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

Percentage Accurate: 90.0% → 94.6%

Time: 17.4s

Alternatives: 17

Speedup: 0.5×

• 47.3% 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: 90.0% 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: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t - \frac{c \cdot \left(t\_1 \cdot i\right)}{z}\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+229}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \end{array} \end{array} \]

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 (* (* c t_1) i)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (* z (- t (/ (* c (* t_1 i)) z))))
     (if (<= t_2 1e+229)
       (* (- (+ (* x y) (* z t)) t_2) 2.0)
       (* (* t_1 (* 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 t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (z * (t - ((c * (t_1 * i)) / z)));
	} else if (t_2 <= 1e+229) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = (t_1 * (c * i)) * -2.0;
	}
	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 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (z * (t - ((c * (t_1 * i)) / z)));
	} else if (t_2 <= 1e+229) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = (t_1 * (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):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * (z * (t - ((c * (t_1 * i)) / z)))
	elif t_2 <= 1e+229:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	else:
		tmp = (t_1 * (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)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(z * Float64(t - Float64(Float64(c * Float64(t_1 * i)) / z))));
	elseif (t_2 <= 1e+229)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	else
		tmp = Float64(Float64(t_1 * Float64(c * i)) * Float64(-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 <= -Inf)
		tmp = 2.0 * (z * (t - ((c * (t_1 * i)) / z)));
	elseif (t_2 <= 1e+229)
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	else
		tmp = (t_1 * (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_] := 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, (-Infinity)], N[(2.0 * N[(z * N[(t - N[(N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+229], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 74.4%

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

      1. fma-define 74.4%

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

      2. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

      1. fma-define 85.9%

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

      2. +-commutative 85.9%

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

   6. Applied egg-rr 85.9%

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

   7. Taylor expanded in c around 0 83.6%

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

   8. Taylor expanded in z around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. div-sub 80.0%

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

   10. Simplified 86.1%

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

   11. Taylor expanded in x around 0 92.2%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.9999999999999999e228

   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

   if 9.9999999999999999e228 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 66.0%

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

      1. fma-define 66.0%

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

      2. associate-*l* 76.8%

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

   3. Simplified 76.8%

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

      1. fma-define 76.8%

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

      2. +-commutative 76.8%

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

   6. Applied egg-rr 76.8%

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

   7. Taylor expanded in c around 0 74.3%

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

   8. Taylor expanded in i around inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. associate-*r* 90.9%

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

      3. distribute-lft-neg-in 90.9%

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

      4. *-commutative 90.9%

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

      5. distribute-rgt-neg-in 90.9%

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

      6. *-commutative 90.9%

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

   10. Simplified 90.9%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot \left(t - \frac{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}{z}\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+229}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.0% accurate, 0.5× speedup

Math

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

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 (* z (- t (/ (* c (* t_1 i)) z)))))))

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 * (z * (t - ((c * (t_1 * i)) / z)));
	}
	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 * (z * (t - ((c * (t_1 * i)) / z)));
	}
	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 * (z * (t - ((c * (t_1 * i)) / z)))
	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(z * Float64(t - Float64(Float64(c * Float64(t_1 * i)) / z))));
	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 * (z * (t - ((c * (t_1 * i)) / z)));
	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[(z * N[(t - N[(N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision] / z), $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 94.8%

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

      1. fma-define 94.8%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

      1. fma-define 98.2%

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

      2. +-commutative 98.2%

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

   6. Applied egg-rr 98.2%

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

   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. Step-by-step derivation

      1. fma-define 0.0%

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

      2. associate-*l* 6.7%

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

   3. Simplified 6.7%

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

      1. fma-define 6.7%

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

      2. +-commutative 6.7%

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

   6. Applied egg-rr 6.7%

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

   7. Taylor expanded in c around 0 13.3%

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

   8. Taylor expanded in z around inf 26.7%

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

      1. associate--l+ 26.7%

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

      2. div-sub 33.3%

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

   10. Simplified 33.3%

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

   11. Taylor expanded in x around 0 86.7%

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

4. Final simplification 97.6%

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

Alternative 3: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.05 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i + \frac{a \cdot i}{c}\right)\right)\right)\\ \end{array} \end{array} \]

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 (+ (* x y) (* z t))))
   (if (<= c -2.05e+43)
     (* 2.0 (- t_1 (* c (* b (* c i)))))
     (if (<= c 3.05e-158)
       (* 2.0 (- t_1 (* i (* a c))))
       (if (<= c 2.3e+58)
         (* 2.0 (- t_1 (* (* b c) (* c i))))
         (* 2.0 (- (* x y) (* c (* c (+ (* b i) (/ (* a i) 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 t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -2.05e+43) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else if (c <= 3.05e-158) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (c <= 2.3e+58) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - (c * (c * ((b * i) + ((a * i) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (c <= (-2.05d+43)) then
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    else if (c <= 3.05d-158) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else if (c <= 2.3d+58) then
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) - (c * (c * ((b * i) + ((a * i) / 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 t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -2.05e+43) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else if (c <= 3.05e-158) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (c <= 2.3e+58) {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) - (c * (c * ((b * i) + ((a * i) / 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):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if c <= -2.05e+43:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	elif c <= 3.05e-158:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	elif c <= 2.3e+58:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	else:
		tmp = 2.0 * ((x * y) - (c * (c * ((b * i) + ((a * i) / 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)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -2.05e+43)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= 3.05e-158)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	elseif (c <= 2.3e+58)
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(c * Float64(Float64(b * i) + Float64(Float64(a * i) / 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)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -2.05e+43)
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	elseif (c <= 3.05e-158)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	elseif (c <= 2.3e+58)
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	else
		tmp = 2.0 * ((x * y) - (c * (c * ((b * i) + ((a * i) / 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.05e+43], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.05e-158], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e+58], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(c * N[(N[(b * i), $MachinePrecision] + N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.05e43

   1. Initial program 77.1%

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

      1. fma-define 77.1%

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

      2. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

      1. fma-define 85.5%

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

      2. +-commutative 85.5%

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

   6. Applied egg-rr 85.5%

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

   7. Taylor expanded in c around 0 88.9%

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

   8. Taylor expanded in a around 0 89.1%

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

   if -2.05e43 < c < 3.0499999999999999e-158

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 92.5%

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

      1. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   if 3.0499999999999999e-158 < c < 2.30000000000000002e58

   1. Initial program 96.0%

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

      1. fma-define 96.0%

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

      2. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

      1. fma-define 96.0%

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

      2. +-commutative 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in a around 0 86.5%

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

   if 2.30000000000000002e58 < c

   1. Initial program 77.9%

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

      1. fma-define 77.9%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

      1. fma-define 89.7%

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

      2. +-commutative 89.7%

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

   6. Applied egg-rr 89.7%

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

   7. Taylor expanded in c around 0 87.3%

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

   8. Taylor expanded in z around 0 87.5%

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

      1. cancel-sign-sub-inv 87.5%

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

      2. +-commutative 87.5%

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

      3. fma-undefine 87.5%

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

      4. cancel-sign-sub-inv 87.5%

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

      5. *-commutative 87.5%

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

      6. fma-undefine 87.5%

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

      7. associate-*r* 89.8%

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

      8. distribute-rgt-in 89.8%

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

      9. +-commutative 89.8%

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

      10. *-commutative 89.8%

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

      11. *-commutative 89.8%

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

   10. Simplified 89.8%

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

   11. Taylor expanded in c around inf 91.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.05 \cdot 10^{-158}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(c \cdot \left(b \cdot i + \frac{a \cdot i}{c}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{+144} \lor \neg \left(c \leq -1.55 \cdot 10^{+54}\right) \land \left(c \leq -7.5 \cdot 10^{-5} \lor \neg \left(c \leq 6.8 \cdot 10^{-18}\right)\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 -5.3e+144)
         (and (not (<= c -1.55e+54)) (or (<= c -7.5e-5) (not (<= c 6.8e-18)))))
   (* (* c (* (+ a (* b c)) i)) -2.0)
   (* 2.0 (+ (* 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 <= -5.3e+144) || (!(c <= -1.55e+54) && ((c <= -7.5e-5) || !(c <= 6.8e-18)))) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = 2.0 * ((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 <= (-5.3d+144)) .or. (.not. (c <= (-1.55d+54))) .and. (c <= (-7.5d-5)) .or. (.not. (c <= 6.8d-18))) then
        tmp = (c * ((a + (b * c)) * i)) * (-2.0d0)
    else
        tmp = 2.0d0 * ((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 <= -5.3e+144) || (!(c <= -1.55e+54) && ((c <= -7.5e-5) || !(c <= 6.8e-18)))) {
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	} else {
		tmp = 2.0 * ((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 <= -5.3e+144) or (not (c <= -1.55e+54) and ((c <= -7.5e-5) or not (c <= 6.8e-18))):
		tmp = (c * ((a + (b * c)) * i)) * -2.0
	else:
		tmp = 2.0 * ((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 ((c <= -5.3e+144) || (!(c <= -1.55e+54) && ((c <= -7.5e-5) || !(c <= 6.8e-18))))
		tmp = Float64(Float64(c * Float64(Float64(a + Float64(b * c)) * i)) * -2.0);
	else
		tmp = Float64(2.0 * 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 <= -5.3e+144) || (~((c <= -1.55e+54)) && ((c <= -7.5e-5) || ~((c <= 6.8e-18)))))
		tmp = (c * ((a + (b * c)) * i)) * -2.0;
	else
		tmp = 2.0 * ((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[c, -5.3e+144], And[N[Not[LessEqual[c, -1.55e+54]], $MachinePrecision], Or[LessEqual[c, -7.5e-5], N[Not[LessEqual[c, 6.8e-18]], $MachinePrecision]]]], N[(N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.2999999999999997e144 or -1.55e54 < c < -7.49999999999999934e-5 or 6.80000000000000002e-18 < c

   1. Initial program 81.8%

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

      1. fma-define 81.8%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

      1. fma-define 90.1%

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

      2. +-commutative 90.1%

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

   6. Applied egg-rr 90.1%

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

   7. Taylor expanded in c around 0 86.5%

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

   8. Taylor expanded in i around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-*r* 79.1%

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

      3. distribute-lft-neg-in 79.1%

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

      4. *-commutative 79.1%

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

      5. distribute-rgt-neg-in 79.1%

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

      6. *-commutative 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in i around 0 79.1%

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

   if -5.2999999999999997e144 < c < -1.55e54 or -7.49999999999999934e-5 < c < 6.80000000000000002e-18

   1. Initial program 95.1%

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

   3. Taylor expanded in c around 0 70.4%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{+144} \lor \neg \left(c \leq -1.55 \cdot 10^{+54}\right) \land \left(c \leq -7.5 \cdot 10^{-5} \lor \neg \left(c \leq 6.8 \cdot 10^{-18}\right)\right):\\ \;\;\;\;\left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+149} \lor \neg \left(c \leq -1.35 \cdot 10^{+109}\right) \land \left(c \leq -2.4 \cdot 10^{+28} \lor \neg \left(c \leq 1.38 \cdot 10^{-17}\right)\right):\\ \;\;\;\;2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 -1.5e+149)
         (and (not (<= c -1.35e+109))
              (or (<= c -2.4e+28) (not (<= c 1.38e-17)))))
   (* 2.0 (* (* b c) (* c (- i))))
   (* 2.0 (+ (* 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 <= -1.5e+149) || (!(c <= -1.35e+109) && ((c <= -2.4e+28) || !(c <= 1.38e-17)))) {
		tmp = 2.0 * ((b * c) * (c * -i));
	} else {
		tmp = 2.0 * ((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 <= (-1.5d+149)) .or. (.not. (c <= (-1.35d+109))) .and. (c <= (-2.4d+28)) .or. (.not. (c <= 1.38d-17))) then
        tmp = 2.0d0 * ((b * c) * (c * -i))
    else
        tmp = 2.0d0 * ((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 <= -1.5e+149) || (!(c <= -1.35e+109) && ((c <= -2.4e+28) || !(c <= 1.38e-17)))) {
		tmp = 2.0 * ((b * c) * (c * -i));
	} else {
		tmp = 2.0 * ((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 <= -1.5e+149) or (not (c <= -1.35e+109) and ((c <= -2.4e+28) or not (c <= 1.38e-17))):
		tmp = 2.0 * ((b * c) * (c * -i))
	else:
		tmp = 2.0 * ((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 ((c <= -1.5e+149) || (!(c <= -1.35e+109) && ((c <= -2.4e+28) || !(c <= 1.38e-17))))
		tmp = Float64(2.0 * Float64(Float64(b * c) * Float64(c * Float64(-i))));
	else
		tmp = Float64(2.0 * 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 <= -1.5e+149) || (~((c <= -1.35e+109)) && ((c <= -2.4e+28) || ~((c <= 1.38e-17)))))
		tmp = 2.0 * ((b * c) * (c * -i));
	else
		tmp = 2.0 * ((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[c, -1.5e+149], And[N[Not[LessEqual[c, -1.35e+109]], $MachinePrecision], Or[LessEqual[c, -2.4e+28], N[Not[LessEqual[c, 1.38e-17]], $MachinePrecision]]]], N[(2.0 * N[(N[(b * c), $MachinePrecision] * N[(c * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.50000000000000002e149 or -1.35000000000000001e109 < c < -2.39999999999999981e28 or 1.3800000000000001e-17 < c

   1. Initial program 79.7%

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

      1. fma-define 79.7%

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

      2. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

      1. fma-define 88.3%

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

      2. +-commutative 88.3%

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

   6. Applied egg-rr 88.3%

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

   7. Taylor expanded in c around 0 86.5%

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

   8. Taylor expanded in i around inf 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-*r* 75.8%

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

      3. distribute-lft-neg-in 75.8%

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

      4. *-commutative 75.8%

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

      5. distribute-rgt-neg-in 75.8%

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

      6. *-commutative 75.8%

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

   10. Simplified 75.8%

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

   11. Taylor expanded in a around 0 61.4%

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

       1. *-commutative 61.4%

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

   13. Simplified 61.4%

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

   if -1.50000000000000002e149 < c < -1.35000000000000001e109 or -2.39999999999999981e28 < c < 1.3800000000000001e-17

   1. Initial program 97.7%

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

   3. Taylor expanded in c around 0 71.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+149} \lor \neg \left(c \leq -1.35 \cdot 10^{+109}\right) \land \left(c \leq -2.4 \cdot 10^{+28} \lor \neg \left(c \leq 1.38 \cdot 10^{-17}\right)\right):\\ \;\;\;\;2 \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{if}\;i \leq -6.8 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-197}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (+ a (* b c)) (* c i)) (- 2.0))))
   (if (<= i -6.8e+131)
     t_1
     (if (<= i 7.5e-197)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= i 7.2e+62) (* 2.0 (- (* x y) (* c (* b (* c i))))) 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 = ((a + (b * c)) * (c * i)) * -2.0;
	double tmp;
	if (i <= -6.8e+131) {
		tmp = t_1;
	} else if (i <= 7.5e-197) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (i <= 7.2e+62) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = 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 = ((a + (b * c)) * (c * i)) * -2.0d0
    if (i <= (-6.8d+131)) then
        tmp = t_1
    else if (i <= 7.5d-197) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (i <= 7.2d+62) then
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    else
        tmp = 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 = ((a + (b * c)) * (c * i)) * -2.0;
	double tmp;
	if (i <= -6.8e+131) {
		tmp = t_1;
	} else if (i <= 7.5e-197) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (i <= 7.2e+62) {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	} else {
		tmp = 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 = ((a + (b * c)) * (c * i)) * -2.0
	tmp = 0
	if i <= -6.8e+131:
		tmp = t_1
	elif i <= 7.5e-197:
		tmp = 2.0 * ((x * y) + (z * t))
	elif i <= 7.2e+62:
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	else:
		tmp = 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(Float64(a + Float64(b * c)) * Float64(c * i)) * Float64(-2.0))
	tmp = 0.0
	if (i <= -6.8e+131)
		tmp = t_1;
	elseif (i <= 7.5e-197)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (i <= 7.2e+62)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = 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 = ((a + (b * c)) * (c * i)) * -2.0;
	tmp = 0.0;
	if (i <= -6.8e+131)
		tmp = t_1;
	elseif (i <= 7.5e-197)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (i <= 7.2e+62)
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	else
		tmp = 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[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision]}, If[LessEqual[i, -6.8e+131], t$95$1, If[LessEqual[i, 7.5e-197], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e+62], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.79999999999999972e131 or 7.2e62 < i

   1. Initial program 89.2%

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

      1. fma-define 89.2%

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

      2. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

      1. fma-define 89.2%

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

      2. +-commutative 89.2%

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

   6. Applied egg-rr 89.2%

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

   7. Taylor expanded in c around 0 73.7%

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

   8. Taylor expanded in i around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. associate-*r* 76.3%

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

      3. distribute-lft-neg-in 76.3%

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

      4. *-commutative 76.3%

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

      5. distribute-rgt-neg-in 76.3%

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

      6. *-commutative 76.3%

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

   10. Simplified 76.3%

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

   if -6.79999999999999972e131 < i < 7.5e-197

   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 c around 0 72.5%

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

   if 7.5e-197 < i < 7.2e62

   1. Initial program 86.2%

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

      1. fma-define 86.2%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

      1. fma-define 92.9%

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

      2. +-commutative 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in c around 0 95.2%

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

   8. Taylor expanded in z around 0 88.6%

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

      1. cancel-sign-sub-inv 88.6%

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

      2. +-commutative 88.6%

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

      3. fma-undefine 88.6%

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

      4. cancel-sign-sub-inv 88.6%

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

      5. *-commutative 88.6%

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

      6. fma-undefine 88.6%

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

      7. associate-*r* 86.2%

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

      8. distribute-rgt-in 86.2%

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

      9. +-commutative 86.2%

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

      10. *-commutative 86.2%

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

      11. *-commutative 86.2%

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

   10. Simplified 86.2%

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

   11. Taylor expanded in a around 0 75.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{+131}:\\ \;\;\;\;\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-197}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-296}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= a -1.55e+26)
     (* (* i (* a c)) (- 2.0))
     (if (<= a -4e-271)
       t_1
       (if (<= a -3.3e-296)
         (* 2.0 (* z t))
         (if (<= a 4.2e+119) t_1 (* -2.0 (* c (* a 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 = (x * y) * 2.0;
	double tmp;
	if (a <= -1.55e+26) {
		tmp = (i * (a * c)) * -2.0;
	} else if (a <= -4e-271) {
		tmp = t_1;
	} else if (a <= -3.3e-296) {
		tmp = 2.0 * (z * t);
	} else if (a <= 4.2e+119) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (a * 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 = (x * y) * 2.0d0
    if (a <= (-1.55d+26)) then
        tmp = (i * (a * c)) * -2.0d0
    else if (a <= (-4d-271)) then
        tmp = t_1
    else if (a <= (-3.3d-296)) then
        tmp = 2.0d0 * (z * t)
    else if (a <= 4.2d+119) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (c * (a * 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 = (x * y) * 2.0;
	double tmp;
	if (a <= -1.55e+26) {
		tmp = (i * (a * c)) * -2.0;
	} else if (a <= -4e-271) {
		tmp = t_1;
	} else if (a <= -3.3e-296) {
		tmp = 2.0 * (z * t);
	} else if (a <= 4.2e+119) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (a * 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 = (x * y) * 2.0
	tmp = 0
	if a <= -1.55e+26:
		tmp = (i * (a * c)) * -2.0
	elif a <= -4e-271:
		tmp = t_1
	elif a <= -3.3e-296:
		tmp = 2.0 * (z * t)
	elif a <= 4.2e+119:
		tmp = t_1
	else:
		tmp = -2.0 * (c * (a * 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(Float64(x * y) * 2.0)
	tmp = 0.0
	if (a <= -1.55e+26)
		tmp = Float64(Float64(i * Float64(a * c)) * Float64(-2.0));
	elseif (a <= -4e-271)
		tmp = t_1;
	elseif (a <= -3.3e-296)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (a <= 4.2e+119)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(a * 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 = (x * y) * 2.0;
	tmp = 0.0;
	if (a <= -1.55e+26)
		tmp = (i * (a * c)) * -2.0;
	elseif (a <= -4e-271)
		tmp = t_1;
	elseif (a <= -3.3e-296)
		tmp = 2.0 * (z * t);
	elseif (a <= 4.2e+119)
		tmp = t_1;
	else
		tmp = -2.0 * (c * (a * 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[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[a, -1.55e+26], N[(N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[a, -4e-271], t$95$1, If[LessEqual[a, -3.3e-296], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+119], t$95$1, N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e26

   1. Initial program 88.1%

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

      1. fma-define 88.1%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

      1. fma-define 90.9%

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

      2. +-commutative 90.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in c around 0 80.7%

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

   8. Taylor expanded in a around inf 52.5%

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

      1. *-commutative 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*r* 53.9%

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

      4. neg-mul-1 53.9%

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

      5. distribute-rgt-neg-in 53.9%

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

      6. *-commutative 53.9%

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

      7. distribute-lft-neg-in 53.9%

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

   10. Simplified 53.9%

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

   if -1.55e26 < a < -3.99999999999999985e-271 or -3.3e-296 < a < 4.19999999999999966e119

   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 40.1%

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

   if -3.99999999999999985e-271 < a < -3.3e-296

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf 64.7%

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

   if 4.19999999999999966e119 < a

   1. Initial program 82.6%

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

      1. fma-define 82.6%

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

      2. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

      1. fma-define 91.1%

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

      2. +-commutative 91.1%

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

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in c around 0 79.8%

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

   8. Taylor expanded in i around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. associate-*r* 57.8%

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

      3. distribute-lft-neg-in 57.8%

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

      4. *-commutative 57.8%

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

      5. distribute-rgt-neg-in 57.8%

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

      6. *-commutative 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in c around 0 47.2%

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

       1. *-commutative 47.2%

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

       2. associate-*r* 49.7%

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

   13. Simplified 49.7%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-271}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-296}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 36.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ \mathbf{if}\;a \leq -8 \cdot 10^{+25}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-297}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* x y) 2.0)))
   (if (<= a -8e+25)
     (* -2.0 (* a (* c i)))
     (if (<= a -1.04e-271)
       t_1
       (if (<= a -3.1e-297)
         (* 2.0 (* z t))
         (if (<= a 9e+119) t_1 (* -2.0 (* c (* a 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 = (x * y) * 2.0;
	double tmp;
	if (a <= -8e+25) {
		tmp = -2.0 * (a * (c * i));
	} else if (a <= -1.04e-271) {
		tmp = t_1;
	} else if (a <= -3.1e-297) {
		tmp = 2.0 * (z * t);
	} else if (a <= 9e+119) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (a * 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 = (x * y) * 2.0d0
    if (a <= (-8d+25)) then
        tmp = (-2.0d0) * (a * (c * i))
    else if (a <= (-1.04d-271)) then
        tmp = t_1
    else if (a <= (-3.1d-297)) then
        tmp = 2.0d0 * (z * t)
    else if (a <= 9d+119) then
        tmp = t_1
    else
        tmp = (-2.0d0) * (c * (a * 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 = (x * y) * 2.0;
	double tmp;
	if (a <= -8e+25) {
		tmp = -2.0 * (a * (c * i));
	} else if (a <= -1.04e-271) {
		tmp = t_1;
	} else if (a <= -3.1e-297) {
		tmp = 2.0 * (z * t);
	} else if (a <= 9e+119) {
		tmp = t_1;
	} else {
		tmp = -2.0 * (c * (a * 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 = (x * y) * 2.0
	tmp = 0
	if a <= -8e+25:
		tmp = -2.0 * (a * (c * i))
	elif a <= -1.04e-271:
		tmp = t_1
	elif a <= -3.1e-297:
		tmp = 2.0 * (z * t)
	elif a <= 9e+119:
		tmp = t_1
	else:
		tmp = -2.0 * (c * (a * 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(Float64(x * y) * 2.0)
	tmp = 0.0
	if (a <= -8e+25)
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	elseif (a <= -1.04e-271)
		tmp = t_1;
	elseif (a <= -3.1e-297)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (a <= 9e+119)
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(c * Float64(a * 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 = (x * y) * 2.0;
	tmp = 0.0;
	if (a <= -8e+25)
		tmp = -2.0 * (a * (c * i));
	elseif (a <= -1.04e-271)
		tmp = t_1;
	elseif (a <= -3.1e-297)
		tmp = 2.0 * (z * t);
	elseif (a <= 9e+119)
		tmp = t_1;
	else
		tmp = -2.0 * (c * (a * 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[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[a, -8e+25], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.04e-271], t$95$1, If[LessEqual[a, -3.1e-297], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+119], t$95$1, N[(-2.0 * N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.00000000000000072e25

   1. Initial program 88.1%

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

      1. fma-define 88.1%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

      1. fma-define 90.9%

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

      2. +-commutative 90.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in c around 0 80.7%

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

   8. Taylor expanded in i around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. associate-*r* 67.3%

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

      3. distribute-lft-neg-in 67.3%

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

      4. *-commutative 67.3%

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

      5. distribute-rgt-neg-in 67.3%

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

      6. *-commutative 67.3%

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

   10. Simplified 67.3%

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

   11. Taylor expanded in c around 0 52.5%

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

   if -8.00000000000000072e25 < a < -1.03999999999999997e-271 or -3.0999999999999997e-297 < a < 9.00000000000000039e119

   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 40.1%

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

   if -1.03999999999999997e-271 < a < -3.0999999999999997e-297

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf 64.7%

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

   if 9.00000000000000039e119 < a

   1. Initial program 82.6%

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

      1. fma-define 82.6%

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

      2. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

      1. fma-define 91.1%

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

      2. +-commutative 91.1%

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

   6. Applied egg-rr 91.1%

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

   7. Taylor expanded in c around 0 79.8%

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

   8. Taylor expanded in i around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. associate-*r* 57.8%

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

      3. distribute-lft-neg-in 57.8%

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

      4. *-commutative 57.8%

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

      5. distribute-rgt-neg-in 57.8%

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

      6. *-commutative 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in c around 0 47.2%

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

       1. *-commutative 47.2%

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

       2. associate-*r* 49.7%

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

   13. Simplified 49.7%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+25}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-271}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-297}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(a \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot 2\\ t_2 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-304}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) 2.0)) (t_2 (* -2.0 (* a (* c i)))))
   (if (<= a -7.5e+25)
     t_2
     (if (<= a -8.8e-272)
       t_1
       (if (<= a -8e-304) (* 2.0 (* z t)) (if (<= a 1.95e+119) 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) * 2.0;
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (a <= -7.5e+25) {
		tmp = t_2;
	} else if (a <= -8.8e-272) {
		tmp = t_1;
	} else if (a <= -8e-304) {
		tmp = 2.0 * (z * t);
	} else if (a <= 1.95e+119) {
		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) * 2.0d0
    t_2 = (-2.0d0) * (a * (c * i))
    if (a <= (-7.5d+25)) then
        tmp = t_2
    else if (a <= (-8.8d-272)) then
        tmp = t_1
    else if (a <= (-8d-304)) then
        tmp = 2.0d0 * (z * t)
    else if (a <= 1.95d+119) 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) * 2.0;
	double t_2 = -2.0 * (a * (c * i));
	double tmp;
	if (a <= -7.5e+25) {
		tmp = t_2;
	} else if (a <= -8.8e-272) {
		tmp = t_1;
	} else if (a <= -8e-304) {
		tmp = 2.0 * (z * t);
	} else if (a <= 1.95e+119) {
		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) * 2.0
	t_2 = -2.0 * (a * (c * i))
	tmp = 0
	if a <= -7.5e+25:
		tmp = t_2
	elif a <= -8.8e-272:
		tmp = t_1
	elif a <= -8e-304:
		tmp = 2.0 * (z * t)
	elif a <= 1.95e+119:
		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(x * y) * 2.0)
	t_2 = Float64(-2.0 * Float64(a * Float64(c * i)))
	tmp = 0.0
	if (a <= -7.5e+25)
		tmp = t_2;
	elseif (a <= -8.8e-272)
		tmp = t_1;
	elseif (a <= -8e-304)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (a <= 1.95e+119)
		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) * 2.0;
	t_2 = -2.0 * (a * (c * i));
	tmp = 0.0;
	if (a <= -7.5e+25)
		tmp = t_2;
	elseif (a <= -8.8e-272)
		tmp = t_1;
	elseif (a <= -8e-304)
		tmp = 2.0 * (z * t);
	elseif (a <= 1.95e+119)
		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[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+25], t$95$2, If[LessEqual[a, -8.8e-272], t$95$1, If[LessEqual[a, -8e-304], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+119], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.49999999999999993e25 or 1.9499999999999999e119 < a

   1. Initial program 86.2%

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

      1. fma-define 86.2%

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

      2. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

      1. fma-define 91.0%

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

      2. +-commutative 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in c around 0 80.4%

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

   8. Taylor expanded in i around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. associate-*r* 64.0%

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

      3. distribute-lft-neg-in 64.0%

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

      4. *-commutative 64.0%

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

      5. distribute-rgt-neg-in 64.0%

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

      6. *-commutative 64.0%

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

   10. Simplified 64.0%

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

   11. Taylor expanded in c around 0 50.7%

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

   if -7.49999999999999993e25 < a < -8.79999999999999952e-272 or -7.99999999999999977e-304 < a < 1.9499999999999999e119

   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 40.1%

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

   if -8.79999999999999952e-272 < a < -7.99999999999999977e-304

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf 64.7%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+25}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-272}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-304}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.32 \cdot 10^{-5} \lor \neg \left(c \leq 1.9 \cdot 10^{-18}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 -1.32e-5) (not (<= c 1.9e-18)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 2.0 (+ (* 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 <= -1.32e-5) || !(c <= 1.9e-18)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((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 <= (-1.32d-5)) .or. (.not. (c <= 1.9d-18))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((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 <= -1.32e-5) || !(c <= 1.9e-18)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((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 <= -1.32e-5) or not (c <= 1.9e-18):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((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 ((c <= -1.32e-5) || !(c <= 1.9e-18))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * 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 <= -1.32e-5) || ~((c <= 1.9e-18)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((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[c, -1.32e-5], N[Not[LessEqual[c, 1.9e-18]], $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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.32000000000000007e-5 or 1.8999999999999999e-18 < c

   1. Initial program 80.5%

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

   3. Taylor expanded in x around 0 81.1%

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

   if -1.32000000000000007e-5 < c < 1.8999999999999999e-18

   1. Initial program 99.1%

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

   3. Taylor expanded in c around 0 72.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.32 \cdot 10^{-5} \lor \neg \left(c \leq 1.9 \cdot 10^{-18}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(t\_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-166}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= c -1.55e+43)
     (* 2.0 (- t_1 (* c (* b (* c i)))))
     (if (<= c 2.3e-166)
       (* 2.0 (- t_1 (* i (* a c))))
       (* 2.0 (- (* x y) (* c (* (+ 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 = (x * y) + (z * t);
	double tmp;
	if (c <= -1.55e+43) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else if (c <= 2.3e-166) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - (c * ((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) :: tmp
    t_1 = (x * y) + (z * t)
    if (c <= (-1.55d+43)) then
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    else if (c <= 2.3d-166) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - (c * ((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 = (x * y) + (z * t);
	double tmp;
	if (c <= -1.55e+43) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else if (c <= 2.3e-166) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - (c * ((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 = (x * y) + (z * t)
	tmp = 0
	if c <= -1.55e+43:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	elif c <= 2.3e-166:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - (c * ((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(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -1.55e+43)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= 2.3e-166)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * 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 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -1.55e+43)
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	elseif (c <= 2.3e-166)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - (c * ((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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+43], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-166], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.5500000000000001e43

   1. Initial program 77.1%

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

      1. fma-define 77.1%

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

      2. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

      1. fma-define 85.5%

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

      2. +-commutative 85.5%

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

   6. Applied egg-rr 85.5%

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

   7. Taylor expanded in c around 0 88.9%

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

   8. Taylor expanded in a around 0 89.1%

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

   if -1.5500000000000001e43 < c < 2.29999999999999999e-166

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 92.3%

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

      1. *-commutative 92.3%

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

   5. Simplified 92.3%

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

   if 2.29999999999999999e-166 < c

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 84.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-166}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-166}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

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))))
   (if (<= c -1.45e+28)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 2.3e-166)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))
       (* 2.0 (- (* x y) 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 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.45e+28) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 2.3e-166) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - 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 = c * ((a + (b * c)) * i)
    if (c <= (-1.45d+28)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 2.3d-166) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - 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 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.45e+28) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 2.3e-166) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - 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 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.45e+28:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 2.3e-166:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - 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(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.45e+28)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 2.3e-166)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.45e+28)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 2.3e-166)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - 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[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.45e+28], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-166], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.4500000000000001e28

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 78.6%

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

   if -1.4500000000000001e28 < c < 2.29999999999999999e-166

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 95.1%

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

      1. *-commutative 95.1%

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

   5. Simplified 95.1%

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

   if 2.29999999999999999e-166 < c

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 84.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-166}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{+131} \lor \neg \left(i \leq 3.5 \cdot 10^{-113}\right):\\ \;\;\;\;\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 (<= i -6.8e+131) (not (<= i 3.5e-113)))
   (* (* (+ a (* b c)) (* c i)) (- 2.0))
   (* 2.0 (+ (* 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 ((i <= -6.8e+131) || !(i <= 3.5e-113)) {
		tmp = ((a + (b * c)) * (c * i)) * -2.0;
	} else {
		tmp = 2.0 * ((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 ((i <= (-6.8d+131)) .or. (.not. (i <= 3.5d-113))) then
        tmp = ((a + (b * c)) * (c * i)) * -2.0d0
    else
        tmp = 2.0d0 * ((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 ((i <= -6.8e+131) || !(i <= 3.5e-113)) {
		tmp = ((a + (b * c)) * (c * i)) * -2.0;
	} else {
		tmp = 2.0 * ((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 (i <= -6.8e+131) or not (i <= 3.5e-113):
		tmp = ((a + (b * c)) * (c * i)) * -2.0
	else:
		tmp = 2.0 * ((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 ((i <= -6.8e+131) || !(i <= 3.5e-113))
		tmp = Float64(Float64(Float64(a + Float64(b * c)) * Float64(c * i)) * Float64(-2.0));
	else
		tmp = Float64(2.0 * 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 ((i <= -6.8e+131) || ~((i <= 3.5e-113)))
		tmp = ((a + (b * c)) * (c * i)) * -2.0;
	else
		tmp = 2.0 * ((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[i, -6.8e+131], N[Not[LessEqual[i, 3.5e-113]], $MachinePrecision]], N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.79999999999999972e131 or 3.50000000000000029e-113 < i

   1. Initial program 89.2%

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

      1. fma-define 89.2%

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

      2. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

      1. fma-define 90.0%

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

      2. +-commutative 90.0%

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

   6. Applied egg-rr 90.0%

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

   7. Taylor expanded in c around 0 78.1%

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

   8. Taylor expanded in i around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. associate-*r* 73.6%

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

      3. distribute-lft-neg-in 73.6%

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

      4. *-commutative 73.6%

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

      5. distribute-rgt-neg-in 73.6%

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

      6. *-commutative 73.6%

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

   10. Simplified 73.6%

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

   if -6.79999999999999972e131 < i < 3.50000000000000029e-113

   1. Initial program 89.4%

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

   3. Taylor expanded in c around 0 72.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{+131} \lor \neg \left(i \leq 3.5 \cdot 10^{-113}\right):\\ \;\;\;\;\left(\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+175}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

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))))
   (if (<= z -5.2e+175) (* 2.0 (- (* z t) t_1)) (* 2.0 (- (* x y) 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 = c * ((a + (b * c)) * i);
	double tmp;
	if (z <= -5.2e+175) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - 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 = c * ((a + (b * c)) * i)
    if (z <= (-5.2d+175)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * ((x * y) - 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 = c * ((a + (b * c)) * i);
	double tmp;
	if (z <= -5.2e+175) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - 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 = c * ((a + (b * c)) * i)
	tmp = 0
	if z <= -5.2e+175:
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * ((x * y) - 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(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (z <= -5.2e+175)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - 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 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (z <= -5.2e+175)
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * ((x * y) - 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[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+175], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000001e175

   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 x around 0 77.4%

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

   if -5.2000000000000001e175 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 77.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+175}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+170} \lor \neg \left(i \leq 5.6 \cdot 10^{+73}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 (<= i -1.1e+170) (not (<= i 5.6e+73)))
   (* -2.0 (* a (* c i)))
   (* 2.0 (+ (* 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 ((i <= -1.1e+170) || !(i <= 5.6e+73)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * ((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 ((i <= (-1.1d+170)) .or. (.not. (i <= 5.6d+73))) then
        tmp = (-2.0d0) * (a * (c * i))
    else
        tmp = 2.0d0 * ((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 ((i <= -1.1e+170) || !(i <= 5.6e+73)) {
		tmp = -2.0 * (a * (c * i));
	} else {
		tmp = 2.0 * ((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 (i <= -1.1e+170) or not (i <= 5.6e+73):
		tmp = -2.0 * (a * (c * i))
	else:
		tmp = 2.0 * ((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 ((i <= -1.1e+170) || !(i <= 5.6e+73))
		tmp = Float64(-2.0 * Float64(a * Float64(c * i)));
	else
		tmp = Float64(2.0 * 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 ((i <= -1.1e+170) || ~((i <= 5.6e+73)))
		tmp = -2.0 * (a * (c * i));
	else
		tmp = 2.0 * ((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[i, -1.1e+170], N[Not[LessEqual[i, 5.6e+73]], $MachinePrecision]], N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.09999999999999994e170 or 5.60000000000000016e73 < i

   1. Initial program 89.8%

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

      1. fma-define 89.8%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. fma-define 89.8%

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

      2. +-commutative 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in c around 0 72.8%

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

   8. Taylor expanded in i around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-*r* 80.4%

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

      3. distribute-lft-neg-in 80.4%

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

      4. *-commutative 80.4%

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

      5. distribute-rgt-neg-in 80.4%

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

      6. *-commutative 80.4%

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

   10. Simplified 80.4%

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

   11. Taylor expanded in c around 0 47.3%

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

   if -1.09999999999999994e170 < i < 5.60000000000000016e73

   1. Initial program 89.1%

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

   3. Taylor expanded in c around 0 65.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+170} \lor \neg \left(i \leq 5.6 \cdot 10^{+73}\right):\\ \;\;\;\;-2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-25} \lor \neg \left(t \leq 1.2 \cdot 10^{+123}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

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 (or (<= t -5.2e-25) (not (<= t 1.2e+123)))
   (* 2.0 (* z t))
   (* (* x y) 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 ((t <= -5.2e-25) || !(t <= 1.2e+123)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 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 ((t <= (-5.2d-25)) .or. (.not. (t <= 1.2d+123))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = (x * y) * 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 ((t <= -5.2e-25) || !(t <= 1.2e+123)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = (x * y) * 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 (t <= -5.2e-25) or not (t <= 1.2e+123):
		tmp = 2.0 * (z * t)
	else:
		tmp = (x * y) * 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 ((t <= -5.2e-25) || !(t <= 1.2e+123))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(Float64(x * y) * 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 ((t <= -5.2e-25) || ~((t <= 1.2e+123)))
		tmp = 2.0 * (z * t);
	else
		tmp = (x * y) * 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[Or[LessEqual[t, -5.2e-25], N[Not[LessEqual[t, 1.2e+123]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2e-25 or 1.19999999999999994e123 < t

   1. Initial program 79.1%

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

   3. Taylor expanded in z around inf 40.1%

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

   if -5.2e-25 < t < 1.19999999999999994e123

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 39.4%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-25} \lor \neg \left(t \leq 1.2 \cdot 10^{+123}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% 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 89.3%

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

3. Taylor expanded in z around inf 23.7%

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

4. Final simplification 23.7%

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

Developer target: 94.1% 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 2024091 
(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))))