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

Percentage Accurate: 90.7% → 94.4%

Time: 14.6s

Alternatives: 14

Speedup: 0.5×

• 46.4% 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: 90.7% 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: 94.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+146}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(\left(t + \frac{x \cdot y}{z}\right) - \frac{c \cdot \left(i \cdot t\_1\right)}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - t\_1 \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* c b))))
   (if (<= z -6.6e+146)
     (* 2.0 (* z (- (+ t (/ (* x y) z)) (/ (* c (* i t_1)) z))))
     (* 2.0 (- (fma x y (* z t)) (* t_1 (* c i)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (c * b);
	double tmp;
	if (z <= -6.6e+146) {
		tmp = 2.0 * (z * ((t + ((x * y) / z)) - ((c * (i * t_1)) / z)));
	} else {
		tmp = 2.0 * (fma(x, y, (z * t)) - (t_1 * (c * i)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(c * b))
	tmp = 0.0
	if (z <= -6.6e+146)
		tmp = Float64(2.0 * Float64(z * Float64(Float64(t + Float64(Float64(x * y) / z)) - Float64(Float64(c * Float64(i * t_1)) / z))));
	else
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+146], N[(2.0 * N[(z * N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.60000000000000032e146

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf 97.5%

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

   if -6.60000000000000032e146 < z

   1. Initial program 90.8%

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

      1. fma-define 91.2%

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

      2. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+146}:\\ \;\;\;\;2 \cdot \left(z \cdot \left(\left(t + \frac{x \cdot y}{z}\right) - \frac{c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.6% accurate, 0.4× speedup

Math

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

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 (* c b))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* i (* c t_1))) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (* z (- (+ t (/ (* x y) z)) (/ (* c (* i t_1)) 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 + (c * b);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (z * ((t + ((x * y) / z)) - ((c * (i * t_1)) / 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 + (c * b);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (z * ((t + ((x * y) / z)) - ((c * (i * t_1)) / 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 + (c * b)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (t_2 - (i * (c * t_1))) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = 2.0 * (z * ((t + ((x * y) / z)) - ((c * (i * t_1)) / 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(c * b))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(i * Float64(c * t_1))) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(z * Float64(Float64(t + Float64(Float64(x * y) / z)) - Float64(Float64(c * Float64(i * t_1)) / 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 + (c * b);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - (i * (c * t_1))) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * (z * ((t + ((x * y) / z)) - ((c * (i * t_1)) / 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[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $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[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(i * t$95$1), $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 96.4%

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

      1. fma-define 96.4%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

      1. fma-define 98.8%

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

      2. +-commutative 98.8%

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

   6. Applied egg-rr 98.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 73.3%

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

4. Final simplification 97.3%

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

Alternative 3: 95.8% accurate, 0.5× speedup

Math

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

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 (* c b))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* i (* c t_1))) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 (* z (+ t (/ (* x y) 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 + (c * b);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (z * (t + ((x * y) / 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 + (c * b);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - (i * (c * t_1))) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * (z * (t + ((x * y) / 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 + (c * b)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (t_2 - (i * (c * t_1))) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = 2.0 * (z * (t + ((x * y) / 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(c * b))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(i * Float64(c * t_1))) <= 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(x * y) / 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 + (c * b);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - (i * (c * t_1))) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * (z * (t + ((x * y) / 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[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $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[(x * y), $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 96.4%

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

      1. fma-define 96.4%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

      1. fma-define 98.8%

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

      2. +-commutative 98.8%

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

   6. Applied egg-rr 98.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 73.3%

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

   4. Taylor expanded in c around 0 53.3%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in a around 0 60.0%

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

4. Final simplification 96.5%

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

Alternative 4: 92.7% accurate, 0.5× speedup

Math

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

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 (- (+ (* x y) (* z t)) (* i (* c (+ a (* c b)))))))
   (if (<= t_1 INFINITY) (* 2.0 t_1) (* 2.0 (* z (+ t (/ (* x y) 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 = ((x * y) + (z * t)) - (i * (c * (a + (c * b))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = 2.0 * t_1;
	} else {
		tmp = 2.0 * (z * (t + ((x * y) / 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 = ((x * y) + (z * t)) - (i * (c * (a + (c * b))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * t_1;
	} else {
		tmp = 2.0 * (z * (t + ((x * y) / 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 = ((x * y) + (z * t)) - (i * (c * (a + (c * b))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = 2.0 * t_1
	else:
		tmp = 2.0 * (z * (t + ((x * y) / 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(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * Float64(a + Float64(c * b)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(2.0 * t_1);
	else
		tmp = Float64(2.0 * Float64(z * Float64(t + Float64(Float64(x * y) / 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 = ((x * y) + (z * t)) - (i * (c * (a + (c * b))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = 2.0 * t_1;
	else
		tmp = 2.0 * (z * (t + ((x * y) / 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[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(2.0 * t$95$1), $MachinePrecision], N[(2.0 * N[(z * N[(t + N[(N[(x * y), $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 96.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 73.3%

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

   4. Taylor expanded in c around 0 53.3%

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

      1. associate-/l* 66.7%

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

      2. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in a around 0 60.0%

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

4. Final simplification 94.3%

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

Alternative 5: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := 2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \mathbf{if}\;c \leq -4.6 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* 2.0 (* c (* i (- (- (* c b)) a))))))
   (if (<= c -4.6e+152)
     t_2
     (if (<= c -2.1e+108)
       t_1
       (if (<= c -9.5e+56)
         (* 2.0 (- (* z t) (* c (* b (* c i)))))
         (if (<= c 1.05e-27) 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 = 2.0 * ((x * y) + (z * t));
	double t_2 = 2.0 * (c * (i * (-(c * b) - a)));
	double tmp;
	if (c <= -4.6e+152) {
		tmp = t_2;
	} else if (c <= -2.1e+108) {
		tmp = t_1;
	} else if (c <= -9.5e+56) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (c <= 1.05e-27) {
		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 = 2.0d0 * ((x * y) + (z * t))
    t_2 = 2.0d0 * (c * (i * (-(c * b) - a)))
    if (c <= (-4.6d+152)) then
        tmp = t_2
    else if (c <= (-2.1d+108)) then
        tmp = t_1
    else if (c <= (-9.5d+56)) then
        tmp = 2.0d0 * ((z * t) - (c * (b * (c * i))))
    else if (c <= 1.05d-27) 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 = 2.0 * ((x * y) + (z * t));
	double t_2 = 2.0 * (c * (i * (-(c * b) - a)));
	double tmp;
	if (c <= -4.6e+152) {
		tmp = t_2;
	} else if (c <= -2.1e+108) {
		tmp = t_1;
	} else if (c <= -9.5e+56) {
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	} else if (c <= 1.05e-27) {
		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 = 2.0 * ((x * y) + (z * t))
	t_2 = 2.0 * (c * (i * (-(c * b) - a)))
	tmp = 0
	if c <= -4.6e+152:
		tmp = t_2
	elif c <= -2.1e+108:
		tmp = t_1
	elif c <= -9.5e+56:
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))))
	elif c <= 1.05e-27:
		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(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-Float64(c * b)) - a))))
	tmp = 0.0
	if (c <= -4.6e+152)
		tmp = t_2;
	elseif (c <= -2.1e+108)
		tmp = t_1;
	elseif (c <= -9.5e+56)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(b * Float64(c * i)))));
	elseif (c <= 1.05e-27)
		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 = 2.0 * ((x * y) + (z * t));
	t_2 = 2.0 * (c * (i * (-(c * b) - a)));
	tmp = 0.0;
	if (c <= -4.6e+152)
		tmp = t_2;
	elseif (c <= -2.1e+108)
		tmp = t_1;
	elseif (c <= -9.5e+56)
		tmp = 2.0 * ((z * t) - (c * (b * (c * i))));
	elseif (c <= 1.05e-27)
		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[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(i * N[((-N[(c * b), $MachinePrecision]) - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.6e+152], t$95$2, If[LessEqual[c, -2.1e+108], t$95$1, If[LessEqual[c, -9.5e+56], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e-27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.5999999999999997e152 or 1.05000000000000008e-27 < c

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf 81.7%

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

   if -4.5999999999999997e152 < c < -2.1000000000000001e108 or -9.4999999999999997e56 < c < 1.05000000000000008e-27

   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 c around 0 81.6%

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

   if -2.1000000000000001e108 < c < -9.4999999999999997e56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in a around 0 100.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+108}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+160}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-99}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

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 -6.8e+160)
     (* 2.0 (* c (* i (- (- (* c b)) a))))
     (if (<= c -5.2e-99)
       (* 2.0 (- t_1 (* i (* c (* c b)))))
       (if (<= c 9.8e-28)
         (* 2.0 (- t_1 (* i (* c a))))
         (* 2.0 (- (* z t) (* c (* i (+ a (* c b)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -6.8e+160) {
		tmp = 2.0 * (c * (i * (-(c * b) - a)));
	} else if (c <= -5.2e-99) {
		tmp = 2.0 * (t_1 - (i * (c * (c * b))));
	} else if (c <= 9.8e-28) {
		tmp = 2.0 * (t_1 - (i * (c * a)));
	} else {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (c <= (-6.8d+160)) then
        tmp = 2.0d0 * (c * (i * (-(c * b) - a)))
    else if (c <= (-5.2d-99)) then
        tmp = 2.0d0 * (t_1 - (i * (c * (c * b))))
    else if (c <= 9.8d-28) then
        tmp = 2.0d0 * (t_1 - (i * (c * a)))
    else
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (c * b)))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -6.8e+160) {
		tmp = 2.0 * (c * (i * (-(c * b) - a)));
	} else if (c <= -5.2e-99) {
		tmp = 2.0 * (t_1 - (i * (c * (c * b))));
	} else if (c <= 9.8e-28) {
		tmp = 2.0 * (t_1 - (i * (c * a)));
	} else {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if c <= -6.8e+160:
		tmp = 2.0 * (c * (i * (-(c * b) - a)))
	elif c <= -5.2e-99:
		tmp = 2.0 * (t_1 - (i * (c * (c * b))))
	elif c <= 9.8e-28:
		tmp = 2.0 * (t_1 - (i * (c * a)))
	else:
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -6.8e+160)
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-Float64(c * b)) - a))));
	elseif (c <= -5.2e-99)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * Float64(c * b)))));
	elseif (c <= 9.8e-28)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(c * a))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -6.8e+160)
		tmp = 2.0 * (c * (i * (-(c * b) - a)));
	elseif (c <= -5.2e-99)
		tmp = 2.0 * (t_1 - (i * (c * (c * b))));
	elseif (c <= 9.8e-28)
		tmp = 2.0 * (t_1 - (i * (c * a)));
	else
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e+160], N[(2.0 * N[(c * N[(i * N[((-N[(c * b), $MachinePrecision]) - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.2e-99], N[(2.0 * N[(t$95$1 - N[(i * N[(c * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.8e-28], N[(2.0 * N[(t$95$1 - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.80000000000000061e160

   1. Initial program 70.1%

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

   3. Taylor expanded in i around inf 86.8%

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

   if -6.80000000000000061e160 < c < -5.2000000000000001e-99

   1. Initial program 96.2%

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

   3. Taylor expanded in a around 0 94.3%

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

   if -5.2000000000000001e-99 < c < 9.80000000000000059e-28

   1. Initial program 99.0%

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

   3. Taylor expanded in a around inf 96.8%

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

      1. *-commutative 96.8%

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

   5. Simplified 96.8%

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

   if 9.80000000000000059e-28 < c

   1. Initial program 82.5%

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

   3. Taylor expanded in x around 0 82.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{+160}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-99}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-28}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+247}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -4.6e+152)
   (* 2.0 (- (* z t) (* c (* i a))))
   (if (<= c 2.8e-36)
     (* 2.0 (+ (* x y) (* z t)))
     (if (<= c 2.1e+247)
       (* 2.0 (- (* x y) (* a (* c i))))
       (* 2.0 (* i (* c a)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.6e+152) {
		tmp = 2.0 * ((z * t) - (c * (i * a)));
	} else if (c <= 2.8e-36) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 2.1e+247) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * (i * (c * a));
	}
	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 <= (-4.6d+152)) then
        tmp = 2.0d0 * ((z * t) - (c * (i * a)))
    else if (c <= 2.8d-36) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 2.1d+247) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else
        tmp = 2.0d0 * (i * (c * a))
    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 <= -4.6e+152) {
		tmp = 2.0 * ((z * t) - (c * (i * a)));
	} else if (c <= 2.8e-36) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 2.1e+247) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * (i * (c * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -4.6e+152:
		tmp = 2.0 * ((z * t) - (c * (i * a)))
	elif c <= 2.8e-36:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 2.1e+247:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	else:
		tmp = 2.0 * (i * (c * a))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -4.6e+152)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * a))));
	elseif (c <= 2.8e-36)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 2.1e+247)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(i * Float64(c * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -4.6e+152)
		tmp = 2.0 * ((z * t) - (c * (i * a)));
	elseif (c <= 2.8e-36)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 2.1e+247)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	else
		tmp = 2.0 * (i * (c * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -4.6e+152], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e-36], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+247], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.5999999999999997e152

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0 87.3%

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

   4. Taylor expanded in a around inf 56.0%

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

      1. *-commutative 56.0%

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

   6. Simplified 56.0%

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

   if -4.5999999999999997e152 < c < 2.8000000000000001e-36

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 79.5%

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

   if 2.8000000000000001e-36 < c < 2.1e247

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf 82.4%

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

   4. Taylor expanded in c around 0 64.2%

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

      1. associate-/l* 64.3%

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

      2. associate-/l* 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in z around 0 62.6%

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

   if 2.1e247 < c

   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 10.4%

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

      1. mul-1-neg 10.4%

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

      2. *-commutative 10.4%

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

      3. associate-*l* 10.3%

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

      4. *-commutative 10.3%

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

      5. distribute-rgt-neg-in 10.3%

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

      6. *-commutative 10.3%

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

      7. distribute-rgt-neg-in 10.3%

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

   5. Simplified 10.3%

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

      1. pow1 10.3%

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

      2. *-commutative 10.3%

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

      3. add-sqr-sqrt 0.1%

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

      4. sqrt-unprod 27.8%

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

      5. sqr-neg 27.8%

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

      6. sqrt-unprod 10.4%

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

      7. add-sqr-sqrt 37.9%

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

   7. Applied egg-rr 37.9%

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

      1. unpow1 37.9%

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

      2. associate-*r* 54.8%

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

   9. Simplified 54.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+247}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(i \cdot a\right)\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+242}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* i a))))))
   (if (<= c -5.5e+152)
     t_1
     (if (<= c 2.7e-21)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 1.02e+242) t_1 (* 2.0 (* i (* c a))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (i * a)));
	double tmp;
	if (c <= -5.5e+152) {
		tmp = t_1;
	} else if (c <= 2.7e-21) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.02e+242) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (i * (c * a));
	}
	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 = 2.0d0 * ((z * t) - (c * (i * a)))
    if (c <= (-5.5d+152)) then
        tmp = t_1
    else if (c <= 2.7d-21) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 1.02d+242) then
        tmp = t_1
    else
        tmp = 2.0d0 * (i * (c * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * (i * a)));
	double tmp;
	if (c <= -5.5e+152) {
		tmp = t_1;
	} else if (c <= 2.7e-21) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 1.02e+242) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (i * (c * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * (i * a)))
	tmp = 0
	if c <= -5.5e+152:
		tmp = t_1
	elif c <= 2.7e-21:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 1.02e+242:
		tmp = t_1
	else:
		tmp = 2.0 * (i * (c * a))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * a))))
	tmp = 0.0
	if (c <= -5.5e+152)
		tmp = t_1;
	elseif (c <= 2.7e-21)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 1.02e+242)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(i * Float64(c * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * (i * a)));
	tmp = 0.0;
	if (c <= -5.5e+152)
		tmp = t_1;
	elseif (c <= 2.7e-21)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 1.02e+242)
		tmp = t_1;
	else
		tmp = 2.0 * (i * (c * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e+152], t$95$1, If[LessEqual[c, 2.7e-21], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e+242], t$95$1, N[(2.0 * N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.4999999999999999e152 or 2.7000000000000001e-21 < c < 1.02e242

   1. Initial program 77.0%

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

   3. Taylor expanded in x around 0 83.4%

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

   4. Taylor expanded in a around inf 57.1%

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

      1. *-commutative 57.1%

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

   6. Simplified 57.1%

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

   if -5.4999999999999999e152 < c < 2.7000000000000001e-21

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 78.9%

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

   if 1.02e242 < c

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 17.9%

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

      1. mul-1-neg 17.9%

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

      2. *-commutative 17.9%

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

      3. associate-*l* 17.7%

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

      4. *-commutative 17.7%

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

      5. distribute-rgt-neg-in 17.7%

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

      6. *-commutative 17.7%

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

      7. distribute-rgt-neg-in 17.7%

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

   5. Simplified 17.7%

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

      1. pow1 17.7%

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

      2. *-commutative 17.7%

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

      3. add-sqr-sqrt 8.5%

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

      4. sqrt-unprod 33.8%

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

      5. sqr-neg 33.8%

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

      6. sqrt-unprod 9.6%

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

      7. add-sqr-sqrt 34.7%

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

   7. Applied egg-rr 34.7%

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

      1. unpow1 34.7%

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

      2. associate-*r* 50.2%

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

   9. Simplified 50.2%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+242}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{-40} \lor \neg \left(c \leq 4.5 \cdot 10^{-27}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.45e-40) (not (<= c 4.5e-27)))
   (* 2.0 (- (* z t) (* c (* i (+ a (* c b))))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* c a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.45e-40) || !(c <= 4.5e-27)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	}
	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 <= (-1.45d-40)) .or. (.not. (c <= 4.5d-27))) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (c * b)))))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (c * a)))
    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 <= -1.45e-40) || !(c <= 4.5e-27)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.45e-40) or not (c <= 4.5e-27):
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.45e-40) || !(c <= 4.5e-27))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * a))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.45e-40) || ~((c <= 4.5e-27)))
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.45e-40], N[Not[LessEqual[c, 4.5e-27]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.4499999999999999e-40 or 4.5000000000000002e-27 < c

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 81.0%

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

   if -1.4499999999999999e-40 < c < 4.5000000000000002e-27

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 94.5%

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

      1. *-commutative 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{-40} \lor \neg \left(c \leq 4.5 \cdot 10^{-27}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{-30} \lor \neg \left(c \leq 2.36 \cdot 10^{-29}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 -1.05e-30) (not (<= c 2.36e-29)))
   (* 2.0 (- (* z t) (* c (* i (+ a (* c b))))))
   (* 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 <= -1.05e-30) || !(c <= 2.36e-29)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} 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 <= (-1.05d-30)) .or. (.not. (c <= 2.36d-29))) then
        tmp = 2.0d0 * ((z * t) - (c * (i * (a + (c * b)))))
    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 <= -1.05e-30) || !(c <= 2.36e-29)) {
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	} 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 <= -1.05e-30) or not (c <= 2.36e-29):
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))))
	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 <= -1.05e-30) || !(c <= 2.36e-29))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * Float64(a + Float64(c * b))))));
	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 <= -1.05e-30) || ~((c <= 2.36e-29)))
		tmp = 2.0 * ((z * t) - (c * (i * (a + (c * b)))));
	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, -1.05e-30], N[Not[LessEqual[c, 2.36e-29]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision]), $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 < -1.0500000000000001e-30 or 2.35999999999999992e-29 < c

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 81.3%

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

   if -1.0500000000000001e-30 < c < 2.35999999999999992e-29

   1. Initial program 97.4%

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

   3. Taylor expanded in c around 0 85.0%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{-30} \lor \neg \left(c \leq 2.36 \cdot 10^{-29}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+152} \lor \neg \left(c \leq 2.2 \cdot 10^{-28}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

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 -4.6e+152) (not (<= c 2.2e-28)))
   (* 2.0 (* c (* i (- (- (* c b)) a))))
   (* 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 <= -4.6e+152) || !(c <= 2.2e-28)) {
		tmp = 2.0 * (c * (i * (-(c * b) - a)));
	} 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 <= (-4.6d+152)) .or. (.not. (c <= 2.2d-28))) then
        tmp = 2.0d0 * (c * (i * (-(c * b) - a)))
    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 <= -4.6e+152) || !(c <= 2.2e-28)) {
		tmp = 2.0 * (c * (i * (-(c * b) - a)));
	} 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 <= -4.6e+152) or not (c <= 2.2e-28):
		tmp = 2.0 * (c * (i * (-(c * b) - a)))
	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 <= -4.6e+152) || !(c <= 2.2e-28))
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(Float64(-Float64(c * b)) - a))));
	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 <= -4.6e+152) || ~((c <= 2.2e-28)))
		tmp = 2.0 * (c * (i * (-(c * b) - a)));
	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, -4.6e+152], N[Not[LessEqual[c, 2.2e-28]], $MachinePrecision]], N[(2.0 * N[(c * N[(i * N[((-N[(c * b), $MachinePrecision]) - a), $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 < -4.5999999999999997e152 or 2.19999999999999996e-28 < c

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf 81.7%

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

   if -4.5999999999999997e152 < c < 2.19999999999999996e-28

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 79.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+152} \lor \neg \left(c \leq 2.2 \cdot 10^{-28}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(\left(-c \cdot b\right) - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* a (* c i)) -2.0)))
   (if (<= c -3.8e+154)
     t_1
     (if (<= c 3.6e-19)
       (* 2.0 (+ (* x y) (* z t)))
       (if (<= c 5.2e+248) t_1 (* 2.0 (* i (* c a))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * (c * i)) * -2.0;
	double tmp;
	if (c <= -3.8e+154) {
		tmp = t_1;
	} else if (c <= 3.6e-19) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 5.2e+248) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (i * (c * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * (c * i)) * (-2.0d0)
    if (c <= (-3.8d+154)) then
        tmp = t_1
    else if (c <= 3.6d-19) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else if (c <= 5.2d+248) then
        tmp = t_1
    else
        tmp = 2.0d0 * (i * (c * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * (c * i)) * -2.0;
	double tmp;
	if (c <= -3.8e+154) {
		tmp = t_1;
	} else if (c <= 3.6e-19) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else if (c <= 5.2e+248) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (i * (c * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (a * (c * i)) * -2.0
	tmp = 0
	if c <= -3.8e+154:
		tmp = t_1
	elif c <= 3.6e-19:
		tmp = 2.0 * ((x * y) + (z * t))
	elif c <= 5.2e+248:
		tmp = t_1
	else:
		tmp = 2.0 * (i * (c * a))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * Float64(c * i)) * -2.0)
	tmp = 0.0
	if (c <= -3.8e+154)
		tmp = t_1;
	elseif (c <= 3.6e-19)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	elseif (c <= 5.2e+248)
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(i * Float64(c * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * (c * i)) * -2.0;
	tmp = 0.0;
	if (c <= -3.8e+154)
		tmp = t_1;
	elseif (c <= 3.6e-19)
		tmp = 2.0 * ((x * y) + (z * t));
	elseif (c <= 5.2e+248)
		tmp = t_1;
	else
		tmp = 2.0 * (i * (c * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]}, If[LessEqual[c, -3.8e+154], t$95$1, If[LessEqual[c, 3.6e-19], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e+248], t$95$1, N[(2.0 * N[(i * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.7999999999999998e154 or 3.6000000000000001e-19 < c < 5.20000000000000019e248

   1. Initial program 76.1%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. mul-1-neg 49.7%

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

      2. *-commutative 49.7%

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

      3. associate-*l* 46.3%

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

      4. *-commutative 46.3%

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

      5. distribute-rgt-neg-in 46.3%

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

      6. *-commutative 46.3%

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

      7. distribute-rgt-neg-in 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in c around 0 49.7%

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

      1. *-commutative 49.7%

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

   8. Simplified 49.7%

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

   if -3.7999999999999998e154 < c < 3.6000000000000001e-19

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 78.9%

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

   if 5.20000000000000019e248 < c

   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 10.4%

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

      1. mul-1-neg 10.4%

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

      2. *-commutative 10.4%

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

      3. associate-*l* 10.3%

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

      4. *-commutative 10.3%

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

      5. distribute-rgt-neg-in 10.3%

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

      6. *-commutative 10.3%

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

      7. distribute-rgt-neg-in 10.3%

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

   5. Simplified 10.3%

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

      1. pow1 10.3%

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

      2. *-commutative 10.3%

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

      3. add-sqr-sqrt 0.1%

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

      4. sqrt-unprod 27.8%

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

      5. sqr-neg 27.8%

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

      6. sqrt-unprod 10.4%

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

      7. add-sqr-sqrt 37.9%

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

   7. Applied egg-rr 37.9%

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

      1. unpow1 37.9%

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

      2. associate-*r* 54.8%

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

   9. Simplified 54.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+154}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+248}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+87} \lor \neg \left(y \leq 1.75 \cdot 10^{+58}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -3.9e+87) (not (<= y 1.75e+58)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.9e+87) || !(y <= 1.75e+58)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-3.9d+87)) .or. (.not. (y <= 1.75d+58))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -3.9e+87) || !(y <= 1.75e+58)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -3.9e+87) or not (y <= 1.75e+58):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -3.9e+87) || !(y <= 1.75e+58))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -3.9e+87) || ~((y <= 1.75e+58)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -3.9e+87], N[Not[LessEqual[y, 1.75e+58]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9000000000000002e87 or 1.7499999999999999e58 < y

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 55.2%

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

   if -3.9000000000000002e87 < y < 1.7499999999999999e58

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 37.5%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+87} \lor \neg \left(y \leq 1.75 \cdot 10^{+58}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.0% 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 90.8%

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

3. Taylor expanded in z around inf 31.4%

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

4. Final simplification 31.4%

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

Developer target: 94.4% 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 2024100 
(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))))