

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

   if -2.0000000000000001e-62 < (*.f64 x y) < -2.00000000000000011e-128 or 1.99999999999999989e-67 < (*.f64 x y) < 4.99999999999999997e88

   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 0 92.7%

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

   4. Taylor expanded in z around inf 83.3%

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

   5. Taylor expanded in c around 0 73.6%

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

   6. Taylor expanded in z around 0 82.9%

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

   if -2.00000000000000011e-128 < (*.f64 x y) < 1.99999999999999989e-67

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 73.7%

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

   if 4.99999999999999997e88 < (*.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 76.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-62}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-128}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-67}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -2.5 \cdot 10^{+166}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* x y) -2.5e+166)
     (* x y)
     (if (<= (* x y) -7e+25)
       t_1
       (if (<= (* x y) 8.2e-58)
         (+ (* a b) (* c i))
         (if (<= (* x y) 1.6e+91) 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) + (z * t);
	double tmp;
	if ((x * y) <= -2.5e+166) {
		tmp = x * y;
	} else if ((x * y) <= -7e+25) {
		tmp = t_1;
	} else if ((x * y) <= 8.2e-58) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.6e+91) {
		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) + (z * t)
    if ((x * y) <= (-2.5d+166)) then
        tmp = x * y
    else if ((x * y) <= (-7d+25)) then
        tmp = t_1
    else if ((x * y) <= 8.2d-58) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.6d+91) 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) + (z * t);
	double tmp;
	if ((x * y) <= -2.5e+166) {
		tmp = x * y;
	} else if ((x * y) <= -7e+25) {
		tmp = t_1;
	} else if ((x * y) <= 8.2e-58) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.6e+91) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (x * y) <= -2.5e+166:
		tmp = x * y
	elif (x * y) <= -7e+25:
		tmp = t_1
	elif (x * y) <= 8.2e-58:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.6e+91:
		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(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -2.5e+166)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -7e+25)
		tmp = t_1;
	elseif (Float64(x * y) <= 8.2e-58)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.6e+91)
		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) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -2.5e+166)
		tmp = x * y;
	elseif ((x * y) <= -7e+25)
		tmp = t_1;
	elseif ((x * y) <= 8.2e-58)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.6e+91)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.5e+166], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -7e+25], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8.2e-58], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.6e+91], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.5000000000000001e166 or 1.59999999999999995e91 < (*.f64 x y)

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 93.3%

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

   4. Taylor expanded in y around inf 96.0%

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

   5. Taylor expanded in y around inf 71.5%

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

   if -2.5000000000000001e166 < (*.f64 x y) < -6.99999999999999999e25 or 8.20000000000000056e-58 < (*.f64 x y) < 1.59999999999999995e91

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 81.3%

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

   4. Taylor expanded in z around inf 74.4%

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

   5. Taylor expanded in c around 0 64.2%

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

   6. Taylor expanded in z around 0 71.1%

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

   if -6.99999999999999999e25 < (*.f64 x y) < 8.20000000000000056e-58

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 72.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.5 \cdot 10^{+166}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+91}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-59}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-59}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -3.5e+154)
   (* x y)
   (if (<= (* x y) -4e-59)
     (+ (* c i) (* z t))
     (if (<= (* x y) 5e-59)
       (+ (* a b) (* c i))
       (if (<= (* x y) 3.6e+90) (+ (* a b) (* z t)) (* 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) <= -3.5e+154) {
		tmp = x * y;
	} else if ((x * y) <= -4e-59) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 5e-59) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 3.6e+90) {
		tmp = (a * b) + (z * t);
	} 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) :: tmp
    if ((x * y) <= (-3.5d+154)) then
        tmp = x * y
    else if ((x * y) <= (-4d-59)) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 5d-59) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 3.6d+90) then
        tmp = (a * b) + (z * t)
    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 tmp;
	if ((x * y) <= -3.5e+154) {
		tmp = x * y;
	} else if ((x * y) <= -4e-59) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 5e-59) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 3.6e+90) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -3.5e+154:
		tmp = x * y
	elif (x * y) <= -4e-59:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 5e-59:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 3.6e+90:
		tmp = (a * b) + (z * t)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -3.5e+154)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4e-59)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 5e-59)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 3.6e+90)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = 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) <= -3.5e+154)
		tmp = x * y;
	elseif ((x * y) <= -4e-59)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 5e-59)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 3.6e+90)
		tmp = (a * b) + (z * t);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.5e+154], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-59], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-59], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.6e+90], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.5000000000000002e154 or 3.6e90 < (*.f64 x y)

   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 y around inf 93.5%

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

   4. Taylor expanded in y around inf 96.1%

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

   5. Taylor expanded in y around inf 70.9%

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

   if -3.5000000000000002e154 < (*.f64 x y) < -4.0000000000000001e-59

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf 71.2%

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

   if -4.0000000000000001e-59 < (*.f64 x y) < 5.0000000000000001e-59

   1. Initial program 96.3%

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

   3. Taylor expanded in a around inf 74.2%

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

   if 5.0000000000000001e-59 < (*.f64 x y) < 3.6e90

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.6%

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

   4. Taylor expanded in z around inf 79.7%

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

   5. Taylor expanded in c around 0 72.6%

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

   6. Taylor expanded in z around 0 82.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-59}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-59}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b)) (*.f64 c i))

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 64.1%

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

   4. Taylor expanded in i around inf 81.8%

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

4. Final simplification 99.2%

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

Alternative 10: 42.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.9 \cdot 10^{+125}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -9.2 \cdot 10^{-171}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.9e+125)
   (* a b)
   (if (<= (* a b) -9.2e-171)
     (* c i)
     (if (<= (* a b) 1.16e-130)
       (* z t)
       (if (<= (* a b) 8.5e-9) (* 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) <= -2.9e+125) {
		tmp = a * b;
	} else if ((a * b) <= -9.2e-171) {
		tmp = c * i;
	} else if ((a * b) <= 1.16e-130) {
		tmp = z * t;
	} else if ((a * b) <= 8.5e-9) {
		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) <= (-2.9d+125)) then
        tmp = a * b
    else if ((a * b) <= (-9.2d-171)) then
        tmp = c * i
    else if ((a * b) <= 1.16d-130) then
        tmp = z * t
    else if ((a * b) <= 8.5d-9) 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) <= -2.9e+125) {
		tmp = a * b;
	} else if ((a * b) <= -9.2e-171) {
		tmp = c * i;
	} else if ((a * b) <= 1.16e-130) {
		tmp = z * t;
	} else if ((a * b) <= 8.5e-9) {
		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) <= -2.9e+125:
		tmp = a * b
	elif (a * b) <= -9.2e-171:
		tmp = c * i
	elif (a * b) <= 1.16e-130:
		tmp = z * t
	elif (a * b) <= 8.5e-9:
		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) <= -2.9e+125)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -9.2e-171)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1.16e-130)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 8.5e-9)
		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) <= -2.9e+125)
		tmp = a * b;
	elseif ((a * b) <= -9.2e-171)
		tmp = c * i;
	elseif ((a * b) <= 1.16e-130)
		tmp = z * t;
	elseif ((a * b) <= 8.5e-9)
		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], -2.9e+125], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -9.2e-171], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.16e-130], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.5e-9], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.89999999999999993e125 or 8.5e-9 < (*.f64 a b)

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 86.9%

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

   4. Taylor expanded in y around inf 78.7%

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

   5. Taylor expanded in a around inf 63.8%

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

   if -2.89999999999999993e125 < (*.f64 a b) < -9.19999999999999911e-171 or 1.1600000000000001e-130 < (*.f64 a b) < 8.5e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in c around inf 42.7%

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

   if -9.19999999999999911e-171 < (*.f64 a b) < 1.1600000000000001e-130

   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 y around inf 97.3%

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

   4. Taylor expanded in y around inf 89.3%

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

   5. Taylor expanded in t around inf 39.1%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.9 \cdot 10^{+125}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -9.2 \cdot 10^{-171}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.16 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.5 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+103}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.62 \cdot 10^{+91}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.15e+103)
   (* x y)
   (if (<= (* x y) -5.6e+32)
     (* z t)
     (if (<= (* x y) 1.62e+91) (+ (* a b) (* c i)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.15e+103) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e+32) {
		tmp = z * t;
	} else if ((x * y) <= 1.62e+91) {
		tmp = (a * b) + (c * i);
	} 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) :: tmp
    if ((x * y) <= (-1.15d+103)) then
        tmp = x * y
    else if ((x * y) <= (-5.6d+32)) then
        tmp = z * t
    else if ((x * y) <= 1.62d+91) then
        tmp = (a * b) + (c * i)
    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 tmp;
	if ((x * y) <= -1.15e+103) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e+32) {
		tmp = z * t;
	} else if ((x * y) <= 1.62e+91) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.15e+103:
		tmp = x * y
	elif (x * y) <= -5.6e+32:
		tmp = z * t
	elif (x * y) <= 1.62e+91:
		tmp = (a * b) + (c * i)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.15e+103)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.6e+32)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.62e+91)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = 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) <= -1.15e+103)
		tmp = x * y;
	elseif ((x * y) <= -5.6e+32)
		tmp = z * t;
	elseif ((x * y) <= 1.62e+91)
		tmp = (a * b) + (c * i);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.15e+103], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.6e+32], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.62e+91], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.15000000000000004e103 or 1.62e91 < (*.f64 x y)

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 94.2%

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

   4. Taylor expanded in y around inf 96.5%

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

   5. Taylor expanded in y around inf 66.9%

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

   if -1.15000000000000004e103 < (*.f64 x y) < -5.6e32

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 86.2%

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

   4. Taylor expanded in y around inf 72.8%

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

   5. Taylor expanded in t around inf 58.1%

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

   if -5.6e32 < (*.f64 x y) < 1.62e91

   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 inf 68.6%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.15 \cdot 10^{+103}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.62 \cdot 10^{+91}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+66} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+88}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4e+66) (not (<= (* x y) 5e+88)))
   (+ (* c i) (+ (* 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) <= -4e+66) || !((x * y) <= 5e+88)) {
		tmp = (c * i) + ((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) <= (-4d+66)) .or. (.not. ((x * y) <= 5d+88))) then
        tmp = (c * i) + ((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) <= -4e+66) || !((x * y) <= 5e+88)) {
		tmp = (c * i) + ((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) <= -4e+66) or not ((x * y) <= 5e+88):
		tmp = (c * i) + ((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) <= -4e+66) || !(Float64(x * y) <= 5e+88))
		tmp = Float64(Float64(c * i) + 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) <= -4e+66) || ~(((x * y) <= 5e+88)))
		tmp = (c * i) + ((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], -4e+66], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+88]], $MachinePrecision]], N[(N[(c * i), $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) < -3.99999999999999978e66 or 4.99999999999999997e88 < (*.f64 x y)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around 0 87.3%

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

   if -3.99999999999999978e66 < (*.f64 x y) < 4.99999999999999997e88

   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. Taylor expanded in x around 0 93.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+66} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+88}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1e+96)
   (+ (* x y) (* z t))
   (if (<= (* x y) 5e+88)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+96) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 5e+88) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1d+96)) then
        tmp = (x * y) + (z * t)
    else if ((x * y) <= 5d+88) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1e+96) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 5e+88) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1e+96:
		tmp = (x * y) + (z * t)
	elif (x * y) <= 5e+88:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1e+96)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(x * y) <= 5e+88)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1e+96)
		tmp = (x * y) + (z * t);
	elseif ((x * y) <= 5e+88)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+96], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+88], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000005e96

   1. Initial program 91.5%

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

   3. Taylor expanded in a around 0 87.4%

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

   4. Taylor expanded in c around 0 79.1%

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

   if -1.00000000000000005e96 < (*.f64 x y) < 4.99999999999999997e88

   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 x around 0 93.2%

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

   if 4.99999999999999997e88 < (*.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 76.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+88}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{+115} \lor \neg \left(a \cdot b \leq 5.5 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.25e+115) (not (<= (* a b) 5.5e-10))) (* 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) <= -1.25e+115) || !((a * b) <= 5.5e-10)) {
		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) <= (-1.25d+115)) .or. (.not. ((a * b) <= 5.5d-10))) 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) <= -1.25e+115) || !((a * b) <= 5.5e-10)) {
		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) <= -1.25e+115) or not ((a * b) <= 5.5e-10):
		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) <= -1.25e+115) || !(Float64(a * b) <= 5.5e-10))
		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) <= -1.25e+115) || ~(((a * b) <= 5.5e-10)))
		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], -1.25e+115], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5.5e-10]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.25000000000000002e115 or 5.4999999999999996e-10 < (*.f64 a b)

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 86.9%

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

   4. Taylor expanded in y around inf 78.7%

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

   5. Taylor expanded in a around inf 63.8%

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

   if -1.25000000000000002e115 < (*.f64 a b) < 5.4999999999999996e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in c around inf 36.9%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{+115} \lor \neg \left(a \cdot b \leq 5.5 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.1% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 y around inf 90.9%

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

4. Taylor expanded in y around inf 81.2%

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

5. Taylor expanded in a around inf 29.9%

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

6. Final simplification 29.9%

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

Reproduce

herbie shell --seed 2024071 
(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)))