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

Percentage Accurate: 95.9% → 97.4%

Time: 11.7s

Alternatives: 15

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: 95.9% 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: 97.4% accurate, 0.4× speedup

Math

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

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 (* y (+ x (/ (* c i) 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) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (x + ((c * i) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((a * b) + ((x * y) + (z * t))) + (c * i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (x + ((c * i) / y));
	}
	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 = y * (x + ((c * i) / y))
	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(y * Float64(x + Float64(Float64(c * i) / y)));
	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 = y * (x + ((c * i) / y));
	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[(y * N[(x + N[(N[(c * i), $MachinePrecision] / y), $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 0 40.0%

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

   4. Taylor expanded in a around 0 50.1%

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

   5. Taylor expanded in y around inf 60.1%

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

4. Final simplification 98.4%

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

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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 96.5%

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

   3. +-commutative 96.5%

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

   4. fma-define 97.3%

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

   5. fma-define 97.6%

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

3. Simplified 97.6%

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

Alternative 3: 43.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -0.000205:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -3 \cdot 10^{-85}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-210}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 9.8 \cdot 10^{+53}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+162}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -3.5e+108)
   (* x y)
   (if (<= (* x y) -2.6e+65)
     (* a b)
     (if (<= (* x y) -0.000205)
       (* c i)
       (if (<= (* x y) -3e-85)
         (* a b)
         (if (<= (* x y) -1.5e-132)
           (* z t)
           (if (<= (* x y) -5e-210)
             (* a b)
             (if (<= (* x y) 9.8e+53)
               (* c i)
               (if (<= (* x y) 1.45e+162) (* a b) (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.5e+108) {
		tmp = x * y;
	} else if ((x * y) <= -2.6e+65) {
		tmp = a * b;
	} else if ((x * y) <= -0.000205) {
		tmp = c * i;
	} else if ((x * y) <= -3e-85) {
		tmp = a * b;
	} else if ((x * y) <= -1.5e-132) {
		tmp = z * t;
	} else if ((x * y) <= -5e-210) {
		tmp = a * b;
	} else if ((x * y) <= 9.8e+53) {
		tmp = c * i;
	} else if ((x * y) <= 1.45e+162) {
		tmp = a * b;
	} 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+108)) then
        tmp = x * y
    else if ((x * y) <= (-2.6d+65)) then
        tmp = a * b
    else if ((x * y) <= (-0.000205d0)) then
        tmp = c * i
    else if ((x * y) <= (-3d-85)) then
        tmp = a * b
    else if ((x * y) <= (-1.5d-132)) then
        tmp = z * t
    else if ((x * y) <= (-5d-210)) then
        tmp = a * b
    else if ((x * y) <= 9.8d+53) then
        tmp = c * i
    else if ((x * y) <= 1.45d+162) then
        tmp = a * b
    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+108) {
		tmp = x * y;
	} else if ((x * y) <= -2.6e+65) {
		tmp = a * b;
	} else if ((x * y) <= -0.000205) {
		tmp = c * i;
	} else if ((x * y) <= -3e-85) {
		tmp = a * b;
	} else if ((x * y) <= -1.5e-132) {
		tmp = z * t;
	} else if ((x * y) <= -5e-210) {
		tmp = a * b;
	} else if ((x * y) <= 9.8e+53) {
		tmp = c * i;
	} else if ((x * y) <= 1.45e+162) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -3.5e+108:
		tmp = x * y
	elif (x * y) <= -2.6e+65:
		tmp = a * b
	elif (x * y) <= -0.000205:
		tmp = c * i
	elif (x * y) <= -3e-85:
		tmp = a * b
	elif (x * y) <= -1.5e-132:
		tmp = z * t
	elif (x * y) <= -5e-210:
		tmp = a * b
	elif (x * y) <= 9.8e+53:
		tmp = c * i
	elif (x * y) <= 1.45e+162:
		tmp = a * b
	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+108)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.6e+65)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -0.000205)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= -3e-85)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -1.5e-132)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -5e-210)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 9.8e+53)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= 1.45e+162)
		tmp = Float64(a * b);
	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+108)
		tmp = x * y;
	elseif ((x * y) <= -2.6e+65)
		tmp = a * b;
	elseif ((x * y) <= -0.000205)
		tmp = c * i;
	elseif ((x * y) <= -3e-85)
		tmp = a * b;
	elseif ((x * y) <= -1.5e-132)
		tmp = z * t;
	elseif ((x * y) <= -5e-210)
		tmp = a * b;
	elseif ((x * y) <= 9.8e+53)
		tmp = c * i;
	elseif ((x * y) <= 1.45e+162)
		tmp = a * b;
	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+108], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.6e+65], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -0.000205], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3e-85], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.5e-132], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-210], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.8e+53], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.45e+162], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.5000000000000002e108 or 1.45000000000000003e162 < (*.f64 x y)

   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 x around inf 72.7%

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

   if -3.5000000000000002e108 < (*.f64 x y) < -2.60000000000000003e65 or -2.05e-4 < (*.f64 x y) < -3.00000000000000022e-85 or -1.5e-132 < (*.f64 x y) < -5.0000000000000002e-210 or 9.80000000000000036e53 < (*.f64 x y) < 1.45000000000000003e162

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 62.1%

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

   if -2.60000000000000003e65 < (*.f64 x y) < -2.05e-4 or -5.0000000000000002e-210 < (*.f64 x y) < 9.80000000000000036e53

   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 c around inf 43.5%

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

   if -3.00000000000000022e-85 < (*.f64 x y) < -1.5e-132

   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 60.4%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -0.000205:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -3 \cdot 10^{-85}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-210}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 9.8 \cdot 10^{+53}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+162}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-312}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-93} \lor \neg \left(a \cdot b \leq 4.5 \cdot 10^{-18}\right) \land a \cdot b \leq 6.2 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* a b) -6e-13)
     t_2
     (if (<= (* a b) -5e-317)
       t_1
       (if (<= (* a b) 4e-312)
         (+ (* x y) (* c i))
         (if (or (<= (* a b) 5e-93)
                 (and (not (<= (* a b) 4.5e-18)) (<= (* a b) 6.2e+156)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -6e-13) {
		tmp = t_2;
	} else if ((a * b) <= -5e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4e-312) {
		tmp = (x * y) + (c * i);
	} else if (((a * b) <= 5e-93) || (!((a * b) <= 4.5e-18) && ((a * b) <= 6.2e+156))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (x * y) + (a * b)
    if ((a * b) <= (-6d-13)) then
        tmp = t_2
    else if ((a * b) <= (-5d-317)) then
        tmp = t_1
    else if ((a * b) <= 4d-312) then
        tmp = (x * y) + (c * i)
    else if (((a * b) <= 5d-93) .or. (.not. ((a * b) <= 4.5d-18)) .and. ((a * b) <= 6.2d+156)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -6e-13) {
		tmp = t_2;
	} else if ((a * b) <= -5e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4e-312) {
		tmp = (x * y) + (c * i);
	} else if (((a * b) <= 5e-93) || (!((a * b) <= 4.5e-18) && ((a * b) <= 6.2e+156))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (a * b)
	tmp = 0
	if (a * b) <= -6e-13:
		tmp = t_2
	elif (a * b) <= -5e-317:
		tmp = t_1
	elif (a * b) <= 4e-312:
		tmp = (x * y) + (c * i)
	elif ((a * b) <= 5e-93) or (not ((a * b) <= 4.5e-18) and ((a * b) <= 6.2e+156)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -6e-13)
		tmp = t_2;
	elseif (Float64(a * b) <= -5e-317)
		tmp = t_1;
	elseif (Float64(a * b) <= 4e-312)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif ((Float64(a * b) <= 5e-93) || (!(Float64(a * b) <= 4.5e-18) && (Float64(a * b) <= 6.2e+156)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((a * b) <= -6e-13)
		tmp = t_2;
	elseif ((a * b) <= -5e-317)
		tmp = t_1;
	elseif ((a * b) <= 4e-312)
		tmp = (x * y) + (c * i);
	elseif (((a * b) <= 5e-93) || (~(((a * b) <= 4.5e-18)) && ((a * b) <= 6.2e+156)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -6e-13], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -5e-317], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4e-312], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 5e-93], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.5e-18]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 6.2e+156]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.99999999999999968e-13 or 4.99999999999999994e-93 < (*.f64 a b) < 4.49999999999999994e-18 or 6.2000000000000004e156 < (*.f64 a b)

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 85.7%

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

   4. Taylor expanded in c around 0 76.6%

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

   if -5.99999999999999968e-13 < (*.f64 a b) < -5.00000017e-317 or 3.9999999999988e-312 < (*.f64 a b) < 4.99999999999999994e-93 or 4.49999999999999994e-18 < (*.f64 a b) < 6.2000000000000004e156

   1. Initial program 97.3%

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

   3. Taylor expanded in a around inf 81.0%

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

      1. associate-/l* 74.0%

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

      2. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around inf 74.5%

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

   if -5.00000017e-317 < (*.f64 a b) < 3.9999999999988e-312

   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 z around 0 86.6%

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

   4. Taylor expanded in a around 0 86.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{-13}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-312}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-93} \lor \neg \left(a \cdot b \leq 4.5 \cdot 10^{-18}\right) \land a \cdot b \leq 6.2 \cdot 10^{+156}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z + \frac{c \cdot i}{t}\right)\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-312}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9.8 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+156}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* t (+ z (/ (* c i) t)))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* a b) -1.7e-12)
     t_2
     (if (<= (* a b) -5e-317)
       t_1
       (if (<= (* a b) 4e-312)
         (+ (* x y) (* c i))
         (if (<= (* a b) 9.8e-157)
           t_1
           (if (<= (* a b) 2.5e+28)
             (+ (* x y) (* z t))
             (if (<= (* a b) 2.5e+156) (+ (* c i) (* z t)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t * (z + ((c * i) / t));
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -1.7e-12) {
		tmp = t_2;
	} else if ((a * b) <= -5e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4e-312) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 9.8e-157) {
		tmp = t_1;
	} else if ((a * b) <= 2.5e+28) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 2.5e+156) {
		tmp = (c * i) + (z * t);
	} 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 = t * (z + ((c * i) / t))
    t_2 = (x * y) + (a * b)
    if ((a * b) <= (-1.7d-12)) then
        tmp = t_2
    else if ((a * b) <= (-5d-317)) then
        tmp = t_1
    else if ((a * b) <= 4d-312) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 9.8d-157) then
        tmp = t_1
    else if ((a * b) <= 2.5d+28) then
        tmp = (x * y) + (z * t)
    else if ((a * b) <= 2.5d+156) then
        tmp = (c * i) + (z * t)
    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 = t * (z + ((c * i) / t));
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -1.7e-12) {
		tmp = t_2;
	} else if ((a * b) <= -5e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4e-312) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 9.8e-157) {
		tmp = t_1;
	} else if ((a * b) <= 2.5e+28) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 2.5e+156) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t * (z + ((c * i) / t))
	t_2 = (x * y) + (a * b)
	tmp = 0
	if (a * b) <= -1.7e-12:
		tmp = t_2
	elif (a * b) <= -5e-317:
		tmp = t_1
	elif (a * b) <= 4e-312:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 9.8e-157:
		tmp = t_1
	elif (a * b) <= 2.5e+28:
		tmp = (x * y) + (z * t)
	elif (a * b) <= 2.5e+156:
		tmp = (c * i) + (z * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t * Float64(z + Float64(Float64(c * i) / t)))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -1.7e-12)
		tmp = t_2;
	elseif (Float64(a * b) <= -5e-317)
		tmp = t_1;
	elseif (Float64(a * b) <= 4e-312)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 9.8e-157)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.5e+28)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(a * b) <= 2.5e+156)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t * (z + ((c * i) / t));
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((a * b) <= -1.7e-12)
		tmp = t_2;
	elseif ((a * b) <= -5e-317)
		tmp = t_1;
	elseif ((a * b) <= 4e-312)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 9.8e-157)
		tmp = t_1;
	elseif ((a * b) <= 2.5e+28)
		tmp = (x * y) + (z * t);
	elseif ((a * b) <= 2.5e+156)
		tmp = (c * i) + (z * t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t * N[(z + N[(N[(c * i), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.7e-12], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -5e-317], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4e-312], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9.8e-157], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.5e+28], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.5e+156], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -1.7e-12 or 2.49999999999999996e156 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in c around 0 77.1%

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

   if -1.7e-12 < (*.f64 a b) < -5.00000017e-317 or 3.9999999999988e-312 < (*.f64 a b) < 9.7999999999999995e-157

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf 77.5%

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

      1. associate-/l* 68.6%

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

      2. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 77.3%

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

   7. Taylor expanded in t around inf 74.7%

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

   if -5.00000017e-317 < (*.f64 a b) < 3.9999999999988e-312

   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 z around 0 86.6%

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

   4. Taylor expanded in a around 0 86.6%

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

   if 9.7999999999999995e-157 < (*.f64 a b) < 2.49999999999999979e28

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 90.6%

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

   4. Taylor expanded in c around 0 68.7%

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

   if 2.49999999999999979e28 < (*.f64 a b) < 2.49999999999999996e156

   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 a around inf 93.6%

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

      1. associate-/l* 90.2%

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

      2. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in t around inf 70.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;t \cdot \left(z + \frac{c \cdot i}{t}\right)\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-312}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9.8 \cdot 10^{-157}:\\ \;\;\;\;t \cdot \left(z + \frac{c \cdot i}{t}\right)\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+156}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := x \cdot y + a \cdot b\\ \mathbf{if}\;a \cdot b \leq -1.12 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-312}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 3.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* x y) (* a b))))
   (if (<= (* a b) -1.12e-11)
     t_2
     (if (<= (* a b) -5e-317)
       t_1
       (if (<= (* a b) 4e-312)
         (+ (* x y) (* c i))
         (if (<= (* a b) 2.1e-125)
           t_1
           (if (<= (* a b) 3.3e+28)
             (+ (* x y) (* z t))
             (if (<= (* a b) 8e+160) 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 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -1.12e-11) {
		tmp = t_2;
	} else if ((a * b) <= -5e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4e-312) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 2.1e-125) {
		tmp = t_1;
	} else if ((a * b) <= 3.3e+28) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 8e+160) {
		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 = (c * i) + (z * t)
    t_2 = (x * y) + (a * b)
    if ((a * b) <= (-1.12d-11)) then
        tmp = t_2
    else if ((a * b) <= (-5d-317)) then
        tmp = t_1
    else if ((a * b) <= 4d-312) then
        tmp = (x * y) + (c * i)
    else if ((a * b) <= 2.1d-125) then
        tmp = t_1
    else if ((a * b) <= 3.3d+28) then
        tmp = (x * y) + (z * t)
    else if ((a * b) <= 8d+160) 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 = (c * i) + (z * t);
	double t_2 = (x * y) + (a * b);
	double tmp;
	if ((a * b) <= -1.12e-11) {
		tmp = t_2;
	} else if ((a * b) <= -5e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4e-312) {
		tmp = (x * y) + (c * i);
	} else if ((a * b) <= 2.1e-125) {
		tmp = t_1;
	} else if ((a * b) <= 3.3e+28) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 8e+160) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (x * y) + (a * b)
	tmp = 0
	if (a * b) <= -1.12e-11:
		tmp = t_2
	elif (a * b) <= -5e-317:
		tmp = t_1
	elif (a * b) <= 4e-312:
		tmp = (x * y) + (c * i)
	elif (a * b) <= 2.1e-125:
		tmp = t_1
	elif (a * b) <= 3.3e+28:
		tmp = (x * y) + (z * t)
	elif (a * b) <= 8e+160:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -1.12e-11)
		tmp = t_2;
	elseif (Float64(a * b) <= -5e-317)
		tmp = t_1;
	elseif (Float64(a * b) <= 4e-312)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(a * b) <= 2.1e-125)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.3e+28)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(a * b) <= 8e+160)
		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 = (c * i) + (z * t);
	t_2 = (x * y) + (a * b);
	tmp = 0.0;
	if ((a * b) <= -1.12e-11)
		tmp = t_2;
	elseif ((a * b) <= -5e-317)
		tmp = t_1;
	elseif ((a * b) <= 4e-312)
		tmp = (x * y) + (c * i);
	elseif ((a * b) <= 2.1e-125)
		tmp = t_1;
	elseif ((a * b) <= 3.3e+28)
		tmp = (x * y) + (z * t);
	elseif ((a * b) <= 8e+160)
		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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.12e-11], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -5e-317], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4e-312], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.1e-125], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.3e+28], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8e+160], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.1200000000000001e-11 or 8.00000000000000005e160 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in c around 0 77.1%

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

   if -1.1200000000000001e-11 < (*.f64 a b) < -5.00000017e-317 or 3.9999999999988e-312 < (*.f64 a b) < 2.1e-125 or 3.3e28 < (*.f64 a b) < 8.00000000000000005e160

   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 a around inf 82.3%

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

      1. associate-/l* 75.4%

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

      2. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in t around inf 75.2%

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

   if -5.00000017e-317 < (*.f64 a b) < 3.9999999999988e-312

   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 z around 0 86.6%

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

   4. Taylor expanded in a around 0 86.6%

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

   if 2.1e-125 < (*.f64 a b) < 3.3e28

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 89.2%

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

   4. Taylor expanded in c around 0 67.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.12 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{-312}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+160}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.55 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.2 \cdot 10^{-143}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-214}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.7 \cdot 10^{-16}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.3 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.55e+64)
   (* a b)
   (if (<= (* a b) -7.2e-143)
     (* c i)
     (if (<= (* a b) -5e-317)
       (* z t)
       (if (<= (* a b) 2.3e-214)
         (* c i)
         (if (<= (* a b) 1.7e-16)
           (* z t)
           (if (<= (* a b) 5.3e+101) (* 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) <= -2.55e+64) {
		tmp = a * b;
	} else if ((a * b) <= -7.2e-143) {
		tmp = c * i;
	} else if ((a * b) <= -5e-317) {
		tmp = z * t;
	} else if ((a * b) <= 2.3e-214) {
		tmp = c * i;
	} else if ((a * b) <= 1.7e-16) {
		tmp = z * t;
	} else if ((a * b) <= 5.3e+101) {
		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) <= (-2.55d+64)) then
        tmp = a * b
    else if ((a * b) <= (-7.2d-143)) then
        tmp = c * i
    else if ((a * b) <= (-5d-317)) then
        tmp = z * t
    else if ((a * b) <= 2.3d-214) then
        tmp = c * i
    else if ((a * b) <= 1.7d-16) then
        tmp = z * t
    else if ((a * b) <= 5.3d+101) 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) <= -2.55e+64) {
		tmp = a * b;
	} else if ((a * b) <= -7.2e-143) {
		tmp = c * i;
	} else if ((a * b) <= -5e-317) {
		tmp = z * t;
	} else if ((a * b) <= 2.3e-214) {
		tmp = c * i;
	} else if ((a * b) <= 1.7e-16) {
		tmp = z * t;
	} else if ((a * b) <= 5.3e+101) {
		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) <= -2.55e+64:
		tmp = a * b
	elif (a * b) <= -7.2e-143:
		tmp = c * i
	elif (a * b) <= -5e-317:
		tmp = z * t
	elif (a * b) <= 2.3e-214:
		tmp = c * i
	elif (a * b) <= 1.7e-16:
		tmp = z * t
	elif (a * b) <= 5.3e+101:
		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) <= -2.55e+64)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -7.2e-143)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= -5e-317)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.3e-214)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 1.7e-16)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.3e+101)
		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) <= -2.55e+64)
		tmp = a * b;
	elseif ((a * b) <= -7.2e-143)
		tmp = c * i;
	elseif ((a * b) <= -5e-317)
		tmp = z * t;
	elseif ((a * b) <= 2.3e-214)
		tmp = c * i;
	elseif ((a * b) <= 1.7e-16)
		tmp = z * t;
	elseif ((a * b) <= 5.3e+101)
		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], -2.55e+64], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -7.2e-143], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -5e-317], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.3e-214], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.7e-16], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.3e+101], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.55000000000000012e64 or 5.30000000000000006e101 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 59.2%

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

   if -2.55000000000000012e64 < (*.f64 a b) < -7.1999999999999996e-143 or -5.00000017e-317 < (*.f64 a b) < 2.30000000000000011e-214 or 1.7e-16 < (*.f64 a b) < 5.30000000000000006e101

   1. Initial program 97.1%

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

   3. Taylor expanded in c around inf 44.3%

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

   if -7.1999999999999996e-143 < (*.f64 a b) < -5.00000017e-317 or 2.30000000000000011e-214 < (*.f64 a b) < 1.7e-16

   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 49.2%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.55 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -7.2 \cdot 10^{-143}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-317}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-214}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.7 \cdot 10^{-16}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.3 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;c \cdot i \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 21000000000000:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -3.6e+178)
     t_2
     (if (<= (* c i) -6e-16)
       t_1
       (if (<= (* c i) -2.8e-46)
         (* y (+ x (/ (* a b) y)))
         (if (<= (* c i) -2.4e-77)
           t_1
           (if (<= (* c i) 21000000000000.0) (+ (* x y) (* a b)) t_2)))))))

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 t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.6e+178) {
		tmp = t_2;
	} else if ((c * i) <= -6e-16) {
		tmp = t_1;
	} else if ((c * i) <= -2.8e-46) {
		tmp = y * (x + ((a * b) / y));
	} else if ((c * i) <= -2.4e-77) {
		tmp = t_1;
	} else if ((c * i) <= 21000000000000.0) {
		tmp = (x * y) + (a * b);
	} 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 = (x * y) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-3.6d+178)) then
        tmp = t_2
    else if ((c * i) <= (-6d-16)) then
        tmp = t_1
    else if ((c * i) <= (-2.8d-46)) then
        tmp = y * (x + ((a * b) / y))
    else if ((c * i) <= (-2.4d-77)) then
        tmp = t_1
    else if ((c * i) <= 21000000000000.0d0) then
        tmp = (x * y) + (a * b)
    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 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.6e+178) {
		tmp = t_2;
	} else if ((c * i) <= -6e-16) {
		tmp = t_1;
	} else if ((c * i) <= -2.8e-46) {
		tmp = y * (x + ((a * b) / y));
	} else if ((c * i) <= -2.4e-77) {
		tmp = t_1;
	} else if ((c * i) <= 21000000000000.0) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -3.6e+178:
		tmp = t_2
	elif (c * i) <= -6e-16:
		tmp = t_1
	elif (c * i) <= -2.8e-46:
		tmp = y * (x + ((a * b) / y))
	elif (c * i) <= -2.4e-77:
		tmp = t_1
	elif (c * i) <= 21000000000000.0:
		tmp = (x * y) + (a * b)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -3.6e+178)
		tmp = t_2;
	elseif (Float64(c * i) <= -6e-16)
		tmp = t_1;
	elseif (Float64(c * i) <= -2.8e-46)
		tmp = Float64(y * Float64(x + Float64(Float64(a * b) / y)));
	elseif (Float64(c * i) <= -2.4e-77)
		tmp = t_1;
	elseif (Float64(c * i) <= 21000000000000.0)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -3.6e+178)
		tmp = t_2;
	elseif ((c * i) <= -6e-16)
		tmp = t_1;
	elseif ((c * i) <= -2.8e-46)
		tmp = y * (x + ((a * b) / y));
	elseif ((c * i) <= -2.4e-77)
		tmp = t_1;
	elseif ((c * i) <= 21000000000000.0)
		tmp = (x * y) + (a * b);
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.6e+178], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -6e-16], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -2.8e-46], N[(y * N[(x + N[(N[(a * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.4e-77], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 21000000000000.0], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -3.5999999999999998e178 or 2.1e13 < (*.f64 c i)

   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 0 88.1%

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

   4. Taylor expanded in x around 0 79.1%

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

   if -3.5999999999999998e178 < (*.f64 c i) < -5.99999999999999987e-16 or -2.7999999999999998e-46 < (*.f64 c i) < -2.3999999999999999e-77

   1. Initial program 93.4%

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

   3. Taylor expanded in a around 0 80.8%

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

   4. Taylor expanded in c around 0 74.7%

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

   if -5.99999999999999987e-16 < (*.f64 c i) < -2.7999999999999998e-46

   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 0 78.5%

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

   4. Taylor expanded in y around inf 78.6%

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

   5. Taylor expanded in c around 0 79.4%

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

   if -2.3999999999999999e-77 < (*.f64 c i) < 2.1e13

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 74.5%

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

   4. Taylor expanded in c around 0 72.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{+178}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -6 \cdot 10^{-16}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(x + \frac{a \cdot b}{y}\right)\\ \mathbf{elif}\;c \cdot i \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 21000000000000:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -7e+225)
     (* x y)
     (if (<= (* x y) -1.6e-85)
       t_1
       (if (<= (* x y) -1.8e-132)
         (* z t)
         (if (<= (* x y) 1.95e+230) 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) <= -7e+225) {
		tmp = x * y;
	} else if ((x * y) <= -1.6e-85) {
		tmp = t_1;
	} else if ((x * y) <= -1.8e-132) {
		tmp = z * t;
	} else if ((x * y) <= 1.95e+230) {
		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) <= (-7d+225)) then
        tmp = x * y
    else if ((x * y) <= (-1.6d-85)) then
        tmp = t_1
    else if ((x * y) <= (-1.8d-132)) then
        tmp = z * t
    else if ((x * y) <= 1.95d+230) 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) <= -7e+225) {
		tmp = x * y;
	} else if ((x * y) <= -1.6e-85) {
		tmp = t_1;
	} else if ((x * y) <= -1.8e-132) {
		tmp = z * t;
	} else if ((x * y) <= 1.95e+230) {
		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) <= -7e+225:
		tmp = x * y
	elif (x * y) <= -1.6e-85:
		tmp = t_1
	elif (x * y) <= -1.8e-132:
		tmp = z * t
	elif (x * y) <= 1.95e+230:
		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) <= -7e+225)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.6e-85)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.8e-132)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.95e+230)
		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) <= -7e+225)
		tmp = x * y;
	elseif ((x * y) <= -1.6e-85)
		tmp = t_1;
	elseif ((x * y) <= -1.8e-132)
		tmp = z * t;
	elseif ((x * y) <= 1.95e+230)
		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], -7e+225], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.6e-85], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.8e-132], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.95e+230], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.0000000000000006e225 or 1.9499999999999999e230 < (*.f64 x y)

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 86.0%

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

   if -7.0000000000000006e225 < (*.f64 x y) < -1.60000000000000014e-85 or -1.80000000000000004e-132 < (*.f64 x y) < 1.9499999999999999e230

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 74.8%

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

   4. Taylor expanded in x around 0 66.0%

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

   if -1.60000000000000014e-85 < (*.f64 x y) < -1.80000000000000004e-132

   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 60.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+225}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.6 \cdot 10^{-85}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{+230}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+247}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= z -1.12e+266)
     t_1
     (if (<= z -2.5e+247)
       (+ (* x y) (* z t))
       (if (<= z -8.5e+138) t_1 (+ (* c i) (+ (* x y) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if (z <= -1.12e+266) {
		tmp = t_1;
	} else if (z <= -2.5e+247) {
		tmp = (x * y) + (z * t);
	} else if (z <= -8.5e+138) {
		tmp = t_1;
	} else {
		tmp = (c * i) + ((x * y) + (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) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if (z <= (-1.12d+266)) then
        tmp = t_1
    else if (z <= (-2.5d+247)) then
        tmp = (x * y) + (z * t)
    else if (z <= (-8.5d+138)) then
        tmp = t_1
    else
        tmp = (c * i) + ((x * y) + (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 t_1 = (c * i) + (z * t);
	double tmp;
	if (z <= -1.12e+266) {
		tmp = t_1;
	} else if (z <= -2.5e+247) {
		tmp = (x * y) + (z * t);
	} else if (z <= -8.5e+138) {
		tmp = t_1;
	} else {
		tmp = (c * i) + ((x * y) + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if z <= -1.12e+266:
		tmp = t_1
	elif z <= -2.5e+247:
		tmp = (x * y) + (z * t)
	elif z <= -8.5e+138:
		tmp = t_1
	else:
		tmp = (c * i) + ((x * y) + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (z <= -1.12e+266)
		tmp = t_1;
	elseif (z <= -2.5e+247)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (z <= -8.5e+138)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if (z <= -1.12e+266)
		tmp = t_1;
	elseif (z <= -2.5e+247)
		tmp = (x * y) + (z * t);
	elseif (z <= -8.5e+138)
		tmp = t_1;
	else
		tmp = (c * i) + ((x * y) + (a * b));
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+266], t$95$1, If[LessEqual[z, -2.5e+247], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e+138], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.11999999999999996e266 or -2.50000000000000011e247 < z < -8.5000000000000006e138

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 77.3%

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

      1. associate-/l* 66.1%

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

      2. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around inf 72.7%

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

   if -1.11999999999999996e266 < z < -2.50000000000000011e247

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 63.0%

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

   4. Taylor expanded in c around 0 63.0%

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

   if -8.5000000000000006e138 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 80.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+266}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+247}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.05 \cdot 10^{-11} \lor \neg \left(a \cdot b \leq 6.1 \cdot 10^{+150}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.05e-11) (not (<= (* a b) 6.1e+150)))
   (+ (* c i) (+ (* x y) (* a b)))
   (+ (* c i) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.05e-11) || !((a * b) <= 6.1e+150)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = (c * i) + ((x * y) + (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 (((a * b) <= (-1.05d-11)) .or. (.not. ((a * b) <= 6.1d+150))) then
        tmp = (c * i) + ((x * y) + (a * b))
    else
        tmp = (c * i) + ((x * y) + (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 (((a * b) <= -1.05e-11) || !((a * b) <= 6.1e+150)) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.05e-11) or not ((a * b) <= 6.1e+150):
		tmp = (c * i) + ((x * y) + (a * b))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1.05e-11) || !(Float64(a * b) <= 6.1e+150))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -1.05e-11) || ~(((a * b) <= 6.1e+150)))
		tmp = (c * i) + ((x * y) + (a * b));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.05e-11], N[Not[LessEqual[N[(a * b), $MachinePrecision], 6.1e+150]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.0499999999999999e-11 or 6.10000000000000026e150 < (*.f64 a b)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 86.7%

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

   if -1.0499999999999999e-11 < (*.f64 a b) < 6.10000000000000026e150

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0 90.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.05 \cdot 10^{-11} \lor \neg \left(a \cdot b \leq 6.1 \cdot 10^{+150}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+176} \lor \neg \left(c \cdot i \leq 21000000000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1e+176) (not (<= (* c i) 21000000000000.0)))
   (+ (* a b) (* c i))
   (+ (* x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1e+176) || !((c * i) <= 21000000000000.0)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-1d+176)) .or. (.not. ((c * i) <= 21000000000000.0d0))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (x * y) + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1e+176) || !((c * i) <= 21000000000000.0)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1e+176) or not ((c * i) <= 21000000000000.0):
		tmp = (a * b) + (c * i)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1e+176) || !(Float64(c * i) <= 21000000000000.0))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1e+176) || ~(((c * i) <= 21000000000000.0)))
		tmp = (a * b) + (c * i);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1e+176], N[Not[LessEqual[N[(c * i), $MachinePrecision], 21000000000000.0]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1e176 or 2.1e13 < (*.f64 c i)

   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 0 87.2%

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

   4. Taylor expanded in x around 0 78.2%

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

   if -1e176 < (*.f64 c i) < 2.1e13

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 69.2%

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

   4. Taylor expanded in c around 0 66.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1 \cdot 10^{+176} \lor \neg \left(c \cdot i \leq 21000000000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 10000000000000:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5.5e+133)
   (+ (* x y) (* c i))
   (if (<= (* c i) 10000000000000.0) (+ (* x y) (* a b)) (+ (* 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) <= -5.5e+133) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 10000000000000.0) {
		tmp = (x * y) + (a * b);
	} 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) <= (-5.5d+133)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= 10000000000000.0d0) then
        tmp = (x * y) + (a * b)
    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) <= -5.5e+133) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 10000000000000.0) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5.5e+133:
		tmp = (x * y) + (c * i)
	elif (c * i) <= 10000000000000.0:
		tmp = (x * y) + (a * b)
	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) <= -5.5e+133)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= 10000000000000.0)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	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) <= -5.5e+133)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= 10000000000000.0)
		tmp = (x * y) + (a * b);
	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], -5.5e+133], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 10000000000000.0], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.5e133

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 88.9%

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

   4. Taylor expanded in a around 0 77.9%

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

   if -5.5e133 < (*.f64 c i) < 1e13

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 69.3%

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

   4. Taylor expanded in c around 0 67.8%

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

   if 1e13 < (*.f64 c i)

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 82.7%

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

   4. Taylor expanded in x around 0 73.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 10000000000000:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.2 \cdot 10^{+61} \lor \neg \left(a \cdot b \leq 9 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -9.2e+61) (not (<= (* a b) 9e+107))) (* 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) <= -9.2e+61) || !((a * b) <= 9e+107)) {
		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) <= (-9.2d+61)) .or. (.not. ((a * b) <= 9d+107))) 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) <= -9.2e+61) || !((a * b) <= 9e+107)) {
		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) <= -9.2e+61) or not ((a * b) <= 9e+107):
		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) <= -9.2e+61) || !(Float64(a * b) <= 9e+107))
		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) <= -9.2e+61) || ~(((a * b) <= 9e+107)))
		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], -9.2e+61], N[Not[LessEqual[N[(a * b), $MachinePrecision], 9e+107]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.1999999999999998e61 or 9e107 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 59.2%

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

   if -9.1999999999999998e61 < (*.f64 a b) < 9e107

   1. Initial program 97.4%

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

   3. Taylor expanded in c around inf 37.0%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.2 \cdot 10^{+61} \lor \neg \left(a \cdot b \leq 9 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 28.4%

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

Reproduce

herbie shell --seed 2024089 
(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)))