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

Percentage Accurate: 95.5% → 98.1%

Time: 9.8s

Alternatives: 14

Speedup: 0.4×

• 41.4% 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: 95.5% 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: 98.1% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-define 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-define 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-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. Add Preprocessing

Alternative 2: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := x \cdot y + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -4.7 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.55 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.52 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* x y) (* c i))))
   (if (<= (* x y) -4.7e+165)
     t_2
     (if (<= (* x y) -3.6e-269)
       t_1
       (if (<= (* x y) 2e-316)
         (+ (* c i) (* z t))
         (if (<= (* x y) 2.55e-117)
           t_1
           (if (<= (* x y) 3.5e+149)
             (+ (* a b) (* c i))
             (if (<= (* x y) 1.52e+199) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -4.7e+165) {
		tmp = t_2;
	} else if ((x * y) <= -3.6e-269) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2.55e-117) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e+149) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.52e+199) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (x * y) + (c * i)
    if ((x * y) <= (-4.7d+165)) then
        tmp = t_2
    else if ((x * y) <= (-3.6d-269)) then
        tmp = t_1
    else if ((x * y) <= 2d-316) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 2.55d-117) then
        tmp = t_1
    else if ((x * y) <= 3.5d+149) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 1.52d+199) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (x * y) + (c * i);
	double tmp;
	if ((x * y) <= -4.7e+165) {
		tmp = t_2;
	} else if ((x * y) <= -3.6e-269) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 2.55e-117) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e+149) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 1.52e+199) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (x * y) + (c * i)
	tmp = 0
	if (x * y) <= -4.7e+165:
		tmp = t_2
	elif (x * y) <= -3.6e-269:
		tmp = t_1
	elif (x * y) <= 2e-316:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 2.55e-117:
		tmp = t_1
	elif (x * y) <= 3.5e+149:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 1.52e+199:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -4.7e+165)
		tmp = t_2;
	elseif (Float64(x * y) <= -3.6e-269)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-316)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 2.55e-117)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.5e+149)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 1.52e+199)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (x * y) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -4.7e+165)
		tmp = t_2;
	elseif ((x * y) <= -3.6e-269)
		tmp = t_1;
	elseif ((x * y) <= 2e-316)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 2.55e-117)
		tmp = t_1;
	elseif ((x * y) <= 3.5e+149)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 1.52e+199)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.7e+165], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -3.6e-269], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-316], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.55e-117], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e+149], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.52e+199], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.70000000000000016e165 or 1.51999999999999995e199 < (*.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 a around 0 86.7%

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

   4. Taylor expanded in t around 0 85.4%

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

   if -4.70000000000000016e165 < (*.f64 x y) < -3.59999999999999998e-269 or 2.000000017e-316 < (*.f64 x y) < 2.5500000000000001e-117 or 3.50000000000000011e149 < (*.f64 x y) < 1.51999999999999995e199

   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 z around inf 91.8%

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

   4. Taylor expanded in z around inf 86.9%

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

   5. Taylor expanded in c around 0 78.3%

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

   if -3.59999999999999998e-269 < (*.f64 x y) < 2.000000017e-316

   1. Initial program 94.9%

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

   3. Taylor expanded in a around 0 82.6%

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

   4. Taylor expanded in x around 0 82.6%

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

   if 2.5500000000000001e-117 < (*.f64 x y) < 3.50000000000000011e149

   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 95.3%

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

   4. Taylor expanded in z around inf 80.9%

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

   5. Taylor expanded in t around 0 66.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.7 \cdot 10^{+165}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-269}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.55 \cdot 10^{-117}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.52 \cdot 10^{+199}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -9.4 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.1 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* x y) -9.4e+225)
     (* x y)
     (if (<= (* x y) -4e-271)
       t_1
       (if (<= (* x y) 2e-316)
         (+ (* c i) (* z t))
         (if (<= (* x y) 5.1e-111)
           t_1
           (if (<= (* x y) 7.5e+149)
             (+ (* a b) (* c i))
             (if (<= (* x y) 2.25e+204) 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) <= -9.4e+225) {
		tmp = x * y;
	} else if ((x * y) <= -4e-271) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 5.1e-111) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+149) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2.25e+204) {
		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) <= (-9.4d+225)) then
        tmp = x * y
    else if ((x * y) <= (-4d-271)) then
        tmp = t_1
    else if ((x * y) <= 2d-316) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 5.1d-111) then
        tmp = t_1
    else if ((x * y) <= 7.5d+149) then
        tmp = (a * b) + (c * i)
    else if ((x * y) <= 2.25d+204) 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) <= -9.4e+225) {
		tmp = x * y;
	} else if ((x * y) <= -4e-271) {
		tmp = t_1;
	} else if ((x * y) <= 2e-316) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 5.1e-111) {
		tmp = t_1;
	} else if ((x * y) <= 7.5e+149) {
		tmp = (a * b) + (c * i);
	} else if ((x * y) <= 2.25e+204) {
		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) <= -9.4e+225:
		tmp = x * y
	elif (x * y) <= -4e-271:
		tmp = t_1
	elif (x * y) <= 2e-316:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 5.1e-111:
		tmp = t_1
	elif (x * y) <= 7.5e+149:
		tmp = (a * b) + (c * i)
	elif (x * y) <= 2.25e+204:
		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) <= -9.4e+225)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4e-271)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-316)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 5.1e-111)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.5e+149)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(x * y) <= 2.25e+204)
		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) <= -9.4e+225)
		tmp = x * y;
	elseif ((x * y) <= -4e-271)
		tmp = t_1;
	elseif ((x * y) <= 2e-316)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 5.1e-111)
		tmp = t_1;
	elseif ((x * y) <= 7.5e+149)
		tmp = (a * b) + (c * i);
	elseif ((x * y) <= 2.25e+204)
		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], -9.4e+225], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-271], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-316], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.1e-111], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+149], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.25e+204], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.40000000000000008e225 or 2.25000000000000001e204 < (*.f64 x y)

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 82.9%

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

   if -9.40000000000000008e225 < (*.f64 x y) < -3.99999999999999985e-271 or 2.000000017e-316 < (*.f64 x y) < 5.10000000000000032e-111 or 7.50000000000000031e149 < (*.f64 x y) < 2.25000000000000001e204

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 90.1%

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

   4. Taylor expanded in z around inf 85.7%

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

   5. Taylor expanded in c around 0 75.9%

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

   if -3.99999999999999985e-271 < (*.f64 x y) < 2.000000017e-316

   1. Initial program 94.9%

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

   3. Taylor expanded in a around 0 82.6%

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

   4. Taylor expanded in x around 0 82.6%

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

   if 5.10000000000000032e-111 < (*.f64 x y) < 7.50000000000000031e149

   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 95.3%

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

   4. Taylor expanded in z around inf 80.9%

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

   5. Taylor expanded in t around 0 66.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.4 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-316}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 5.1 \cdot 10^{-111}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+136}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.35 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.2 \cdot 10^{-149}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3.8e+136)
   (* a b)
   (if (<= (* a b) -1.35e-176)
     (* x y)
     (if (<= (* a b) 2.2e-149)
       (* z t)
       (if (<= (* a b) 4.4e-64)
         (* x y)
         (if (<= (* a b) 1.45e+140) (* z t) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3.8e+136) {
		tmp = a * b;
	} else if ((a * b) <= -1.35e-176) {
		tmp = x * y;
	} else if ((a * b) <= 2.2e-149) {
		tmp = z * t;
	} else if ((a * b) <= 4.4e-64) {
		tmp = x * y;
	} else if ((a * b) <= 1.45e+140) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-3.8d+136)) then
        tmp = a * b
    else if ((a * b) <= (-1.35d-176)) then
        tmp = x * y
    else if ((a * b) <= 2.2d-149) then
        tmp = z * t
    else if ((a * b) <= 4.4d-64) then
        tmp = x * y
    else if ((a * b) <= 1.45d+140) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -3.8e+136) {
		tmp = a * b;
	} else if ((a * b) <= -1.35e-176) {
		tmp = x * y;
	} else if ((a * b) <= 2.2e-149) {
		tmp = z * t;
	} else if ((a * b) <= 4.4e-64) {
		tmp = x * y;
	} else if ((a * b) <= 1.45e+140) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -3.8e+136:
		tmp = a * b
	elif (a * b) <= -1.35e-176:
		tmp = x * y
	elif (a * b) <= 2.2e-149:
		tmp = z * t
	elif (a * b) <= 4.4e-64:
		tmp = x * y
	elif (a * b) <= 1.45e+140:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -3.8e+136)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.35e-176)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.2e-149)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 4.4e-64)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 1.45e+140)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -3.8e+136)
		tmp = a * b;
	elseif ((a * b) <= -1.35e-176)
		tmp = x * y;
	elseif ((a * b) <= 2.2e-149)
		tmp = z * t;
	elseif ((a * b) <= 4.4e-64)
		tmp = x * y;
	elseif ((a * b) <= 1.45e+140)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -3.8e+136], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.35e-176], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.2e-149], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.4e-64], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.45e+140], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.80000000000000015e136 or 1.4499999999999999e140 < (*.f64 a b)

   1. Initial program 92.3%

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

   3. Taylor expanded in a around inf 74.0%

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

   if -3.80000000000000015e136 < (*.f64 a b) < -1.3499999999999999e-176 or 2.1999999999999998e-149 < (*.f64 a b) < 4.3999999999999999e-64

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 50.8%

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

   if -1.3499999999999999e-176 < (*.f64 a b) < 2.1999999999999998e-149 or 4.3999999999999999e-64 < (*.f64 a b) < 1.4499999999999999e140

   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 inf 45.8%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+136}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.35 \cdot 10^{-176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.2 \cdot 10^{-149}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-169}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -6e+225)
     (* x y)
     (if (<= (* x y) -1e-108)
       t_1
       (if (<= (* x y) -4.5e-169)
         (* z t)
         (if (<= (* x y) 2.8e+131) 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) <= -6e+225) {
		tmp = x * y;
	} else if ((x * y) <= -1e-108) {
		tmp = t_1;
	} else if ((x * y) <= -4.5e-169) {
		tmp = z * t;
	} else if ((x * y) <= 2.8e+131) {
		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) <= (-6d+225)) then
        tmp = x * y
    else if ((x * y) <= (-1d-108)) then
        tmp = t_1
    else if ((x * y) <= (-4.5d-169)) then
        tmp = z * t
    else if ((x * y) <= 2.8d+131) 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) <= -6e+225) {
		tmp = x * y;
	} else if ((x * y) <= -1e-108) {
		tmp = t_1;
	} else if ((x * y) <= -4.5e-169) {
		tmp = z * t;
	} else if ((x * y) <= 2.8e+131) {
		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) <= -6e+225:
		tmp = x * y
	elif (x * y) <= -1e-108:
		tmp = t_1
	elif (x * y) <= -4.5e-169:
		tmp = z * t
	elif (x * y) <= 2.8e+131:
		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) <= -6e+225)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1e-108)
		tmp = t_1;
	elseif (Float64(x * y) <= -4.5e-169)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 2.8e+131)
		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) <= -6e+225)
		tmp = x * y;
	elseif ((x * y) <= -1e-108)
		tmp = t_1;
	elseif ((x * y) <= -4.5e-169)
		tmp = z * t;
	elseif ((x * y) <= 2.8e+131)
		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], -6e+225], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-108], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e-169], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.8e+131], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.000000000000001e225 or 2.8000000000000001e131 < (*.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf 74.3%

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

   if -6.000000000000001e225 < (*.f64 x y) < -1.00000000000000004e-108 or -4.4999999999999999e-169 < (*.f64 x y) < 2.8000000000000001e131

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 92.8%

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

   4. Taylor expanded in z around inf 88.1%

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

   5. Taylor expanded in t around 0 62.4%

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

   if -1.00000000000000004e-108 < (*.f64 x y) < -4.4999999999999999e-169

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf 82.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-108}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-169}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{+131}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.4% accurate, 0.4× speedup

Math

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

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 (* z (+ t (/ (* x y) z))))))

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 = z * (t + ((x * y) / z));
	}
	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 = z * (t + ((x * y) / z));
	}
	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 = z * (t + ((x * y) / z))
	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(z * Float64(t + Float64(Float64(x * y) / z)));
	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 = z * (t + ((x * y) / z));
	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[(z * N[(t + N[(N[(x * y), $MachinePrecision] / z), $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 z around inf 10.0%

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

   4. Taylor expanded in a around 0 20.0%

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

   5. Taylor expanded in c around 0 50.4%

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

4. Final simplification 98.0%

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

Alternative 7: 42.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.65 \cdot 10^{+24}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.06 \cdot 10^{+143}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.65e+24)
   (* a b)
   (if (<= (* a b) 1.25e-8)
     (* z t)
     (if (<= (* a b) 2.5e+35)
       (* c i)
       (if (<= (* a b) 1.06e+143) (* z t) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.65e+24) {
		tmp = a * b;
	} else if ((a * b) <= 1.25e-8) {
		tmp = z * t;
	} else if ((a * b) <= 2.5e+35) {
		tmp = c * i;
	} else if ((a * b) <= 1.06e+143) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-1.65d+24)) then
        tmp = a * b
    else if ((a * b) <= 1.25d-8) then
        tmp = z * t
    else if ((a * b) <= 2.5d+35) then
        tmp = c * i
    else if ((a * b) <= 1.06d+143) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1.65e+24) {
		tmp = a * b;
	} else if ((a * b) <= 1.25e-8) {
		tmp = z * t;
	} else if ((a * b) <= 2.5e+35) {
		tmp = c * i;
	} else if ((a * b) <= 1.06e+143) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.65e+24:
		tmp = a * b
	elif (a * b) <= 1.25e-8:
		tmp = z * t
	elif (a * b) <= 2.5e+35:
		tmp = c * i
	elif (a * b) <= 1.06e+143:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.65e+24)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.25e-8)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.5e+35)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1.06e+143)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1.65e+24)
		tmp = a * b;
	elseif ((a * b) <= 1.25e-8)
		tmp = z * t;
	elseif ((a * b) <= 2.5e+35)
		tmp = c * i;
	elseif ((a * b) <= 1.06e+143)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1.65e+24], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.25e-8], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.5e+35], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.06e+143], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.6499999999999999e24 or 1.06e143 < (*.f64 a b)

   1. Initial program 93.7%

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

   3. Taylor expanded in a around inf 64.5%

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

   if -1.6499999999999999e24 < (*.f64 a b) < 1.2499999999999999e-8 or 2.50000000000000011e35 < (*.f64 a b) < 1.06e143

   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 inf 40.8%

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

   if 1.2499999999999999e-8 < (*.f64 a b) < 2.50000000000000011e35

   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 64.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.65 \cdot 10^{+24}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.06 \cdot 10^{+143}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.4 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.2e+140)
   (+ (* a b) (* z t))
   (if (<= (* a b) 4.5e-18)
     (+ (* x y) (* z t))
     (if (<= (* a b) 7.4e+140) (+ (* c i) (* 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) {
	double tmp;
	if ((a * b) <= -4.2e+140) {
		tmp = (a * b) + (z * t);
	} else if ((a * b) <= 4.5e-18) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 7.4e+140) {
		tmp = (c * i) + (z * t);
	} 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 ((a * b) <= (-4.2d+140)) then
        tmp = (a * b) + (z * t)
    else if ((a * b) <= 4.5d-18) then
        tmp = (x * y) + (z * t)
    else if ((a * b) <= 7.4d+140) then
        tmp = (c * i) + (z * t)
    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 ((a * b) <= -4.2e+140) {
		tmp = (a * b) + (z * t);
	} else if ((a * b) <= 4.5e-18) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 7.4e+140) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4.2e+140:
		tmp = (a * b) + (z * t)
	elif (a * b) <= 4.5e-18:
		tmp = (x * y) + (z * t)
	elif (a * b) <= 7.4e+140:
		tmp = (c * i) + (z * t)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4.2e+140)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(a * b) <= 4.5e-18)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(a * b) <= 7.4e+140)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	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 ((a * b) <= -4.2e+140)
		tmp = (a * b) + (z * t);
	elseif ((a * b) <= 4.5e-18)
		tmp = (x * y) + (z * t);
	elseif ((a * b) <= 7.4e+140)
		tmp = (c * i) + (z * t);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -4.2e+140], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.5e-18], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 7.4e+140], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.2000000000000004e140

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf 84.6%

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

   4. Taylor expanded in z around inf 90.6%

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

   5. Taylor expanded in c around 0 85.1%

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

   if -4.2000000000000004e140 < (*.f64 a b) < 4.49999999999999994e-18

   1. Initial program 97.9%

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

   3. Taylor expanded in a around 0 90.6%

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

      1. associate-+l+ 90.6%

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

      2. +-commutative 90.6%

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

      3. fma-define 90.6%

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

      4. *-commutative 90.6%

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

   5. Applied egg-rr 90.6%

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

   6. Taylor expanded in c around 0 73.0%

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

   if 4.49999999999999994e-18 < (*.f64 a b) < 7.40000000000000006e140

   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 a around 0 90.9%

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

   4. Taylor expanded in x around 0 70.1%

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

   if 7.40000000000000006e140 < (*.f64 a b)

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf 86.9%

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

   4. Taylor expanded in z around inf 85.0%

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

   5. Taylor expanded in t around 0 87.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.5 \cdot 10^{-18}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 7.4 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq 6 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.9e-16) (not (<= (* x y) 6e+59)))
   (+ (* 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) <= -2.9e-16) || !((x * y) <= 6e+59)) {
		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) <= (-2.9d-16)) .or. (.not. ((x * y) <= 6d+59))) 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) <= -2.9e-16) || !((x * y) <= 6e+59)) {
		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) <= -2.9e-16) or not ((x * y) <= 6e+59):
		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) <= -2.9e-16) || !(Float64(x * y) <= 6e+59))
		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) <= -2.9e-16) || ~(((x * y) <= 6e+59)))
		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], -2.9e-16], N[Not[LessEqual[N[(x * y), $MachinePrecision], 6e+59]], $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) < -2.8999999999999998e-16 or 6.0000000000000001e59 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in c around 0 88.5%

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

   if -2.8999999999999998e-16 < (*.f64 x y) < 6.0000000000000001e59

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 92.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.9 \cdot 10^{-16} \lor \neg \left(x \cdot y \leq 6 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2.7 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{elif}\;c \cdot i \leq 1.22 \cdot 10^{-52}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= (* c i) -2.7e+119)
     (+ (* c i) t_1)
     (if (<= (* c i) 1.22e-52)
       (+ (* a b) t_1)
       (+ (* 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 t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -2.7e+119) {
		tmp = (c * i) + t_1;
	} else if ((c * i) <= 1.22e-52) {
		tmp = (a * b) + t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((c * i) <= (-2.7d+119)) then
        tmp = (c * i) + t_1
    else if ((c * i) <= 1.22d-52) then
        tmp = (a * b) + t_1
    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 t_1 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -2.7e+119) {
		tmp = (c * i) + t_1;
	} else if ((c * i) <= 1.22e-52) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -2.7e+119:
		tmp = (c * i) + t_1
	elif (c * i) <= 1.22e-52:
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	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(c * i) <= -2.7e+119)
		tmp = Float64(Float64(c * i) + t_1);
	elseif (Float64(c * i) <= 1.22e-52)
		tmp = Float64(Float64(a * b) + t_1);
	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)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2.7e+119)
		tmp = (c * i) + t_1;
	elseif ((c * i) <= 1.22e-52)
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.7e+119], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.22e-52], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.6999999999999998e119

   1. Initial program 92.5%

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

   3. Taylor expanded in a around 0 85.3%

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

   if -2.6999999999999998e119 < (*.f64 c i) < 1.22e-52

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 95.2%

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

   if 1.22e-52 < (*.f64 c i)

   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 x around 0 84.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.7 \cdot 10^{+119}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 1.22 \cdot 10^{-52}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{+194}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.8e+119)
   (+ (* x y) (* c i))
   (if (<= (* c i) 9.2e+194)
     (+ (* a b) (+ (* 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) {
	double tmp;
	if ((c * i) <= -1.8e+119) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 9.2e+194) {
		tmp = (a * b) + ((x * y) + (z * t));
	} 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 ((c * i) <= (-1.8d+119)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= 9.2d+194) then
        tmp = (a * b) + ((x * y) + (z * t))
    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 ((c * i) <= -1.8e+119) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 9.2e+194) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.8e+119:
		tmp = (x * y) + (c * i)
	elif (c * i) <= 9.2e+194:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.8e+119)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= 9.2e+194)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	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 ((c * i) <= -1.8e+119)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= 9.2e+194)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.8e+119], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.2e+194], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.80000000000000001e119

   1. Initial program 92.5%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in t around 0 80.6%

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

   if -1.80000000000000001e119 < (*.f64 c i) < 9.2000000000000002e194

   1. Initial program 98.4%

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

   3. Taylor expanded in c around 0 92.4%

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

   if 9.2000000000000002e194 < (*.f64 c i)

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 83.3%

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

   4. Taylor expanded in z around inf 80.3%

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

   5. Taylor expanded in t around 0 83.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.8 \cdot 10^{+119}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{+194}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+56} \lor \neg \left(c \cdot i \leq 580000000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.45e+56) (not (<= (* c i) 580000000000.0)))
   (+ (* a b) (* c i))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.45e+56) || !((c * i) <= 580000000000.0)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-1.45d+56)) .or. (.not. ((c * i) <= 580000000000.0d0))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.45e+56) || !((c * i) <= 580000000000.0)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.45e+56) or not ((c * i) <= 580000000000.0):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.45e+56) || !(Float64(c * i) <= 580000000000.0))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.45e+56) || ~(((c * i) <= 580000000000.0)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.45e+56], N[Not[LessEqual[N[(c * i), $MachinePrecision], 580000000000.0]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.45000000000000004e56 or 5.8e11 < (*.f64 c i)

   1. Initial program 93.1%

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

   3. Taylor expanded in z around inf 87.5%

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

   4. Taylor expanded in z around inf 78.1%

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

   5. Taylor expanded in t around 0 72.5%

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

   if -1.45000000000000004e56 < (*.f64 c i) < 5.8e11

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 88.2%

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

   4. Taylor expanded in z around inf 68.3%

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

   5. Taylor expanded in c around 0 66.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+56} \lor \neg \left(c \cdot i \leq 580000000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+22} \lor \neg \left(a \cdot b \leq 1.2 \cdot 10^{+126}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -2.6e+22) (not (<= (* a b) 1.2e+126))) (* 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) <= -2.6e+22) || !((a * b) <= 1.2e+126)) {
		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) <= (-2.6d+22)) .or. (.not. ((a * b) <= 1.2d+126))) 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) <= -2.6e+22) || !((a * b) <= 1.2e+126)) {
		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) <= -2.6e+22) or not ((a * b) <= 1.2e+126):
		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) <= -2.6e+22) || !(Float64(a * b) <= 1.2e+126))
		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) <= -2.6e+22) || ~(((a * b) <= 1.2e+126)))
		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], -2.6e+22], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.2e+126]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.6e22 or 1.20000000000000006e126 < (*.f64 a b)

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf 64.2%

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

   if -2.6e22 < (*.f64 a b) < 1.20000000000000006e126

   1. Initial program 97.5%

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

   3. Taylor expanded in c around inf 30.9%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.6 \cdot 10^{+22} \lor \neg \left(a \cdot b \leq 1.2 \cdot 10^{+126}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.8% 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 96.1%

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

3. Taylor expanded in a around inf 28.6%

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

Reproduce

herbie shell --seed 2024096 
(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)))