Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 90.1% → 97.2%

Time: 14.5s

Alternatives: 13

Speedup: 0.6×

• 46.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * 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 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 - \left(c \cdot t\_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(t\_2 - t\_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - c \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot \frac{i}{y}\right)\right)\right)\\ \end{array} \end{array} \]

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 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (* y (- x (* c (* (fma c b a) (/ i 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);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (y * (x - (c * (fma(c, b, a) * (i / 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(a + Float64(b * c))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(y * Float64(x - Float64(c * Float64(fma(c, b, a) * Float64(i / y))))));
	end
	return 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 * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * N[(x - N[(c * N[(N[(c * b + a), $MachinePrecision] * N[(i / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.4%

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

      1. fma-define 96.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 99.7%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 50.0%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(\left(y + \frac{t \cdot z}{x}\right) - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]

   4. Taylor expanded in t around 0 66.7%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]

   5. Taylor expanded in y around inf 66.7%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot \left(x + -1 \cdot \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{y}\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 66.7%

         \[\leadsto 2 \cdot \left(y \cdot \left(x + \color{blue}{\left(-\frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{y}\right)}\right)\right) \]

      2. unsub-neg 66.7%

         \[\leadsto 2 \cdot \left(y \cdot \color{blue}{\left(x - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{y}\right)}\right) \]

      3. associate-/l* 75.0%

         \[\leadsto 2 \cdot \left(y \cdot \left(x - \color{blue}{c \cdot \frac{i \cdot \left(a + b \cdot c\right)}{y}}\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto 2 \cdot \left(y \cdot \left(x - c \cdot \frac{\color{blue}{\left(a + b \cdot c\right) \cdot i}}{y}\right)\right) \]

      5. associate-/l* 75.0%

         \[\leadsto 2 \cdot \left(y \cdot \left(x - c \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot \frac{i}{y}\right)}\right)\right) \]

      6. +-commutative 75.0%

         \[\leadsto 2 \cdot \left(y \cdot \left(x - c \cdot \left(\color{blue}{\left(b \cdot c + a\right)} \cdot \frac{i}{y}\right)\right)\right) \]

      7. *-commutative 75.0%

         \[\leadsto 2 \cdot \left(y \cdot \left(x - c \cdot \left(\left(\color{blue}{c \cdot b} + a\right) \cdot \frac{i}{y}\right)\right)\right) \]

      8. fma-define 75.0%

         \[\leadsto 2 \cdot \left(y \cdot \left(x - c \cdot \left(\color{blue}{\mathsf{fma}\left(c, b, a\right)} \cdot \frac{i}{y}\right)\right)\right) \]

   7. Simplified 75.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot \left(x - c \cdot \left(\mathsf{fma}\left(c, b, a\right) \cdot \frac{i}{y}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 39.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ t_3 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* 2.0 (* z t)))
        (t_2 (* (* a (* c i)) -2.0))
        (t_3 (* (* x y) 2.0)))
   (if (<= y -7.5e-41)
     t_3
     (if (<= y -3.6e-124)
       t_1
       (if (<= y -6e-291)
         t_2
         (if (<= y 3.6e-151)
           t_1
           (if (<= y 1.5e-65)
             t_2
             (if (<= y 4.4e-10)
               t_1
               (if (<= y 1.8e+17) t_2 (if (<= y 5.5e+111) t_1 t_3))))))))))

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 = 2.0 * (z * t);
	double t_2 = (a * (c * i)) * -2.0;
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (y <= -7.5e-41) {
		tmp = t_3;
	} else if (y <= -3.6e-124) {
		tmp = t_1;
	} else if (y <= -6e-291) {
		tmp = t_2;
	} else if (y <= 3.6e-151) {
		tmp = t_1;
	} else if (y <= 1.5e-65) {
		tmp = t_2;
	} else if (y <= 4.4e-10) {
		tmp = t_1;
	} else if (y <= 1.8e+17) {
		tmp = t_2;
	} else if (y <= 5.5e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = 2.0d0 * (z * t)
    t_2 = (a * (c * i)) * (-2.0d0)
    t_3 = (x * y) * 2.0d0
    if (y <= (-7.5d-41)) then
        tmp = t_3
    else if (y <= (-3.6d-124)) then
        tmp = t_1
    else if (y <= (-6d-291)) then
        tmp = t_2
    else if (y <= 3.6d-151) then
        tmp = t_1
    else if (y <= 1.5d-65) then
        tmp = t_2
    else if (y <= 4.4d-10) then
        tmp = t_1
    else if (y <= 1.8d+17) then
        tmp = t_2
    else if (y <= 5.5d+111) then
        tmp = t_1
    else
        tmp = t_3
    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 = 2.0 * (z * t);
	double t_2 = (a * (c * i)) * -2.0;
	double t_3 = (x * y) * 2.0;
	double tmp;
	if (y <= -7.5e-41) {
		tmp = t_3;
	} else if (y <= -3.6e-124) {
		tmp = t_1;
	} else if (y <= -6e-291) {
		tmp = t_2;
	} else if (y <= 3.6e-151) {
		tmp = t_1;
	} else if (y <= 1.5e-65) {
		tmp = t_2;
	} else if (y <= 4.4e-10) {
		tmp = t_1;
	} else if (y <= 1.8e+17) {
		tmp = t_2;
	} else if (y <= 5.5e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = 2.0 * (z * t)
	t_2 = (a * (c * i)) * -2.0
	t_3 = (x * y) * 2.0
	tmp = 0
	if y <= -7.5e-41:
		tmp = t_3
	elif y <= -3.6e-124:
		tmp = t_1
	elif y <= -6e-291:
		tmp = t_2
	elif y <= 3.6e-151:
		tmp = t_1
	elif y <= 1.5e-65:
		tmp = t_2
	elif y <= 4.4e-10:
		tmp = t_1
	elif y <= 1.8e+17:
		tmp = t_2
	elif y <= 5.5e+111:
		tmp = t_1
	else:
		tmp = t_3
	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(2.0 * Float64(z * t))
	t_2 = Float64(Float64(a * Float64(c * i)) * -2.0)
	t_3 = Float64(Float64(x * y) * 2.0)
	tmp = 0.0
	if (y <= -7.5e-41)
		tmp = t_3;
	elseif (y <= -3.6e-124)
		tmp = t_1;
	elseif (y <= -6e-291)
		tmp = t_2;
	elseif (y <= 3.6e-151)
		tmp = t_1;
	elseif (y <= 1.5e-65)
		tmp = t_2;
	elseif (y <= 4.4e-10)
		tmp = t_1;
	elseif (y <= 1.8e+17)
		tmp = t_2;
	elseif (y <= 5.5e+111)
		tmp = t_1;
	else
		tmp = t_3;
	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 = 2.0 * (z * t);
	t_2 = (a * (c * i)) * -2.0;
	t_3 = (x * y) * 2.0;
	tmp = 0.0;
	if (y <= -7.5e-41)
		tmp = t_3;
	elseif (y <= -3.6e-124)
		tmp = t_1;
	elseif (y <= -6e-291)
		tmp = t_2;
	elseif (y <= 3.6e-151)
		tmp = t_1;
	elseif (y <= 1.5e-65)
		tmp = t_2;
	elseif (y <= 4.4e-10)
		tmp = t_1;
	elseif (y <= 1.8e+17)
		tmp = t_2;
	elseif (y <= 5.5e+111)
		tmp = t_1;
	else
		tmp = t_3;
	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[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[y, -7.5e-41], t$95$3, If[LessEqual[y, -3.6e-124], t$95$1, If[LessEqual[y, -6e-291], t$95$2, If[LessEqual[y, 3.6e-151], t$95$1, If[LessEqual[y, 1.5e-65], t$95$2, If[LessEqual[y, 4.4e-10], t$95$1, If[LessEqual[y, 1.8e+17], t$95$2, If[LessEqual[y, 5.5e+111], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000049e-41 or 5.4999999999999998e111 < y

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 43.8%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -7.50000000000000049e-41 < y < -3.6000000000000001e-124 or -6.0000000000000001e-291 < y < 3.60000000000000032e-151 or 1.49999999999999999e-65 < y < 4.3999999999999998e-10 or 1.8e17 < y < 5.4999999999999998e111

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 38.2%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -3.6000000000000001e-124 < y < -6.0000000000000001e-291 or 3.60000000000000032e-151 < y < 1.49999999999999999e-65 or 4.3999999999999998e-10 < y < 1.8e17

   1. Initial program 88.3%

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

   3. Taylor expanded in a around inf 31.7%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 31.7%

         \[\leadsto 2 \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \]

      2. *-commutative 31.7%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot i\right) \cdot a}\right) \]

      3. associate-*l* 30.1%

         \[\leadsto 2 \cdot \left(-\color{blue}{c \cdot \left(i \cdot a\right)}\right) \]

      4. *-commutative 30.1%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(a \cdot i\right)}\right) \]

      5. distribute-rgt-neg-in 30.1%

         \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(-a \cdot i\right)\right)} \]

      6. *-commutative 30.1%

         \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{i \cdot a}\right)\right) \]

      7. distribute-rgt-neg-in 30.1%

         \[\leadsto 2 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(-a\right)\right)}\right) \]

   5. Simplified 30.1%

      \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(-a\right)\right)\right)} \]

   6. Taylor expanded in c around 0 31.7%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-41}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-124}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-291}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-151}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-65}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{+40}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+122}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+292}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - c \cdot \left(a \cdot \frac{i}{x}\right)\right)\right)\\ \end{array} \end{array} \]

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 (* (+ a (* b c)) i))) (t_2 (* 2.0 (- (* x y) t_1))))
   (if (<= (* x y) -5e+34)
     t_2
     (if (<= (* x y) 1e+40)
       (* 2.0 (- (* z t) t_1))
       (if (<= (* x y) 5e+122)
         (* (+ (* x y) (* z t)) 2.0)
         (if (<= (* x y) 4e+292)
           t_2
           (* 2.0 (* x (- y (* c (* a (/ i x))))))))))))

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 * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double tmp;
	if ((x * y) <= -5e+34) {
		tmp = t_2;
	} else if ((x * y) <= 1e+40) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((x * y) <= 5e+122) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 4e+292) {
		tmp = t_2;
	} else {
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))));
	}
	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 = c * ((a + (b * c)) * i)
    t_2 = 2.0d0 * ((x * y) - t_1)
    if ((x * y) <= (-5d+34)) then
        tmp = t_2
    else if ((x * y) <= 1d+40) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if ((x * y) <= 5d+122) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if ((x * y) <= 4d+292) then
        tmp = t_2
    else
        tmp = 2.0d0 * (x * (y - (c * (a * (i / x)))))
    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 = c * ((a + (b * c)) * i);
	double t_2 = 2.0 * ((x * y) - t_1);
	double tmp;
	if ((x * y) <= -5e+34) {
		tmp = t_2;
	} else if ((x * y) <= 1e+40) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if ((x * y) <= 5e+122) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if ((x * y) <= 4e+292) {
		tmp = t_2;
	} else {
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))));
	}
	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 * ((a + (b * c)) * i)
	t_2 = 2.0 * ((x * y) - t_1)
	tmp = 0
	if (x * y) <= -5e+34:
		tmp = t_2
	elif (x * y) <= 1e+40:
		tmp = 2.0 * ((z * t) - t_1)
	elif (x * y) <= 5e+122:
		tmp = ((x * y) + (z * t)) * 2.0
	elif (x * y) <= 4e+292:
		tmp = t_2
	else:
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))))
	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(c * Float64(Float64(a + Float64(b * c)) * i))
	t_2 = Float64(2.0 * Float64(Float64(x * y) - t_1))
	tmp = 0.0
	if (Float64(x * y) <= -5e+34)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e+40)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (Float64(x * y) <= 5e+122)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (Float64(x * y) <= 4e+292)
		tmp = t_2;
	else
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(c * Float64(a * Float64(i / x))))));
	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 * ((a + (b * c)) * i);
	t_2 = 2.0 * ((x * y) - t_1);
	tmp = 0.0;
	if ((x * y) <= -5e+34)
		tmp = t_2;
	elseif ((x * y) <= 1e+40)
		tmp = 2.0 * ((z * t) - t_1);
	elseif ((x * y) <= 5e+122)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif ((x * y) <= 4e+292)
		tmp = t_2;
	else
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))));
	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[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+34], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e+40], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+122], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+292], t$95$2, N[(2.0 * N[(x * N[(y - N[(c * N[(a * N[(i / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4.9999999999999998e34 or 4.99999999999999989e122 < (*.f64 x y) < 4.0000000000000001e292

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 79.6%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if -4.9999999999999998e34 < (*.f64 x y) < 1.00000000000000003e40

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0 88.8%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if 1.00000000000000003e40 < (*.f64 x y) < 4.99999999999999989e122

   1. Initial program 87.3%

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

   3. Taylor expanded in c around 0 93.3%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 4.0000000000000001e292 < (*.f64 x y)

   1. Initial program 80.8%

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

   3. Taylor expanded in x around inf 84.6%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(\left(y + \frac{t \cdot z}{x}\right) - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]

   4. Taylor expanded in t around 0 88.5%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]

   5. Taylor expanded in b around 0 96.2%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - \frac{a \cdot \left(c \cdot i\right)}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-/l* 96.2%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{a \cdot \frac{c \cdot i}{x}}\right)\right) \]

      2. associate-/l* 96.2%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - a \cdot \color{blue}{\left(c \cdot \frac{i}{x}\right)}\right)\right) \]

      3. associate-*r* 96.2%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{\left(a \cdot c\right) \cdot \frac{i}{x}}\right)\right) \]

      4. *-commutative 96.2%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{\left(c \cdot a\right)} \cdot \frac{i}{x}\right)\right) \]

      5. associate-*r* 96.2%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{c \cdot \left(a \cdot \frac{i}{x}\right)}\right)\right) \]

   7. Simplified 96.2%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - c \cdot \left(a \cdot \frac{i}{x}\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+40}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+122}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+292}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - c \cdot \left(a \cdot \frac{i}{x}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t\_2 - \left(c \cdot t\_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(t\_2 - t\_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z - a \cdot \left(c \cdot \frac{i}{t}\right)\right)\right)\\ \end{array} \end{array} \]

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 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (* t (- z (* a (* c (/ i 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 t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (t * (z - (a * (c * (i / t)))));
	}
	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 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (t * (z - (a * (c * (i / 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):
	t_1 = a + (b * c)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (t_2 - ((c * t_1) * i)) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = 2.0 * (t * (z - (a * (c * (i / 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)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(t * Float64(z - Float64(a * Float64(c * Float64(i / 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)
	t_1 = a + (b * c);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * (t * (z - (a * (c * (i / 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_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t * N[(z - N[(a * N[(c * N[(i / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.4%

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

      1. fma-define 96.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

      2. associate-*l* 99.7%

         \[\leadsto 2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 99.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 50.0%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in c around 0 42.3%

      \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{a \cdot \left(c \cdot i\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{\left(c \cdot i\right) \cdot a}\right) \]

      2. associate-*r* 42.3%

         \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{c \cdot \left(i \cdot a\right)}\right) \]

   6. Simplified 42.3%

      \[\leadsto 2 \cdot \left(t \cdot z - \color{blue}{c \cdot \left(i \cdot a\right)}\right) \]

   7. Taylor expanded in t around inf 58.3%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot \left(z + -1 \cdot \frac{a \cdot \left(c \cdot i\right)}{t}\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.3%

         \[\leadsto 2 \cdot \left(t \cdot \left(z + \color{blue}{\left(-\frac{a \cdot \left(c \cdot i\right)}{t}\right)}\right)\right) \]

      2. unsub-neg 58.3%

         \[\leadsto 2 \cdot \left(t \cdot \color{blue}{\left(z - \frac{a \cdot \left(c \cdot i\right)}{t}\right)}\right) \]

      3. associate-/l* 66.7%

         \[\leadsto 2 \cdot \left(t \cdot \left(z - \color{blue}{a \cdot \frac{c \cdot i}{t}}\right)\right) \]

      4. associate-/l* 66.7%

         \[\leadsto 2 \cdot \left(t \cdot \left(z - a \cdot \color{blue}{\left(c \cdot \frac{i}{t}\right)}\right)\right) \]

   9. Simplified 66.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot \left(z - a \cdot \left(c \cdot \frac{i}{t}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot i\right)\\ \mathbf{if}\;c \leq -15:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-256}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-182}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

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 (* a (* c i))))
   (if (<= c -15.0)
     (* 2.0 (* c (* (+ a (* b c)) (- i))))
     (if (<= c 2.15e-256)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= c 3.9e-182)
         (* 2.0 (- (* z t) t_1))
         (if (<= c 1.85e-44)
           (* 2.0 (- (* x y) t_1))
           (* 2.0 (- (* z t) (* c (* 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 * (c * i);
	double tmp;
	if (c <= -15.0) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else if (c <= 2.15e-256) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 3.9e-182) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 1.85e-44) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - (c * (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) :: tmp
    t_1 = a * (c * i)
    if (c <= (-15.0d0)) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else if (c <= 2.15d-256) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 3.9d-182) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 1.85d-44) then
        tmp = 2.0d0 * ((x * y) - t_1)
    else
        tmp = 2.0d0 * ((z * t) - (c * (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 * (c * i);
	double tmp;
	if (c <= -15.0) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else if (c <= 2.15e-256) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 3.9e-182) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 1.85e-44) {
		tmp = 2.0 * ((x * y) - t_1);
	} else {
		tmp = 2.0 * ((z * t) - (c * (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 * (c * i)
	tmp = 0
	if c <= -15.0:
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	elif c <= 2.15e-256:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 3.9e-182:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 1.85e-44:
		tmp = 2.0 * ((x * y) - t_1)
	else:
		tmp = 2.0 * ((z * t) - (c * (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(c * i))
	tmp = 0.0
	if (c <= -15.0)
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	elseif (c <= 2.15e-256)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 3.9e-182)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 1.85e-44)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(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 * (c * i);
	tmp = 0.0;
	if (c <= -15.0)
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	elseif (c <= 2.15e-256)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 3.9e-182)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 1.85e-44)
		tmp = 2.0 * ((x * y) - t_1);
	else
		tmp = 2.0 * ((z * t) - (c * (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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -15.0], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.15e-256], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 3.9e-182], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e-44], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -15

   1. Initial program 83.6%

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

   3. Taylor expanded in i around inf 74.9%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]

   if -15 < c < 2.1500000000000001e-256

   1. Initial program 97.5%

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

   3. Taylor expanded in c around 0 82.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 2.1500000000000001e-256 < c < 3.9e-182

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 93.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 93.1%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 93.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in x around 0 97.3%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - a \cdot \left(c \cdot i\right)\right)} \]

   if 3.9e-182 < c < 1.85e-44

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 99.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 99.1%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 99.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in z around 0 70.4%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y - a \cdot \left(c \cdot i\right)\right)} \]

   if 1.85e-44 < c

   1. Initial program 88.9%

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

   3. Taylor expanded in x around 0 90.2%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in a around 0 79.1%

      \[\leadsto 2 \cdot \left(t \cdot z - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -15:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{-256}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-182}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -32000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-192}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -32000.0)
     t_2
     (if (<= c 7.2e-256)
       t_1
       (if (<= c 1.1e-192)
         (* 2.0 (- (* z t) (* a (* c i))))
         (if (<= c 1.8e-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 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -32000.0) {
		tmp = t_2;
	} else if (c <= 7.2e-256) {
		tmp = t_1;
	} else if (c <= 1.1e-192) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 1.8e-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 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-32000.0d0)) then
        tmp = t_2
    else if (c <= 7.2d-256) then
        tmp = t_1
    else if (c <= 1.1d-192) then
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    else if (c <= 1.8d-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 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -32000.0) {
		tmp = t_2;
	} else if (c <= 7.2e-256) {
		tmp = t_1;
	} else if (c <= 1.1e-192) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else if (c <= 1.8e-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 = ((x * y) + (z * t)) * 2.0
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -32000.0:
		tmp = t_2
	elif c <= 7.2e-256:
		tmp = t_1
	elif c <= 1.1e-192:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	elif c <= 1.8e-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(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -32000.0)
		tmp = t_2;
	elseif (c <= 7.2e-256)
		tmp = t_1;
	elseif (c <= 1.1e-192)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	elseif (c <= 1.8e-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 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -32000.0)
		tmp = t_2;
	elseif (c <= 7.2e-256)
		tmp = t_1;
	elseif (c <= 1.1e-192)
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	elseif (c <= 1.8e-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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -32000.0], t$95$2, If[LessEqual[c, 7.2e-256], t$95$1, If[LessEqual[c, 1.1e-192], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e-64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -32000 or 1.7999999999999999e-64 < c

   1. Initial program 86.8%

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

   3. Taylor expanded in i around inf 75.2%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]

   if -32000 < c < 7.2000000000000004e-256 or 1.10000000000000003e-192 < c < 1.7999999999999999e-64

   1. Initial program 98.1%

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

   3. Taylor expanded in c around 0 81.3%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 7.2000000000000004e-256 < c < 1.10000000000000003e-192

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf 92.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 92.6%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 92.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in x around 0 97.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -32000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-256}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-192}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+263}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t\_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2\right) \cdot 2\\ \end{array} \end{array} \]

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 c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 -2e+263)
     (* 2.0 (* c (* t_1 (- i))))
     (* (- (+ (* x y) (* z t)) t_2) 2.0))))

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);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -2e+263) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	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 * c)
    t_2 = (c * t_1) * i
    if (t_2 <= (-2d+263)) then
        tmp = 2.0d0 * (c * (t_1 * -i))
    else
        tmp = (((x * y) + (z * t)) - t_2) * 2.0d0
    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);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -2e+263) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	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)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -2e+263:
		tmp = 2.0 * (c * (t_1 * -i))
	else:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	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 * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= -2e+263)
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	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);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= -2e+263)
		tmp = 2.0 * (c * (t_1 * -i));
	else
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	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 * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+263], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -2.00000000000000003e263

   1. Initial program 75.9%

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

   3. Taylor expanded in i around inf 93.9%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]

   if -2.00000000000000003e263 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 95.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -2 \cdot 10^{+263}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -170000 \lor \neg \left(c \leq 1.4 \cdot 10^{-55}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

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
 (if (or (<= c -170000.0) (not (<= c 1.4e-55)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

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 <= -170000.0) || !(c <= 1.4e-55)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	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 <= (-170000.0d0)) .or. (.not. (c <= 1.4d-55))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    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 <= -170000.0) || !(c <= 1.4e-55)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	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 <= -170000.0) or not (c <= 1.4e-55):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	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 ((c <= -170000.0) || !(c <= 1.4e-55))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	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 <= -170000.0) || ~((c <= 1.4e-55)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	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[c, -170000.0], N[Not[LessEqual[c, 1.4e-55]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.7e5 or 1.39999999999999992e-55 < c

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 87.4%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if -1.7e5 < c < 1.39999999999999992e-55

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf 92.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 92.6%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 92.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -170000 \lor \neg \left(c \leq 1.4 \cdot 10^{-55}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-22} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-45}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

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
 (if (or (<= (* x y) -5e-22) (not (<= (* x y) 5e-45)))
   (* (+ (* x y) (* z t)) 2.0)
   (* 2.0 (- (* z t) (* a (* 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 (((x * y) <= -5e-22) || !((x * y) <= 5e-45)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (a * (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 (((x * y) <= (-5d-22)) .or. (.not. ((x * y) <= 5d-45))) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((z * t) - (a * (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 (((x * y) <= -5e-22) || !((x * y) <= 5e-45)) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (a * (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 ((x * y) <= -5e-22) or not ((x * y) <= 5e-45):
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (a * (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(x * y) <= -5e-22) || !(Float64(x * y) <= 5e-45))
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * 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 (((x * y) <= -5e-22) || ~(((x * y) <= 5e-45)))
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (a * (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[Or[LessEqual[N[(x * y), $MachinePrecision], -5e-22], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-45]], $MachinePrecision]], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999954e-22 or 4.99999999999999976e-45 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in c around 0 66.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if -4.99999999999999954e-22 < (*.f64 x y) < 4.99999999999999976e-45

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 65.4%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a \cdot c\right)} \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 65.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   5. Simplified 65.4%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot a\right)} \cdot i\right) \]

   6. Taylor expanded in x around 0 65.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-22} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-45}\right):\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - c \cdot \left(a \cdot \frac{i}{x}\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

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
 (if (<= y -1.16e+70)
   (* 2.0 (* x (- y (* c (* a (/ i x))))))
   (if (<= y 2.5e+105)
     (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
     (* (+ (* x y) (* z t)) 2.0))))

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 (y <= -1.16e+70) {
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))));
	} else if (y <= 2.5e+105) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	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 (y <= (-1.16d+70)) then
        tmp = 2.0d0 * (x * (y - (c * (a * (i / x)))))
    else if (y <= 2.5d+105) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    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 (y <= -1.16e+70) {
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))));
	} else if (y <= 2.5e+105) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	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 y <= -1.16e+70:
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))))
	elif y <= 2.5e+105:
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	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 (y <= -1.16e+70)
		tmp = Float64(2.0 * Float64(x * Float64(y - Float64(c * Float64(a * Float64(i / x))))));
	elseif (y <= 2.5e+105)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	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 (y <= -1.16e+70)
		tmp = 2.0 * (x * (y - (c * (a * (i / x)))));
	elseif (y <= 2.5e+105)
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	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[y, -1.16e+70], N[(2.0 * N[(x * N[(y - N[(c * N[(a * N[(i / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+105], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1599999999999999e70

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 83.1%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(\left(y + \frac{t \cdot z}{x}\right) - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]

   4. Taylor expanded in t around 0 71.1%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]

   5. Taylor expanded in b around 0 53.5%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - \frac{a \cdot \left(c \cdot i\right)}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-/l* 53.6%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{a \cdot \frac{c \cdot i}{x}}\right)\right) \]

      2. associate-/l* 50.6%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - a \cdot \color{blue}{\left(c \cdot \frac{i}{x}\right)}\right)\right) \]

      3. associate-*r* 49.0%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{\left(a \cdot c\right) \cdot \frac{i}{x}}\right)\right) \]

      4. *-commutative 49.0%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{\left(c \cdot a\right)} \cdot \frac{i}{x}\right)\right) \]

      5. associate-*r* 44.6%

         \[\leadsto 2 \cdot \left(x \cdot \left(y - \color{blue}{c \cdot \left(a \cdot \frac{i}{x}\right)}\right)\right) \]

   7. Simplified 44.6%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y - c \cdot \left(a \cdot \frac{i}{x}\right)\right)\right)} \]

   if -1.1599999999999999e70 < y < 2.50000000000000023e105

   1. Initial program 93.4%

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

   3. Taylor expanded in x around 0 82.3%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)} \]

   if 2.50000000000000023e105 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in c around 0 75.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y - c \cdot \left(a \cdot \frac{i}{x}\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-35} \lor \neg \left(y \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

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 (<= y -7e-35) (not (<= y 2e+111))) (* (* x y) 2.0) (* 2.0 (* 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 ((y <= -7e-35) || !(y <= 2e+111)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (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 ((y <= (-7d-35)) .or. (.not. (y <= 2d+111))) then
        tmp = (x * y) * 2.0d0
    else
        tmp = 2.0d0 * (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 ((y <= -7e-35) || !(y <= 2e+111)) {
		tmp = (x * y) * 2.0;
	} else {
		tmp = 2.0 * (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 (y <= -7e-35) or not (y <= 2e+111):
		tmp = (x * y) * 2.0
	else:
		tmp = 2.0 * (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 ((y <= -7e-35) || !(y <= 2e+111))
		tmp = Float64(Float64(x * y) * 2.0);
	else
		tmp = Float64(2.0 * 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 ((y <= -7e-35) || ~((y <= 2e+111)))
		tmp = (x * y) * 2.0;
	else
		tmp = 2.0 * (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[y, -7e-35], N[Not[LessEqual[y, 2e+111]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999992e-35 or 1.99999999999999991e111 < y

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 43.4%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -6.99999999999999992e-35 < y < 1.99999999999999991e111

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf 33.9%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-35} \lor \neg \left(y \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq 1.5 \cdot 10^{+167}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

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
 (if (<= i 1.5e+167) (* (+ (* x y) (* z t)) 2.0) (* (* a (* c i)) -2.0)))

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 (i <= 1.5e+167) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	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 (i <= 1.5d+167) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (a * (c * i)) * (-2.0d0)
    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 (i <= 1.5e+167) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	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 i <= 1.5e+167:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = (a * (c * i)) * -2.0
	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 (i <= 1.5e+167)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	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 (i <= 1.5e+167)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = (a * (c * i)) * -2.0;
	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[i, 1.5e+167], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 1.50000000000000006e167

   1. Initial program 91.8%

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

   3. Taylor expanded in c around 0 58.8%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z + x \cdot y\right)} \]

   if 1.50000000000000006e167 < i

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf 58.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(c \cdot i\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto 2 \cdot \color{blue}{\left(-a \cdot \left(c \cdot i\right)\right)} \]

      2. *-commutative 58.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot i\right) \cdot a}\right) \]

      3. associate-*l* 53.8%

         \[\leadsto 2 \cdot \left(-\color{blue}{c \cdot \left(i \cdot a\right)}\right) \]

      4. *-commutative 53.8%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(a \cdot i\right)}\right) \]

      5. distribute-rgt-neg-in 53.8%

         \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(-a \cdot i\right)\right)} \]

      6. *-commutative 53.8%

         \[\leadsto 2 \cdot \left(c \cdot \left(-\color{blue}{i \cdot a}\right)\right) \]

      7. distribute-rgt-neg-in 53.8%

         \[\leadsto 2 \cdot \left(c \cdot \color{blue}{\left(i \cdot \left(-a\right)\right)}\right) \]

   5. Simplified 53.8%

      \[\leadsto 2 \cdot \color{blue}{\left(c \cdot \left(i \cdot \left(-a\right)\right)\right)} \]

   6. Taylor expanded in c around 0 58.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq 1.5 \cdot 10^{+167}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ 2 \cdot \left(z \cdot t\right) \end{array} \]

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 (* 2.0 (* 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 2.0 * (z * t);
}

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 = 2.0d0 * (z * t)
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 2.0 * (z * t);
}

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 2.0 * (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 Float64(2.0 * Float64(z * t))
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 = 2.0 * (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[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.9%

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

3. Taylor expanded in z around inf 28.4%

   \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

4. Final simplification 28.4%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]
5. Add Preprocessing

Developer target: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (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 = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (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 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))