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

Percentage Accurate: 95.9% → 98.5%

Time: 11.7s

Alternatives: 16

Speedup: 0.4×

• 41.6% 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: 98.5% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (* a (+ b (+ (* t (/ z a)) (* x (/ y a))))))))

C

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

Java

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

Python

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

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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(a * Float64(b + Float64(Float64(t * Float64(z / a)) + Float64(x * Float64(y / a)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (b + ((t * (z / a)) + (x * (y / a))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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[(a * N[(b + N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $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 c around 0 33.3%

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

   4. Taylor expanded in a around inf 44.4%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 98.8%

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

Alternative 2: 97.9% accurate, 0.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma c i (fma x y (fma z t (* a b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.7%

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

   3. associate-+l+ 97.7%

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

   4. fma-define 98.0%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

Alternative 3: 98.0% accurate, 0.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma c i (fma a b (fma x y (* z t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-define 97.7%

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

   3. +-commutative 97.7%

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

   4. fma-define 98.0%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

Alternative 4: 65.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ t_2 := c \cdot i + z \cdot t\\ t_3 := x \cdot y + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-233}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-111}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 10^{-47}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* a (+ b (/ (* x y) a))))
        (t_2 (+ (* c i) (* z t)))
        (t_3 (+ (* x y) (* c i))))
   (if (<= (* a b) -5e+246)
     t_1
     (if (<= (* a b) -5e+144)
       t_2
       (if (<= (* a b) -2e+104)
         t_1
         (if (<= (* a b) -1e-85)
           t_2
           (if (<= (* a b) 5e-233)
             t_3
             (if (<= (* a b) 5e-111)
               (+ (* x y) (* z t))
               (if (<= (* a b) 1e-47)
                 t_3
                 (if (<= (* a b) 4e+121) t_2 (+ (* a b) (* c i))))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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) / a));
	double t_2 = (c * i) + (z * t);
	double t_3 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -5e+246) {
		tmp = t_1;
	} else if ((a * b) <= -5e+144) {
		tmp = t_2;
	} else if ((a * b) <= -2e+104) {
		tmp = t_1;
	} else if ((a * b) <= -1e-85) {
		tmp = t_2;
	} else if ((a * b) <= 5e-233) {
		tmp = t_3;
	} else if ((a * b) <= 5e-111) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 1e-47) {
		tmp = t_3;
	} else if ((a * b) <= 4e+121) {
		tmp = t_2;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (b + ((x * y) / a))
    t_2 = (c * i) + (z * t)
    t_3 = (x * y) + (c * i)
    if ((a * b) <= (-5d+246)) then
        tmp = t_1
    else if ((a * b) <= (-5d+144)) then
        tmp = t_2
    else if ((a * b) <= (-2d+104)) then
        tmp = t_1
    else if ((a * b) <= (-1d-85)) then
        tmp = t_2
    else if ((a * b) <= 5d-233) then
        tmp = t_3
    else if ((a * b) <= 5d-111) then
        tmp = (x * y) + (z * t)
    else if ((a * b) <= 1d-47) then
        tmp = t_3
    else if ((a * b) <= 4d+121) then
        tmp = t_2
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) / a));
	double t_2 = (c * i) + (z * t);
	double t_3 = (x * y) + (c * i);
	double tmp;
	if ((a * b) <= -5e+246) {
		tmp = t_1;
	} else if ((a * b) <= -5e+144) {
		tmp = t_2;
	} else if ((a * b) <= -2e+104) {
		tmp = t_1;
	} else if ((a * b) <= -1e-85) {
		tmp = t_2;
	} else if ((a * b) <= 5e-233) {
		tmp = t_3;
	} else if ((a * b) <= 5e-111) {
		tmp = (x * y) + (z * t);
	} else if ((a * b) <= 1e-47) {
		tmp = t_3;
	} else if ((a * b) <= 4e+121) {
		tmp = t_2;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = a * (b + ((x * y) / a))
	t_2 = (c * i) + (z * t)
	t_3 = (x * y) + (c * i)
	tmp = 0
	if (a * b) <= -5e+246:
		tmp = t_1
	elif (a * b) <= -5e+144:
		tmp = t_2
	elif (a * b) <= -2e+104:
		tmp = t_1
	elif (a * b) <= -1e-85:
		tmp = t_2
	elif (a * b) <= 5e-233:
		tmp = t_3
	elif (a * b) <= 5e-111:
		tmp = (x * y) + (z * t)
	elif (a * b) <= 1e-47:
		tmp = t_3
	elif (a * b) <= 4e+121:
		tmp = t_2
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a * Float64(b + Float64(Float64(x * y) / a)))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	t_3 = Float64(Float64(x * y) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -5e+246)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e+144)
		tmp = t_2;
	elseif (Float64(a * b) <= -2e+104)
		tmp = t_1;
	elseif (Float64(a * b) <= -1e-85)
		tmp = t_2;
	elseif (Float64(a * b) <= 5e-233)
		tmp = t_3;
	elseif (Float64(a * b) <= 5e-111)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(a * b) <= 1e-47)
		tmp = t_3;
	elseif (Float64(a * b) <= 4e+121)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a * (b + ((x * y) / a));
	t_2 = (c * i) + (z * t);
	t_3 = (x * y) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -5e+246)
		tmp = t_1;
	elseif ((a * b) <= -5e+144)
		tmp = t_2;
	elseif ((a * b) <= -2e+104)
		tmp = t_1;
	elseif ((a * b) <= -1e-85)
		tmp = t_2;
	elseif ((a * b) <= 5e-233)
		tmp = t_3;
	elseif ((a * b) <= 5e-111)
		tmp = (x * y) + (z * t);
	elseif ((a * b) <= 1e-47)
		tmp = t_3;
	elseif ((a * b) <= 4e+121)
		tmp = t_2;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a * N[(b + N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+246], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e+144], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2e+104], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1e-85], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 5e-233], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 5e-111], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e-47], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 4e+121], t$95$2, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -4.99999999999999976e246 or -4.9999999999999999e144 < (*.f64 a b) < -2e104

   1. Initial program 86.2%

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

   3. Taylor expanded in c around 0 89.7%

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

   4. Taylor expanded in a around inf 89.7%

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

      1. associate-/l* 96.6%

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

      2. associate-/l* 96.6%

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

   6. Simplified 96.6%

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

   7. Taylor expanded in t around 0 93.2%

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

   if -4.99999999999999976e246 < (*.f64 a b) < -4.9999999999999999e144 or -2e104 < (*.f64 a b) < -9.9999999999999998e-86 or 9.9999999999999997e-48 < (*.f64 a b) < 4.00000000000000015e121

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 88.7%

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

   4. Taylor expanded in x around 0 79.5%

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

   if -9.9999999999999998e-86 < (*.f64 a b) < 5.00000000000000012e-233 or 5.0000000000000003e-111 < (*.f64 a b) < 9.9999999999999997e-48

   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 a around 0 95.4%

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

   4. Taylor expanded in t around 0 77.9%

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

   if 5.00000000000000012e-233 < (*.f64 a b) < 5.0000000000000003e-111

   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 0 93.3%

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

   4. Taylor expanded in a around inf 74.5%

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

      1. associate-/l* 74.5%

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

      2. associate-/l* 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in a around 0 93.3%

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

   if 4.00000000000000015e121 < (*.f64 a b)

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0 91.1%

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

   4. Taylor expanded in t around 0 84.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+246}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+144}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(b + \frac{x \cdot y}{a}\right)\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-85}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-233}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-111}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 10^{-47}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+121}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -105:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -3.9 \cdot 10^{-43}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* c i) -3.8e+103)
     t_2
     (if (<= (* c i) -105.0)
       t_1
       (if (<= (* c i) -3.9e-43)
         (+ (* x y) (* c i))
         (if (<= (* c i) -1.55e-279)
           (+ (* x y) (* z t))
           (if (<= (* c i) 4.5e+65) t_1 t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3.8e+103) {
		tmp = t_2;
	} else if ((c * i) <= -105.0) {
		tmp = t_1;
	} else if ((c * i) <= -3.9e-43) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -1.55e-279) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 4.5e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = (c * i) + (z * t)
    if ((c * i) <= (-3.8d+103)) then
        tmp = t_2
    else if ((c * i) <= (-105.0d0)) then
        tmp = t_1
    else if ((c * i) <= (-3.9d-43)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= (-1.55d-279)) then
        tmp = (x * y) + (z * t)
    else if ((c * i) <= 4.5d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -3.8e+103) {
		tmp = t_2;
	} else if ((c * i) <= -105.0) {
		tmp = t_1;
	} else if ((c * i) <= -3.9e-43) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= -1.55e-279) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 4.5e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -3.8e+103:
		tmp = t_2
	elif (c * i) <= -105.0:
		tmp = t_1
	elif (c * i) <= -3.9e-43:
		tmp = (x * y) + (c * i)
	elif (c * i) <= -1.55e-279:
		tmp = (x * y) + (z * t)
	elif (c * i) <= 4.5e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -3.8e+103)
		tmp = t_2;
	elseif (Float64(c * i) <= -105.0)
		tmp = t_1;
	elseif (Float64(c * i) <= -3.9e-43)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= -1.55e-279)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(c * i) <= 4.5e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -3.8e+103)
		tmp = t_2;
	elseif ((c * i) <= -105.0)
		tmp = t_1;
	elseif ((c * i) <= -3.9e-43)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= -1.55e-279)
		tmp = (x * y) + (z * t);
	elseif ((c * i) <= 4.5e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.8e+103], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -105.0], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -3.9e-43], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.55e-279], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.5e+65], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -3.7999999999999997e103 or 4.5e65 < (*.f64 c i)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 90.6%

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

   4. Taylor expanded in x around 0 84.5%

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

   if -3.7999999999999997e103 < (*.f64 c i) < -105 or -1.55e-279 < (*.f64 c i) < 4.5e65

   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 x around 0 73.2%

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

   4. Taylor expanded in c around 0 69.9%

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

   if -105 < (*.f64 c i) < -3.9e-43

   1. Initial program 88.9%

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

   3. Taylor expanded in a around 0 68.0%

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

   4. Taylor expanded in t around 0 79.1%

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

   if -3.9e-43 < (*.f64 c i) < -1.55e-279

   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 0 100.0%

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

   4. Taylor expanded in a around inf 74.9%

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

      1. associate-/l* 74.9%

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

      2. associate-/l* 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in a around 0 77.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -105:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -3.9 \cdot 10^{-43}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9 \cdot 10^{+102}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.8 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -9e+102)
   (* c i)
   (if (<= (* c i) -2.8e-279)
     (* x y)
     (if (<= (* c i) 2.5e-20)
       (* a b)
       (if (<= (* c i) 1.5e+32)
         (* x y)
         (if (<= (* c i) 9.5e+56) (* z t) (* c i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -9e+102) {
		tmp = c * i;
	} else if ((c * i) <= -2.8e-279) {
		tmp = x * y;
	} else if ((c * i) <= 2.5e-20) {
		tmp = a * b;
	} else if ((c * i) <= 1.5e+32) {
		tmp = x * y;
	} else if ((c * i) <= 9.5e+56) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-9d+102)) then
        tmp = c * i
    else if ((c * i) <= (-2.8d-279)) then
        tmp = x * y
    else if ((c * i) <= 2.5d-20) then
        tmp = a * b
    else if ((c * i) <= 1.5d+32) then
        tmp = x * y
    else if ((c * i) <= 9.5d+56) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -9e+102) {
		tmp = c * i;
	} else if ((c * i) <= -2.8e-279) {
		tmp = x * y;
	} else if ((c * i) <= 2.5e-20) {
		tmp = a * b;
	} else if ((c * i) <= 1.5e+32) {
		tmp = x * y;
	} else if ((c * i) <= 9.5e+56) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -9e+102:
		tmp = c * i
	elif (c * i) <= -2.8e-279:
		tmp = x * y
	elif (c * i) <= 2.5e-20:
		tmp = a * b
	elif (c * i) <= 1.5e+32:
		tmp = x * y
	elif (c * i) <= 9.5e+56:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -9e+102)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.8e-279)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 2.5e-20)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1.5e+32)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 9.5e+56)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -9e+102)
		tmp = c * i;
	elseif ((c * i) <= -2.8e-279)
		tmp = x * y;
	elseif ((c * i) <= 2.5e-20)
		tmp = a * b;
	elseif ((c * i) <= 1.5e+32)
		tmp = x * y;
	elseif ((c * i) <= 9.5e+56)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -9e+102], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.8e-279], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.5e-20], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.5e+32], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.5e+56], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -9.00000000000000042e102 or 9.4999999999999997e56 < (*.f64 c i)

   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 inf 66.9%

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

   if -9.00000000000000042e102 < (*.f64 c i) < -2.8000000000000001e-279 or 2.4999999999999999e-20 < (*.f64 c i) < 1.5e32

   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 0 94.3%

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

   4. Taylor expanded in a around inf 72.5%

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

      1. associate-/l* 73.9%

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

      2. associate-/l* 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in x around inf 45.7%

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

   if -2.8000000000000001e-279 < (*.f64 c i) < 2.4999999999999999e-20

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 44.0%

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

   if 1.5e32 < (*.f64 c i) < 9.4999999999999997e56

   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 0 100.0%

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

   4. Taylor expanded in a around inf 66.7%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in t around inf 66.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9 \cdot 10^{+102}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.8 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+56}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -0.0024:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* c i) -6.5e+104)
     t_2
     (if (<= (* c i) -0.0024)
       t_1
       (if (<= (* c i) -1.55e-70)
         (+ (* x y) (* c i))
         (if (<= (* c i) 8.5e+64) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -6.5e+104) {
		tmp = t_2;
	} else if ((c * i) <= -0.0024) {
		tmp = t_1;
	} else if ((c * i) <= -1.55e-70) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 8.5e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = (c * i) + (z * t)
    if ((c * i) <= (-6.5d+104)) then
        tmp = t_2
    else if ((c * i) <= (-0.0024d0)) then
        tmp = t_1
    else if ((c * i) <= (-1.55d-70)) then
        tmp = (x * y) + (c * i)
    else if ((c * i) <= 8.5d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -6.5e+104) {
		tmp = t_2;
	} else if ((c * i) <= -0.0024) {
		tmp = t_1;
	} else if ((c * i) <= -1.55e-70) {
		tmp = (x * y) + (c * i);
	} else if ((c * i) <= 8.5e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -6.5e+104:
		tmp = t_2
	elif (c * i) <= -0.0024:
		tmp = t_1
	elif (c * i) <= -1.55e-70:
		tmp = (x * y) + (c * i)
	elif (c * i) <= 8.5e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -6.5e+104)
		tmp = t_2;
	elseif (Float64(c * i) <= -0.0024)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.55e-70)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(c * i) <= 8.5e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -6.5e+104)
		tmp = t_2;
	elseif ((c * i) <= -0.0024)
		tmp = t_1;
	elseif ((c * i) <= -1.55e-70)
		tmp = (x * y) + (c * i);
	elseif ((c * i) <= 8.5e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -6.5e+104], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -0.0024], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.55e-70], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.5e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.5000000000000005e104 or 8.4999999999999998e64 < (*.f64 c i)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 90.6%

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

   4. Taylor expanded in x around 0 84.5%

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

   if -6.5000000000000005e104 < (*.f64 c i) < -0.00239999999999999979 or -1.55e-70 < (*.f64 c i) < 8.4999999999999998e64

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 70.2%

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

   4. Taylor expanded in c around 0 67.7%

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

   if -0.00239999999999999979 < (*.f64 c i) < -1.55e-70

   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 a around 0 73.8%

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

   4. Taylor expanded in t around 0 82.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+104}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -0.0024:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.4 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -6.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.7 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* c i) -1.4e+104)
     t_2
     (if (<= (* c i) -6.5)
       t_1
       (if (<= (* c i) -1.55e-70)
         (* x y)
         (if (<= (* c i) 1.7e+64) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1.4e+104) {
		tmp = t_2;
	} else if ((c * i) <= -6.5) {
		tmp = t_1;
	} else if ((c * i) <= -1.55e-70) {
		tmp = x * y;
	} else if ((c * i) <= 1.7e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = (c * i) + (z * t)
    if ((c * i) <= (-1.4d+104)) then
        tmp = t_2
    else if ((c * i) <= (-6.5d0)) then
        tmp = t_1
    else if ((c * i) <= (-1.55d-70)) then
        tmp = x * y
    else if ((c * i) <= 1.7d+64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1.4e+104) {
		tmp = t_2;
	} else if ((c * i) <= -6.5) {
		tmp = t_1;
	} else if ((c * i) <= -1.55e-70) {
		tmp = x * y;
	} else if ((c * i) <= 1.7e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -1.4e+104:
		tmp = t_2
	elif (c * i) <= -6.5:
		tmp = t_1
	elif (c * i) <= -1.55e-70:
		tmp = x * y
	elif (c * i) <= 1.7e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.4e+104)
		tmp = t_2;
	elseif (Float64(c * i) <= -6.5)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.55e-70)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 1.7e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.4e+104)
		tmp = t_2;
	elseif ((c * i) <= -6.5)
		tmp = t_1;
	elseif ((c * i) <= -1.55e-70)
		tmp = x * y;
	elseif ((c * i) <= 1.7e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.4e+104], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -6.5], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.55e-70], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.7e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.4e104 or 1.7000000000000001e64 < (*.f64 c i)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 90.6%

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

   4. Taylor expanded in x around 0 84.5%

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

   if -1.4e104 < (*.f64 c i) < -6.5 or -1.55e-70 < (*.f64 c i) < 1.7000000000000001e64

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 70.2%

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

   4. Taylor expanded in c around 0 67.7%

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

   if -6.5 < (*.f64 c i) < -1.55e-70

   1. Initial program 90.9%

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

   3. Taylor expanded in c around 0 82.1%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. associate-/l* 65.3%

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

      2. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in x around inf 74.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.4 \cdot 10^{+104}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -6.5:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.7 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -2.35 \cdot 10^{+244}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -2.35e+244)
     (* x y)
     (if (<= (* x y) -1.7e-16)
       t_1
       (if (<= (* x y) -2.6e-36)
         (* z t)
         (if (<= (* x y) 4.8e+197) t_1 (* x y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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) <= -2.35e+244) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e-16) {
		tmp = t_1;
	} else if ((x * y) <= -2.6e-36) {
		tmp = z * t;
	} else if ((x * y) <= 4.8e+197) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-2.35d+244)) then
        tmp = x * y
    else if ((x * y) <= (-1.7d-16)) then
        tmp = t_1
    else if ((x * y) <= (-2.6d-36)) then
        tmp = z * t
    else if ((x * y) <= 4.8d+197) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -2.35e+244) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e-16) {
		tmp = t_1;
	} else if ((x * y) <= -2.6e-36) {
		tmp = z * t;
	} else if ((x * y) <= 4.8e+197) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -2.35e+244:
		tmp = x * y
	elif (x * y) <= -1.7e-16:
		tmp = t_1
	elif (x * y) <= -2.6e-36:
		tmp = z * t
	elif (x * y) <= 4.8e+197:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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) <= -2.35e+244)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.7e-16)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.6e-36)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 4.8e+197)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -2.35e+244)
		tmp = x * y;
	elseif ((x * y) <= -1.7e-16)
		tmp = t_1;
	elseif ((x * y) <= -2.6e-36)
		tmp = z * t;
	elseif ((x * y) <= 4.8e+197)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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], -2.35e+244], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.7e-16], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e-36], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.8e+197], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.35000000000000006e244 or 4.7999999999999998e197 < (*.f64 x y)

   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 c around 0 81.8%

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

   4. Taylor expanded in a around inf 63.4%

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

      1. associate-/l* 65.3%

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

      2. associate-/l* 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in x around inf 73.0%

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

   if -2.35000000000000006e244 < (*.f64 x y) < -1.7e-16 or -2.6e-36 < (*.f64 x y) < 4.7999999999999998e197

   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 x around 0 87.7%

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

   4. Taylor expanded in t around 0 65.7%

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

   if -1.7e-16 < (*.f64 x y) < -2.6e-36

   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 0 89.4%

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

   4. Taylor expanded in a around inf 78.3%

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

      1. associate-/l* 78.3%

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

      2. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in t around inf 78.5%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.35 \cdot 10^{+244}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+197}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+274}:\\ \;\;\;\;a \cdot \left(b + \left(t \cdot \frac{z}{a} + x \cdot \frac{y}{a}\right)\right)\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+84} \lor \neg \left(a \cdot b \leq 10^{-47}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1e+274)
   (* a (+ b (+ (* t (/ z a)) (* x (/ y a)))))
   (if (or (<= (* a b) -5e+84) (not (<= (* a b) 1e-47)))
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* x y) (* z t))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -1e+274) {
		tmp = a * (b + ((t * (z / a)) + (x * (y / a))));
	} else if (((a * b) <= -5e+84) || !((a * b) <= 1e-47)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-1d+274)) then
        tmp = a * (b + ((t * (z / a)) + (x * (y / a))))
    else if (((a * b) <= (-5d+84)) .or. (.not. ((a * b) <= 1d-47))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -1e+274) {
		tmp = a * (b + ((t * (z / a)) + (x * (y / a))));
	} else if (((a * b) <= -5e+84) || !((a * b) <= 1e-47)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1e+274:
		tmp = a * (b + ((t * (z / a)) + (x * (y / a))))
	elif ((a * b) <= -5e+84) or not ((a * b) <= 1e-47):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1e+274)
		tmp = Float64(a * Float64(b + Float64(Float64(t * Float64(z / a)) + Float64(x * Float64(y / a)))));
	elseif ((Float64(a * b) <= -5e+84) || !(Float64(a * b) <= 1e-47))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -1e+274)
		tmp = a * (b + ((t * (z / a)) + (x * (y / a))));
	elseif (((a * b) <= -5e+84) || ~(((a * b) <= 1e-47)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+274], N[(a * N[(b + N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+84], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e-47]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999921e273

   1. Initial program 77.8%

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

   3. Taylor expanded in c around 0 83.3%

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

   4. Taylor expanded in a around inf 88.9%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -9.99999999999999921e273 < (*.f64 a b) < -5.0000000000000001e84 or 9.9999999999999997e-48 < (*.f64 a b)

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 92.7%

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

   if -5.0000000000000001e84 < (*.f64 a b) < 9.9999999999999997e-48

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 95.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+274}:\\ \;\;\;\;a \cdot \left(b + \left(t \cdot \frac{z}{a} + x \cdot \frac{y}{a}\right)\right)\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+84} \lor \neg \left(a \cdot b \leq 10^{-47}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+84} \lor \neg \left(a \cdot b \leq 10^{-47}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -5e+84) (not (<= (* a b) 1e-47)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* c i) (+ (* x y) (* z t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -5e+84) || !((a * b) <= 1e-47)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-5d+84)) .or. (.not. ((a * b) <= 1d-47))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -5e+84) || !((a * b) <= 1e-47)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -5e+84) or not ((a * b) <= 1e-47):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+84) || !(Float64(a * b) <= 1e-47))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -5e+84) || ~(((a * b) <= 1e-47)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+84], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e-47]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $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) < -5.0000000000000001e84 or 9.9999999999999997e-48 < (*.f64 a b)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 89.7%

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

   if -5.0000000000000001e84 < (*.f64 a b) < 9.9999999999999997e-48

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0 95.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+84} \lor \neg \left(a \cdot b \leq 10^{-47}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -9 \cdot 10^{+102} \lor \neg \left(c \cdot i \leq 7.6 \cdot 10^{+66}\right):\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* c i) -9e+102) (not (<= (* c i) 7.6e+66)))
     (+ (* c i) t_1)
     (+ (* a b) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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) <= -9e+102) || !((c * i) <= 7.6e+66)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-9d+102)) .or. (.not. ((c * i) <= 7.6d+66))) then
        tmp = (c * i) + t_1
    else
        tmp = (a * b) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -9e+102) || !((c * i) <= 7.6e+66)) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (a * b) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((c * i) <= -9e+102) or not ((c * i) <= 7.6e+66):
		tmp = (c * i) + t_1
	else:
		tmp = (a * b) + t_1
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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) <= -9e+102) || !(Float64(c * i) <= 7.6e+66))
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(a * b) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((c * i) <= -9e+102) || ~(((c * i) <= 7.6e+66)))
		tmp = (c * i) + t_1;
	else
		tmp = (a * b) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(c * i), $MachinePrecision], -9e+102], N[Not[LessEqual[N[(c * i), $MachinePrecision], 7.6e+66]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.00000000000000042e102 or 7.6000000000000004e66 < (*.f64 c i)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 90.6%

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

   if -9.00000000000000042e102 < (*.f64 c i) < 7.6000000000000004e66

   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 0 94.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9 \cdot 10^{+102} \lor \neg \left(c \cdot i \leq 7.6 \cdot 10^{+66}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+106} \lor \neg \left(c \cdot i \leq 4.5 \cdot 10^{+145}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.05e+106) (not (<= (* c i) 4.5e+145)))
   (+ (* c i) (* z t))
   (+ (* a b) (+ (* x y) (* z t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.05e+106) || !((c * i) <= 4.5e+145)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-1.05d+106)) .or. (.not. ((c * i) <= 4.5d+145))) then
        tmp = (c * i) + (z * t)
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -1.05e+106) || !((c * i) <= 4.5e+145)) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.05e+106) or not ((c * i) <= 4.5e+145):
		tmp = (c * i) + (z * t)
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.05e+106) || !(Float64(c * i) <= 4.5e+145))
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.05e+106) || ~(((c * i) <= 4.5e+145)))
		tmp = (c * i) + (z * t);
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.05e+106], N[Not[LessEqual[N[(c * i), $MachinePrecision], 4.5e+145]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.05000000000000002e106 or 4.4999999999999998e145 < (*.f64 c i)

   1. Initial program 94.3%

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

   3. Taylor expanded in a around 0 92.0%

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

   4. Taylor expanded in x around 0 88.8%

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

   if -1.05000000000000002e106 < (*.f64 c i) < 4.4999999999999998e145

   1. Initial program 97.6%

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

   3. Taylor expanded in c around 0 90.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+106} \lor \neg \left(c \cdot i \leq 4.5 \cdot 10^{+145}\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7 \cdot 10^{+101} \lor \neg \left(c \cdot i \leq 2.8 \cdot 10^{+155}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -7e+101) (not (<= (* c i) 2.8e+155)))
   (+ (* a b) (* c i))
   (+ (* a b) (* z t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7e+101) || !((c * i) <= 2.8e+155)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-7d+101)) .or. (.not. ((c * i) <= 2.8d+155))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -7e+101) || !((c * i) <= 2.8e+155)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -7e+101) or not ((c * i) <= 2.8e+155):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -7e+101) || !(Float64(c * i) <= 2.8e+155))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -7e+101) || ~(((c * i) <= 2.8e+155)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -7e+101], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.8e+155]], $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) < -7.00000000000000046e101 or 2.80000000000000016e155 < (*.f64 c i)

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 89.9%

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

   4. Taylor expanded in t around 0 80.0%

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

   if -7.00000000000000046e101 < (*.f64 c i) < 2.80000000000000016e155

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 69.8%

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

   4. Taylor expanded in c around 0 63.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7 \cdot 10^{+101} \lor \neg \left(c \cdot i \leq 2.8 \cdot 10^{+155}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.1 \cdot 10^{+105} \lor \neg \left(c \cdot i \leq 1.22 \cdot 10^{+64}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.1e+105) (not (<= (* c i) 1.22e+64))) (* c i) (* a b)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -3.1e+105) || !((c * i) <= 1.22e+64)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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) <= (-3.1d+105)) .or. (.not. ((c * i) <= 1.22d+64))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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) <= -3.1e+105) || !((c * i) <= 1.22e+64)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -3.1e+105) or not ((c * i) <= 1.22e+64):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -3.1e+105) || !(Float64(c * i) <= 1.22e+64))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -3.1e+105) || ~(((c * i) <= 1.22e+64)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -3.1e+105], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.22e+64]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.10000000000000004e105 or 1.21999999999999994e64 < (*.f64 c i)

   1. Initial program 95.4%

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

   3. Taylor expanded in c around inf 67.7%

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

   if -3.10000000000000004e105 < (*.f64 c i) < 1.21999999999999994e64

   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 37.2%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.1 \cdot 10^{+105} \lor \neg \left(c \cdot i \leq 1.22 \cdot 10^{+64}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.4% accurate, 5.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (* a b))

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a * b;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a * b), $MachinePrecision]

Derivation

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 a around inf 25.7%

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

Reproduce

herbie shell --seed 2024085 
(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)))