Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 80.0% → 91.8%

Time: 15.6s

Alternatives: 16

Speedup: 0.7×

• 38.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot \frac{9 \cdot y + \frac{b}{x}}{z} + t\_1}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + \left(\frac{b}{z} + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -9.6e+79)
     (/ (+ (* x (/ (+ (* 9.0 y) (/ b x)) z)) t_1) c)
     (if (<= z 3.5e-12)
       (/ (+ b (- (* x (* 9.0 y)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ t_1 (+ (/ b z) (* 9.0 (* x (/ y z))))) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -9.6e+79) {
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_1) / c;
	} else if (z <= 3.5e-12) {
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-9.6d+79)) then
        tmp = ((x * (((9.0d0 * y) + (b / x)) / z)) + t_1) / c
    else if (z <= 3.5d-12) then
        tmp = (b + ((x * (9.0d0 * y)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (t_1 + ((b / z) + (9.0d0 * (x * (y / z))))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -9.6e+79) {
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_1) / c;
	} else if (z <= 3.5e-12) {
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -9.6e+79:
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_1) / c
	elif z <= 3.5e-12:
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -9.6e+79)
		tmp = Float64(Float64(Float64(x * Float64(Float64(Float64(9.0 * y) + Float64(b / x)) / z)) + t_1) / c);
	elseif (z <= 3.5e-12)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(Float64(b / z) + Float64(9.0 * Float64(x * Float64(y / z))))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -9.6e+79)
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_1) / c;
	elseif (z <= 3.5e-12)
		tmp = (b + ((x * (9.0 * y)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+79], N[(N[(N[(x * N[(N[(N[(9.0 * y), $MachinePrecision] + N[(b / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.5e-12], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.59999999999999942e79

   1. Initial program 46.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(9 \cdot \frac{y}{z}\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{9 \cdot y}{z}\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot y\right), z\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{\frac{b}{x}}{z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(\left(\frac{b}{x}\right), z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. /-lowering-/.f64 86.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, x\right), z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 86.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(\frac{9 \cdot y}{z} + \frac{\frac{b}{x}}{z}\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(\frac{9 \cdot y + \frac{b}{x}}{z}\right)}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(9 \cdot y + \frac{b}{x}\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot y\right), \left(\frac{b}{x}\right)\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, y\right), \left(\frac{b}{x}\right)\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 86.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, y\right), \mathsf{/.f64}\left(b, x\right)\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   10. Simplified 86.6%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{9 \cdot y + \frac{b}{x}}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -9.59999999999999942e79 < z < 3.5e-12

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \left(9 \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(\left(9 \cdot y\right) \cdot x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(9 \cdot y\right), x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      4. *-lowering-*.f64 94.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(9, y\right), x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 4\right), t\right), a\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   4. Applied egg-rr 94.1%

      \[\leadsto \frac{\left(\color{blue}{\left(9 \cdot y\right) \cdot x} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if 3.5e-12 < z

   1. Initial program 68.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 92.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 92.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]
   7. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{9 \cdot \left(x \cdot y\right)}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\left(x \cdot y\right) \cdot 9}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x \cdot \left(y \cdot 9\right)}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right)}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \frac{9 \cdot y}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \frac{1}{z} + x \cdot \frac{9 \cdot y}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \frac{1}{z}\right), \left(x \cdot \frac{9 \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{b}{z}\right), \left(x \cdot \frac{9 \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(x \cdot \frac{9 \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(\frac{9 \cdot y}{z} \cdot x\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(\left(9 \cdot \frac{y}{z}\right) \cdot x\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(9 \cdot \left(\frac{y}{z} \cdot x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(9, \left(\frac{y}{z} \cdot x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\left(\frac{y}{z}\right), x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      16. /-lowering-/.f64 93.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   8. Applied egg-rr 93.7%

      \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right)} + t \cdot \left(a \cdot -4\right)}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot \frac{9 \cdot y + \frac{b}{x}}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \left(\frac{b}{z} + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x \cdot \frac{9 \cdot y + \frac{b}{x}}{z} + t\_2}{c}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{1}{\frac{c}{t\_2 + \frac{t\_1}{z}}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-247}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot t\_1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2 + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ b (* 9.0 (* x y)))) (t_2 (* t (* a -4.0))))
   (if (<= z -3.8e+57)
     (/ (+ (* x (/ (+ (* 9.0 y) (/ b x)) z)) t_2) c)
     (if (<= z -9.2e-148)
       (/ 1.0 (/ c (+ t_2 (/ t_1 z))))
       (if (<= z 6.6e-247)
         (/ (* (/ 1.0 c) t_1) z)
         (/ (+ t_2 (/ (+ b (* x (* 9.0 y))) z)) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -3.8e+57) {
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_2) / c;
	} else if (z <= -9.2e-148) {
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	} else if (z <= 6.6e-247) {
		tmp = ((1.0 / c) * t_1) / z;
	} else {
		tmp = (t_2 + ((b + (x * (9.0 * y))) / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b + (9.0d0 * (x * y))
    t_2 = t * (a * (-4.0d0))
    if (z <= (-3.8d+57)) then
        tmp = ((x * (((9.0d0 * y) + (b / x)) / z)) + t_2) / c
    else if (z <= (-9.2d-148)) then
        tmp = 1.0d0 / (c / (t_2 + (t_1 / z)))
    else if (z <= 6.6d-247) then
        tmp = ((1.0d0 / c) * t_1) / z
    else
        tmp = (t_2 + ((b + (x * (9.0d0 * y))) / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double t_2 = t * (a * -4.0);
	double tmp;
	if (z <= -3.8e+57) {
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_2) / c;
	} else if (z <= -9.2e-148) {
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	} else if (z <= 6.6e-247) {
		tmp = ((1.0 / c) * t_1) / z;
	} else {
		tmp = (t_2 + ((b + (x * (9.0 * y))) / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (x * y))
	t_2 = t * (a * -4.0)
	tmp = 0
	if z <= -3.8e+57:
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_2) / c
	elif z <= -9.2e-148:
		tmp = 1.0 / (c / (t_2 + (t_1 / z)))
	elif z <= 6.6e-247:
		tmp = ((1.0 / c) * t_1) / z
	else:
		tmp = (t_2 + ((b + (x * (9.0 * y))) / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	t_2 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -3.8e+57)
		tmp = Float64(Float64(Float64(x * Float64(Float64(Float64(9.0 * y) + Float64(b / x)) / z)) + t_2) / c);
	elseif (z <= -9.2e-148)
		tmp = Float64(1.0 / Float64(c / Float64(t_2 + Float64(t_1 / z))));
	elseif (z <= 6.6e-247)
		tmp = Float64(Float64(Float64(1.0 / c) * t_1) / z);
	else
		tmp = Float64(Float64(t_2 + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (x * y));
	t_2 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -3.8e+57)
		tmp = ((x * (((9.0 * y) + (b / x)) / z)) + t_2) / c;
	elseif (z <= -9.2e-148)
		tmp = 1.0 / (c / (t_2 + (t_1 / z)));
	elseif (z <= 6.6e-247)
		tmp = ((1.0 / c) * t_1) / z;
	else
		tmp = (t_2 + ((b + (x * (9.0 * y))) / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+57], N[(N[(N[(x * N[(N[(N[(9.0 * y), $MachinePrecision] + N[(b / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -9.2e-148], N[(1.0 / N[(c / N[(t$95$2 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-247], N[(N[(N[(1.0 / c), $MachinePrecision] * t$95$1), $MachinePrecision] / z), $MachinePrecision], N[(N[(t$95$2 + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999999e57

   1. Initial program 52.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(9 \cdot \frac{y}{z}\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{9 \cdot y}{z}\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot y\right), z\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{\frac{b}{x}}{z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(\left(\frac{b}{x}\right), z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. /-lowering-/.f64 88.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, x\right), z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 88.2%

      \[\leadsto \frac{\color{blue}{x \cdot \left(\frac{9 \cdot y}{z} + \frac{\frac{b}{x}}{z}\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(\frac{9 \cdot y + \frac{b}{x}}{z}\right)}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(9 \cdot y + \frac{b}{x}\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot y\right), \left(\frac{b}{x}\right)\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, y\right), \left(\frac{b}{x}\right)\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 88.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, y\right), \mathsf{/.f64}\left(b, x\right)\right), z\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   10. Simplified 88.2%

       \[\leadsto \frac{x \cdot \color{blue}{\frac{9 \cdot y + \frac{b}{x}}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -3.7999999999999999e57 < z < -9.1999999999999999e-148

   1. Initial program 89.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right)\right) \]

      13. *-lowering-*.f64 87.4%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 87.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{c}{\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

   if -9.1999999999999999e-148 < z < 6.59999999999999943e-247

   1. Initial program 94.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}, c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      4. *-lowering-*.f64 74.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right), c\right) \]

   7. Simplified 74.2%

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

      1. div-inv N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{z} \cdot \color{blue}{\frac{1}{c}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(y \cdot x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      9. /-lowering-/.f64 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \mathsf{/.f64}\left(1, c\right)\right), z\right) \]

   9. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{\frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{c}}{z}} \]

   if 6.59999999999999943e-247 < z

   1. Initial program 80.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
3. Recombined 4 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x \cdot \frac{9 \cdot y + \frac{b}{x}}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{1}{\frac{c}{t \cdot \left(a \cdot -4\right) + \frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-247}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c \cdot -0.25}{t \cdot a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= t -2.35e+210)
     (* t (/ (* a -4.0) c))
     (if (<= t -6.4e+186)
       t_1
       (if (<= t -1.5e+115)
         (/ a (/ c (* t -4.0)))
         (if (<= t 1.4e-17) t_1 (/ 1.0 (/ (* c -0.25) (* t a)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (t <= -2.35e+210) {
		tmp = t * ((a * -4.0) / c);
	} else if (t <= -6.4e+186) {
		tmp = t_1;
	} else if (t <= -1.5e+115) {
		tmp = a / (c / (t * -4.0));
	} else if (t <= 1.4e-17) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((c * -0.25) / (t * a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    if (t <= (-2.35d+210)) then
        tmp = t * ((a * (-4.0d0)) / c)
    else if (t <= (-6.4d+186)) then
        tmp = t_1
    else if (t <= (-1.5d+115)) then
        tmp = a / (c / (t * (-4.0d0)))
    else if (t <= 1.4d-17) then
        tmp = t_1
    else
        tmp = 1.0d0 / ((c * (-0.25d0)) / (t * a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (t <= -2.35e+210) {
		tmp = t * ((a * -4.0) / c);
	} else if (t <= -6.4e+186) {
		tmp = t_1;
	} else if (t <= -1.5e+115) {
		tmp = a / (c / (t * -4.0));
	} else if (t <= 1.4e-17) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((c * -0.25) / (t * a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if t <= -2.35e+210:
		tmp = t * ((a * -4.0) / c)
	elif t <= -6.4e+186:
		tmp = t_1
	elif t <= -1.5e+115:
		tmp = a / (c / (t * -4.0))
	elif t <= 1.4e-17:
		tmp = t_1
	else:
		tmp = 1.0 / ((c * -0.25) / (t * a))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (t <= -2.35e+210)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	elseif (t <= -6.4e+186)
		tmp = t_1;
	elseif (t <= -1.5e+115)
		tmp = Float64(a / Float64(c / Float64(t * -4.0)));
	elseif (t <= 1.4e-17)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(c * -0.25) / Float64(t * a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (t <= -2.35e+210)
		tmp = t * ((a * -4.0) / c);
	elseif (t <= -6.4e+186)
		tmp = t_1;
	elseif (t <= -1.5e+115)
		tmp = a / (c / (t * -4.0));
	elseif (t <= 1.4e-17)
		tmp = t_1;
	else
		tmp = 1.0 / ((c * -0.25) / (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e+210], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.4e+186], t$95$1, If[LessEqual[t, -1.5e+115], N[(a / N[(c / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-17], t$95$1, N[(1.0 / N[(N[(c * -0.25), $MachinePrecision] / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.35e210

   1. Initial program 68.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 78.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 78.0%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, c\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot -4\right), c\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot -4\right)\right), c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), c\right) \]

      6. *-lowering-*.f64 62.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), c\right) \]

   9. Simplified 62.4%

      \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]
   10. Step-by-step derivation

       1. associate-/l* N/A

          \[\leadsto t \cdot \color{blue}{\frac{-4 \cdot a}{c}} \]

       2. *-commutative N/A

          \[\leadsto \frac{-4 \cdot a}{c} \cdot \color{blue}{t} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{-4 \cdot a}{c}\right), \color{blue}{t}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-4 \cdot a\right), c\right), t\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(a \cdot -4\right), c\right), t\right) \]

       6. *-lowering-*.f64 70.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, -4\right), c\right), t\right) \]

   11. Applied egg-rr 70.5%

       \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]

   if -2.35e210 < t < -6.3999999999999999e186 or -1.5e115 < t < 1.3999999999999999e-17

   1. Initial program 84.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 67.8%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if -6.3999999999999999e186 < t < -1.5e115

   1. Initial program 54.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, c\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot -4\right), c\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot -4\right)\right), c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), c\right) \]

      6. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), c\right) \]

   9. Simplified 71.2%

      \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

       2. *-commutative N/A

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right)}{c} \]

       3. associate-/l* N/A

          \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

       4. clear-num N/A

          \[\leadsto a \cdot \frac{1}{\color{blue}{\frac{c}{t \cdot -4}}} \]

       5. un-div-inv N/A

          \[\leadsto \frac{a}{\color{blue}{\frac{c}{t \cdot -4}}} \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{c}{t \cdot -4}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \color{blue}{\left(t \cdot -4\right)}\right)\right) \]

       8. *-lowering-*.f64 79.7%

          \[\leadsto \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(c, \mathsf{*.f64}\left(t, \color{blue}{-4}\right)\right)\right) \]

   11. Applied egg-rr 79.7%

       \[\leadsto \color{blue}{\frac{a}{\frac{c}{t \cdot -4}}} \]

   if 1.3999999999999999e-17 < t

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right)\right) \]

      13. *-lowering-*.f64 87.1%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 87.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{c}{\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{-1}{4} \cdot \frac{c}{a \cdot t}\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\frac{-1}{4} \cdot c}{\color{blue}{a \cdot t}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{-1}{4} \cdot c\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{4}, c\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 65.5%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{4}, c\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   9. Simplified 65.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{-0.25 \cdot c}{a \cdot t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{+186}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{a}{\frac{c}{t \cdot -4}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c \cdot -0.25}{t \cdot a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{t\_1 + x \cdot \left(9 \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))) (t_2 (/ (+ t_1 (/ b z)) c)))
   (if (<= b -5.4e+45)
     t_2
     (if (<= b 7.1e-99)
       (/ (+ t_1 (* x (* 9.0 (/ y z)))) c)
       (if (<= b 2.5e-35) t_2 (/ (* (/ 1.0 c) (+ b (* 9.0 (* x y)))) z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double t_2 = (t_1 + (b / z)) / c;
	double tmp;
	if (b <= -5.4e+45) {
		tmp = t_2;
	} else if (b <= 7.1e-99) {
		tmp = (t_1 + (x * (9.0 * (y / z)))) / c;
	} else if (b <= 2.5e-35) {
		tmp = t_2;
	} else {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    t_2 = (t_1 + (b / z)) / c
    if (b <= (-5.4d+45)) then
        tmp = t_2
    else if (b <= 7.1d-99) then
        tmp = (t_1 + (x * (9.0d0 * (y / z)))) / c
    else if (b <= 2.5d-35) then
        tmp = t_2
    else
        tmp = ((1.0d0 / c) * (b + (9.0d0 * (x * y)))) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double t_2 = (t_1 + (b / z)) / c;
	double tmp;
	if (b <= -5.4e+45) {
		tmp = t_2;
	} else if (b <= 7.1e-99) {
		tmp = (t_1 + (x * (9.0 * (y / z)))) / c;
	} else if (b <= 2.5e-35) {
		tmp = t_2;
	} else {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	t_2 = (t_1 + (b / z)) / c
	tmp = 0
	if b <= -5.4e+45:
		tmp = t_2
	elif b <= 7.1e-99:
		tmp = (t_1 + (x * (9.0 * (y / z)))) / c
	elif b <= 2.5e-35:
		tmp = t_2
	else:
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(Float64(t_1 + Float64(b / z)) / c)
	tmp = 0.0
	if (b <= -5.4e+45)
		tmp = t_2;
	elseif (b <= 7.1e-99)
		tmp = Float64(Float64(t_1 + Float64(x * Float64(9.0 * Float64(y / z)))) / c);
	elseif (b <= 2.5e-35)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(1.0 / c) * Float64(b + Float64(9.0 * Float64(x * y)))) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	t_2 = (t_1 + (b / z)) / c;
	tmp = 0.0;
	if (b <= -5.4e+45)
		tmp = t_2;
	elseif (b <= 7.1e-99)
		tmp = (t_1 + (x * (9.0 * (y / z)))) / c;
	elseif (b <= 2.5e-35)
		tmp = t_2;
	else
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[b, -5.4e+45], t$95$2, If[LessEqual[b, 7.1e-99], N[(N[(t$95$1 + N[(x * N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 2.5e-35], t$95$2, N[(N[(N[(1.0 / c), $MachinePrecision] * N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.39999999999999968e45 or 7.09999999999999994e-99 < b < 2.49999999999999982e-35

   1. Initial program 90.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 79.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 79.0%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -5.39999999999999968e45 < b < 7.09999999999999994e-99

   1. Initial program 70.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(9 \cdot \frac{y}{z}\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{9 \cdot y}{z}\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(9 \cdot y\right), z\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{b}{x \cdot z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \left(\frac{\frac{b}{x}}{z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(\left(\frac{b}{x}\right), z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. /-lowering-/.f64 89.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(9, y\right), z\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, x\right), z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 89.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(\frac{9 \cdot y}{z} + \frac{\frac{b}{x}}{z}\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{\left(9 \cdot \frac{y}{z}\right)}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(9, \left(\frac{y}{z}\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(9, \mathsf{/.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   10. Simplified 85.4%

       \[\leadsto \frac{x \cdot \color{blue}{\left(9 \cdot \frac{y}{z}\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   if 2.49999999999999982e-35 < b

   1. Initial program 83.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}, c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      4. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right), c\right) \]

   7. Simplified 71.2%

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

      1. div-inv N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{z} \cdot \color{blue}{\frac{1}{c}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(y \cdot x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      9. /-lowering-/.f64 80.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \mathsf{/.f64}\left(1, c\right)\right), z\right) \]

   9. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + x \cdot \left(9 \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-140}:\\ \;\;\;\;\frac{t\_1 + \left(\frac{b}{z} + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -1.25e-140)
     (/ (+ t_1 (+ (/ b z) (* 9.0 (* x (/ y z))))) c)
     (if (<= z 9.5e-249)
       (/ (* (/ 1.0 c) (+ b (* 9.0 (* x y)))) z)
       (/ (+ t_1 (/ (+ b (* x (* 9.0 y))) z)) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -1.25e-140) {
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c;
	} else if (z <= 9.5e-249) {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	} else {
		tmp = (t_1 + ((b + (x * (9.0 * y))) / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (z <= (-1.25d-140)) then
        tmp = (t_1 + ((b / z) + (9.0d0 * (x * (y / z))))) / c
    else if (z <= 9.5d-249) then
        tmp = ((1.0d0 / c) * (b + (9.0d0 * (x * y)))) / z
    else
        tmp = (t_1 + ((b + (x * (9.0d0 * y))) / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -1.25e-140) {
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c;
	} else if (z <= 9.5e-249) {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	} else {
		tmp = (t_1 + ((b + (x * (9.0 * y))) / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if z <= -1.25e-140:
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c
	elif z <= 9.5e-249:
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z
	else:
		tmp = (t_1 + ((b + (x * (9.0 * y))) / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -1.25e-140)
		tmp = Float64(Float64(t_1 + Float64(Float64(b / z) + Float64(9.0 * Float64(x * Float64(y / z))))) / c);
	elseif (z <= 9.5e-249)
		tmp = Float64(Float64(Float64(1.0 / c) * Float64(b + Float64(9.0 * Float64(x * y)))) / z);
	else
		tmp = Float64(Float64(t_1 + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (z <= -1.25e-140)
		tmp = (t_1 + ((b / z) + (9.0 * (x * (y / z))))) / c;
	elseif (z <= 9.5e-249)
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	else
		tmp = (t_1 + ((b + (x * (9.0 * y))) / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e-140], N[(N[(t$95$1 + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 9.5e-249], N[(N[(N[(1.0 / c), $MachinePrecision] * N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(t$95$1 + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25000000000000004e-140

   1. Initial program 68.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 85.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 85.5%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]
   7. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{9 \cdot \left(x \cdot y\right)}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{\left(x \cdot y\right) \cdot 9}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x \cdot \left(y \cdot 9\right)}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right)}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(x \cdot \frac{9 \cdot y}{z} + b \cdot \frac{1}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \frac{1}{z} + x \cdot \frac{9 \cdot y}{z}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(b \cdot \frac{1}{z}\right), \left(x \cdot \frac{9 \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{b}{z}\right), \left(x \cdot \frac{9 \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(x \cdot \frac{9 \cdot y}{z}\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(\frac{9 \cdot y}{z} \cdot x\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(\left(9 \cdot \frac{y}{z}\right) \cdot x\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \left(9 \cdot \left(\frac{y}{z} \cdot x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(9, \left(\frac{y}{z} \cdot x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\left(\frac{y}{z}\right), x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      16. /-lowering-/.f64 92.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), x\right)\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   8. Applied egg-rr 92.0%

      \[\leadsto \frac{\color{blue}{\left(\frac{b}{z} + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -1.25000000000000004e-140 < z < 9.4999999999999997e-249

   1. Initial program 94.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}, c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      4. *-lowering-*.f64 74.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right), c\right) \]

   7. Simplified 74.2%

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

      1. div-inv N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{z} \cdot \color{blue}{\frac{1}{c}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(y \cdot x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      9. /-lowering-/.f64 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \mathsf{/.f64}\left(1, c\right)\right), z\right) \]

   9. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{\frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{c}}{z}} \]

   if 9.4999999999999997e-249 < z

   1. Initial program 80.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \left(\frac{b}{z} + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-248}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ (+ b (* x (* 9.0 y))) z)) c)))
   (if (<= z -5.8e-145)
     t_1
     (if (<= z 2.1e-248) (/ (* (/ 1.0 c) (+ b (* 9.0 (* x y)))) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	double tmp;
	if (z <= -5.8e-145) {
		tmp = t_1;
	} else if (z <= 2.1e-248) {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + ((b + (x * (9.0d0 * y))) / z)) / c
    if (z <= (-5.8d-145)) then
        tmp = t_1
    else if (z <= 2.1d-248) then
        tmp = ((1.0d0 / c) * (b + (9.0d0 * (x * y)))) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	double tmp;
	if (z <= -5.8e-145) {
		tmp = t_1;
	} else if (z <= 2.1e-248) {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c
	tmp = 0
	if z <= -5.8e-145:
		tmp = t_1
	elif z <= 2.1e-248:
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c)
	tmp = 0.0
	if (z <= -5.8e-145)
		tmp = t_1;
	elseif (z <= 2.1e-248)
		tmp = Float64(Float64(Float64(1.0 / c) * Float64(b + Float64(9.0 * Float64(x * y)))) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	tmp = 0.0;
	if (z <= -5.8e-145)
		tmp = t_1;
	elseif (z <= 2.1e-248)
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -5.8e-145], t$95$1, If[LessEqual[z, 2.1e-248], N[(N[(N[(1.0 / c), $MachinePrecision] * N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999968e-145 or 2.1e-248 < z

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   if -5.79999999999999968e-145 < z < 2.1e-248

   1. Initial program 94.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}, c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      4. *-lowering-*.f64 74.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right), c\right) \]

   7. Simplified 74.2%

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

      1. div-inv N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{z} \cdot \color{blue}{\frac{1}{c}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(y \cdot x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      9. /-lowering-/.f64 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \mathsf{/.f64}\left(1, c\right)\right), z\right) \]

   9. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{\frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-145}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-248}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.85e-140)
     t_1
     (if (<= z 4.2e+14) (/ (* (/ 1.0 c) (+ b (* 9.0 (* x y)))) z) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.85e-140) {
		tmp = t_1;
	} else if (z <= 4.2e+14) {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.85d-140)) then
        tmp = t_1
    else if (z <= 4.2d+14) then
        tmp = ((1.0d0 / c) * (b + (9.0d0 * (x * y)))) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.85e-140) {
		tmp = t_1;
	} else if (z <= 4.2e+14) {
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.85e-140:
		tmp = t_1
	elif z <= 4.2e+14:
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.85e-140)
		tmp = t_1;
	elseif (z <= 4.2e+14)
		tmp = Float64(Float64(Float64(1.0 / c) * Float64(b + Float64(9.0 * Float64(x * y)))) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.85e-140)
		tmp = t_1;
	elseif (z <= 4.2e+14)
		tmp = ((1.0 / c) * (b + (9.0 * (x * y)))) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.85e-140], t$95$1, If[LessEqual[z, 4.2e+14], N[(N[(N[(1.0 / c), $MachinePrecision] * N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999989e-140 or 4.2e14 < z

   1. Initial program 66.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 77.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 77.8%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -1.84999999999999989e-140 < z < 4.2e14

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{b + 9 \cdot \left(x \cdot y\right)}{z}\right)}, c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), z\right), c\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), z\right), c\right) \]

      4. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right)\right), z\right), c\right) \]

   7. Simplified 70.6%

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

      1. div-inv N/A

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{z} \cdot \color{blue}{\frac{1}{c}} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(b + 9 \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{c}\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(b + 9 \cdot \left(x \cdot y\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \left(9 \cdot \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(x \cdot y\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \left(y \cdot x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \left(\frac{1}{c}\right)\right), z\right) \]

      9. /-lowering-/.f64 82.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(9, \mathsf{*.f64}\left(y, x\right)\right)\right), \mathsf{/.f64}\left(1, c\right)\right), z\right) \]

   9. Applied egg-rr 82.1%

      \[\leadsto \color{blue}{\frac{\left(b + 9 \cdot \left(y \cdot x\right)\right) \cdot \frac{1}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{1}{c} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+14}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.7e-142)
     t_1
     (if (<= z 1.55e+14) (/ (+ b (* 9.0 (* x y))) (* z c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.7e-142) {
		tmp = t_1;
	} else if (z <= 1.55e+14) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.7d-142)) then
        tmp = t_1
    else if (z <= 1.55d+14) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.7e-142) {
		tmp = t_1;
	} else if (z <= 1.55e+14) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.7e-142:
		tmp = t_1
	elif z <= 1.55e+14:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.7e-142)
		tmp = t_1;
	elseif (z <= 1.55e+14)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.7e-142)
		tmp = t_1;
	elseif (z <= 1.55e+14)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.7e-142], t$95$1, If[LessEqual[z, 1.55e+14], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000014e-142 or 1.55e14 < z

   1. Initial program 66.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{b}{z}\right)}, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 77.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(b, z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   7. Simplified 77.8%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -1.70000000000000014e-142 < z < 1.55e14

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(9 \cdot \left(x \cdot y\right)\right)}, b\right), \mathsf{*.f64}\left(z, c\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

      2. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), \mathsf{*.f64}\left(z, c\right)\right) \]

   5. Simplified 80.7%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+14}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{1}{\frac{c \cdot -0.25}{t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.06e+85)
   (/ 1.0 (/ z (/ b c)))
   (if (<= b 2.5e-35) (/ 1.0 (/ (* c -0.25) (* t a))) (/ (/ 1.0 z) (/ c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.06e+85) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.5e-35) {
		tmp = 1.0 / ((c * -0.25) / (t * a));
	} else {
		tmp = (1.0 / z) / (c / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (b <= (-1.06d+85)) then
        tmp = 1.0d0 / (z / (b / c))
    else if (b <= 2.5d-35) then
        tmp = 1.0d0 / ((c * (-0.25d0)) / (t * a))
    else
        tmp = (1.0d0 / z) / (c / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.06e+85) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.5e-35) {
		tmp = 1.0 / ((c * -0.25) / (t * a));
	} else {
		tmp = (1.0 / z) / (c / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.06e+85:
		tmp = 1.0 / (z / (b / c))
	elif b <= 2.5e-35:
		tmp = 1.0 / ((c * -0.25) / (t * a))
	else:
		tmp = (1.0 / z) / (c / b)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.06e+85)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	elseif (b <= 2.5e-35)
		tmp = Float64(1.0 / Float64(Float64(c * -0.25) / Float64(t * a)));
	else
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.06e+85)
		tmp = 1.0 / (z / (b / c));
	elseif (b <= 2.5e-35)
		tmp = 1.0 / ((c * -0.25) / (t * a));
	else
		tmp = (1.0 / z) / (c / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.06e+85], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e-35], N[(1.0 / N[(N[(c * -0.25), $MachinePrecision] / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0600000000000001e85

   1. Initial program 89.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z \cdot c}{b}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z \cdot c}{b}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(z \cdot c\right), \color{blue}{b}\right)\right) \]

      4. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, c\right), b\right)\right) \]

   7. Applied egg-rr 54.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{b}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{b}{z \cdot c}}}\right)\right) \]

      2. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\frac{b}{c}}{\color{blue}{z}}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{z}{\color{blue}{\frac{b}{c}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{b}{c}\right)}\right)\right) \]

      5. /-lowering-/.f64 56.3%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(b, \color{blue}{c}\right)\right)\right) \]

   9. Applied egg-rr 56.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{b}{c}}}} \]

   if -1.0600000000000001e85 < b < 2.49999999999999982e-35

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{c}{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \color{blue}{\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\left(\frac{x \cdot \left(9 \cdot y\right) + b}{z}\right), \color{blue}{\left(t \cdot \left(a \cdot -4\right)\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \left(9 \cdot y\right) + b\right), z\right), \left(\color{blue}{t} \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\left(x \cdot 9\right) \cdot y + b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \left(t \cdot \left(a \cdot -4\right)\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \color{blue}{\left(a \cdot -4\right)}\right)\right)\right)\right) \]

      13. *-lowering-*.f64 86.0%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(c, \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right), z\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, \color{blue}{-4}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{c}{\frac{9 \cdot \left(x \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{-1}{4} \cdot \frac{c}{a \cdot t}\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{\frac{-1}{4} \cdot c}{\color{blue}{a \cdot t}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{-1}{4} \cdot c\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{4}, c\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 59.0%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{4}, c\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   9. Simplified 59.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{-0.25 \cdot c}{a \cdot t}}} \]

   if 2.49999999999999982e-35 < b

   1. Initial program 83.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 60.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 66.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{\frac{1}{\frac{c}{b}}}{z} \]

      2. associate-/l/ N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{b}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{z}}{\color{blue}{\frac{c}{b}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{z}\right), \color{blue}{\left(\frac{c}{b}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\frac{\color{blue}{c}}{b}\right)\right) \]

      6. /-lowering-/.f64 66.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{/.f64}\left(c, \color{blue}{b}\right)\right) \]

   9. Applied egg-rr 66.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{b}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{1}{\frac{c \cdot -0.25}{t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4e+84)
   (/ 1.0 (/ z (/ b c)))
   (if (<= b 2.5e-35) (* (* t a) (/ -4.0 c)) (/ (/ 1.0 z) (/ c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e+84) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = (1.0 / z) / (c / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (b <= (-4d+84)) then
        tmp = 1.0d0 / (z / (b / c))
    else if (b <= 2.5d-35) then
        tmp = (t * a) * ((-4.0d0) / c)
    else
        tmp = (1.0d0 / z) / (c / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4e+84) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = (1.0 / z) / (c / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4e+84:
		tmp = 1.0 / (z / (b / c))
	elif b <= 2.5e-35:
		tmp = (t * a) * (-4.0 / c)
	else:
		tmp = (1.0 / z) / (c / b)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4e+84)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	elseif (b <= 2.5e-35)
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	else
		tmp = Float64(Float64(1.0 / z) / Float64(c / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4e+84)
		tmp = 1.0 / (z / (b / c));
	elseif (b <= 2.5e-35)
		tmp = (t * a) * (-4.0 / c);
	else
		tmp = (1.0 / z) / (c / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4e+84], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e-35], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.00000000000000023e84

   1. Initial program 89.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z \cdot c}{b}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z \cdot c}{b}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(z \cdot c\right), \color{blue}{b}\right)\right) \]

      4. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, c\right), b\right)\right) \]

   7. Applied egg-rr 54.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{b}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{b}{z \cdot c}}}\right)\right) \]

      2. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\frac{b}{c}}{\color{blue}{z}}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{z}{\color{blue}{\frac{b}{c}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{b}{c}\right)}\right)\right) \]

      5. /-lowering-/.f64 56.3%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(b, \color{blue}{c}\right)\right)\right) \]

   9. Applied egg-rr 56.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{b}{c}}}} \]

   if -4.00000000000000023e84 < b < 2.49999999999999982e-35

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 86.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 86.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, c\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot -4\right), c\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot -4\right)\right), c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), c\right) \]

      6. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), c\right) \]

   9. Simplified 58.3%

      \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

       2. *-commutative N/A

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right)}{c} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(a \cdot t\right) \cdot -4}{c} \]

       4. associate-/l* N/A

          \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot t\right), \color{blue}{\left(\frac{-4}{c}\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\frac{\color{blue}{-4}}{c}\right)\right) \]

       7. /-lowering-/.f64 58.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right) \]

   11. Applied egg-rr 58.9%

       \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} \]

   if 2.49999999999999982e-35 < b

   1. Initial program 83.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 60.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 66.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{\frac{1}{\frac{c}{b}}}{z} \]

      2. associate-/l/ N/A

         \[\leadsto \frac{1}{\color{blue}{z \cdot \frac{c}{b}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{1}{z}}{\color{blue}{\frac{c}{b}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{z}\right), \color{blue}{\left(\frac{c}{b}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\frac{\color{blue}{c}}{b}\right)\right) \]

      6. /-lowering-/.f64 66.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{/.f64}\left(c, \color{blue}{b}\right)\right) \]

   9. Applied egg-rr 66.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{b}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+84}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+83}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -6.6e+83)
   (/ 1.0 (/ z (/ b c)))
   (if (<= b 2.5e-35) (* (* t a) (/ -4.0 c)) (* (/ b c) (/ 1.0 z)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -6.6e+83) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = (b / c) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (b <= (-6.6d+83)) then
        tmp = 1.0d0 / (z / (b / c))
    else if (b <= 2.5d-35) then
        tmp = (t * a) * ((-4.0d0) / c)
    else
        tmp = (b / c) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -6.6e+83) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = (b / c) * (1.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -6.6e+83:
		tmp = 1.0 / (z / (b / c))
	elif b <= 2.5e-35:
		tmp = (t * a) * (-4.0 / c)
	else:
		tmp = (b / c) * (1.0 / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -6.6e+83)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	elseif (b <= 2.5e-35)
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	else
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -6.6e+83)
		tmp = 1.0 / (z / (b / c));
	elseif (b <= 2.5e-35)
		tmp = (t * a) * (-4.0 / c);
	else
		tmp = (b / c) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -6.6e+83], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e-35], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.59999999999999969e83

   1. Initial program 89.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{z \cdot c}{b}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z \cdot c}{b}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(z \cdot c\right), \color{blue}{b}\right)\right) \]

      4. *-lowering-*.f64 54.1%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, c\right), b\right)\right) \]

   7. Applied egg-rr 54.1%

      \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{b}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{b}{z \cdot c}}}\right)\right) \]

      2. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\frac{b}{c}}{\color{blue}{z}}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{z}{\color{blue}{\frac{b}{c}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{b}{c}\right)}\right)\right) \]

      5. /-lowering-/.f64 56.3%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(b, \color{blue}{c}\right)\right)\right) \]

   9. Applied egg-rr 56.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{b}{c}}}} \]

   if -6.59999999999999969e83 < b < 2.49999999999999982e-35

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 86.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 86.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, c\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot -4\right), c\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot -4\right)\right), c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), c\right) \]

      6. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), c\right) \]

   9. Simplified 58.3%

      \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

       2. *-commutative N/A

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right)}{c} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(a \cdot t\right) \cdot -4}{c} \]

       4. associate-/l* N/A

          \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot t\right), \color{blue}{\left(\frac{-4}{c}\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\frac{\color{blue}{-4}}{c}\right)\right) \]

       7. /-lowering-/.f64 58.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right) \]

   11. Applied egg-rr 58.9%

       \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} \]

   if 2.49999999999999982e-35 < b

   1. Initial program 83.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 60.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{c \cdot \color{blue}{z}} \]

      4. times-frac N/A

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \left(\frac{\color{blue}{1}}{z}\right)\right) \]

      7. /-lowering-/.f64 66.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+83}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{if}\;b \leq -7 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ b c) (/ 1.0 z))))
   (if (<= b -7e+82) t_1 (if (<= b 2.5e-35) (* (* t a) (/ -4.0 c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) * (1.0 / z);
	double tmp;
	if (b <= -7e+82) {
		tmp = t_1;
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (b / c) * (1.0d0 / z)
    if (b <= (-7d+82)) then
        tmp = t_1
    else if (b <= 2.5d-35) then
        tmp = (t * a) * ((-4.0d0) / c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) * (1.0 / z);
	double tmp;
	if (b <= -7e+82) {
		tmp = t_1;
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) * (1.0 / z)
	tmp = 0
	if b <= -7e+82:
		tmp = t_1
	elif b <= 2.5e-35:
		tmp = (t * a) * (-4.0 / c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) * Float64(1.0 / z))
	tmp = 0.0
	if (b <= -7e+82)
		tmp = t_1;
	elseif (b <= 2.5e-35)
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) * (1.0 / z);
	tmp = 0.0;
	if (b <= -7e+82)
		tmp = t_1;
	elseif (b <= 2.5e-35)
		tmp = (t * a) * (-4.0 / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+82], t$95$1, If[LessEqual[b, 2.5e-35], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.0000000000000001e82 or 2.49999999999999982e-35 < b

   1. Initial program 85.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{b \cdot 1}{\color{blue}{z \cdot c}} \]

      3. *-commutative N/A

         \[\leadsto \frac{b \cdot 1}{c \cdot \color{blue}{z}} \]

      4. times-frac N/A

         \[\leadsto \frac{b}{c} \cdot \color{blue}{\frac{1}{z}} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{c}\right), \color{blue}{\left(\frac{1}{z}\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \left(\frac{\color{blue}{1}}{z}\right)\right) \]

      7. /-lowering-/.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, c\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 62.9%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   if -7.0000000000000001e82 < b < 2.49999999999999982e-35

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 86.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 86.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, c\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot -4\right), c\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot -4\right)\right), c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), c\right) \]

      6. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), c\right) \]

   9. Simplified 58.3%

      \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

       2. *-commutative N/A

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right)}{c} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(a \cdot t\right) \cdot -4}{c} \]

       4. associate-/l* N/A

          \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot t\right), \color{blue}{\left(\frac{-4}{c}\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\frac{\color{blue}{-4}}{c}\right)\right) \]

       7. /-lowering-/.f64 58.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right) \]

   11. Applied egg-rr 58.9%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+82}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -4.6e+83) t_1 (if (<= b 2.5e-35) (* (* t a) (/ -4.0 c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -4.6e+83) {
		tmp = t_1;
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-4.6d+83)) then
        tmp = t_1
    else if (b <= 2.5d-35) then
        tmp = (t * a) * ((-4.0d0) / c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -4.6e+83) {
		tmp = t_1;
	} else if (b <= 2.5e-35) {
		tmp = (t * a) * (-4.0 / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -4.6e+83:
		tmp = t_1
	elif b <= 2.5e-35:
		tmp = (t * a) * (-4.0 / c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -4.6e+83)
		tmp = t_1;
	elseif (b <= 2.5e-35)
		tmp = Float64(Float64(t * a) * Float64(-4.0 / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -4.6e+83)
		tmp = t_1;
	elseif (b <= 2.5e-35)
		tmp = (t * a) * (-4.0 / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -4.6e+83], t$95$1, If[LessEqual[b, 2.5e-35], N[(N[(t * a), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.5999999999999999e83 or 2.49999999999999982e-35 < b

   1. Initial program 85.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -4.5999999999999999e83 < b < 2.49999999999999982e-35

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 86.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 86.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, c\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(a \cdot t\right) \cdot -4\right), c\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(t \cdot a\right) \cdot -4\right), c\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(a \cdot -4\right)\right), c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-4 \cdot a\right)\right), c\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-4 \cdot a\right)\right), c\right) \]

      6. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), c\right) \]

   9. Simplified 58.3%

      \[\leadsto \frac{\color{blue}{t \cdot \left(-4 \cdot a\right)}}{c} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{\left(t \cdot -4\right) \cdot a}{c} \]

       2. *-commutative N/A

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right)}{c} \]

       3. associate-*r* N/A

          \[\leadsto \frac{\left(a \cdot t\right) \cdot -4}{c} \]

       4. associate-/l* N/A

          \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{\frac{-4}{c}} \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(a \cdot t\right), \color{blue}{\left(\frac{-4}{c}\right)}\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\frac{\color{blue}{-4}}{c}\right)\right) \]

       7. /-lowering-/.f64 58.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{/.f64}\left(-4, \color{blue}{c}\right)\right) \]

   11. Applied egg-rr 58.9%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -2.7e+84) t_1 (if (<= b 2.5e-35) (* a (* -4.0 (/ t c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.7e+84) {
		tmp = t_1;
	} else if (b <= 2.5e-35) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-2.7d+84)) then
        tmp = t_1
    else if (b <= 2.5d-35) then
        tmp = a * ((-4.0d0) * (t / c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.7e+84) {
		tmp = t_1;
	} else if (b <= 2.5e-35) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -2.7e+84:
		tmp = t_1
	elif b <= 2.5e-35:
		tmp = a * (-4.0 * (t / c))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -2.7e+84)
		tmp = t_1;
	elseif (b <= 2.5e-35)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -2.7e+84)
		tmp = t_1;
	elseif (b <= 2.5e-35)
		tmp = a * (-4.0 * (t / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.7e+84], t$95$1, If[LessEqual[b, 2.5e-35], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7e84 or 2.49999999999999982e-35 < b

   1. Initial program 85.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

      3. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

      2. associate-/r* N/A

         \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

      4. /-lowering-/.f64 62.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

   7. Applied egg-rr 62.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -2.7e84 < b < 2.49999999999999982e-35

   1. Initial program 74.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{\color{blue}{c}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}\right), \color{blue}{c}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      2. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{z} \cdot \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{z}\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(x \cdot \left(9 \cdot y\right) + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \left(\left(x \cdot 9\right) \cdot y + b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(x \cdot 9\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(\left(9 \cdot x\right) \cdot y\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\left(9 \cdot \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \left(x \cdot y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

      10. *-lowering-*.f64 86.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(9, \mathsf{*.f64}\left(x, y\right)\right), b\right)\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(a, -4\right)\right)\right), c\right) \]

   6. Applied egg-rr 86.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{z} \cdot \left(9 \cdot \left(x \cdot y\right) + b\right)} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{\frac{t}{c}}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot \color{blue}{\frac{t}{c}} \]

      3. *-commutative N/A

         \[\leadsto \left(a \cdot -4\right) \cdot \frac{\color{blue}{t}}{c} \]

      4. associate-*r* N/A

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot \frac{t}{c}\right)} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-4 \cdot \frac{t}{c}\right)}\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, \color{blue}{\left(\frac{t}{c}\right)}\right)\right) \]

      7. /-lowering-/.f64 59.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(t, \color{blue}{c}\right)\right)\right) \]

   9. Simplified 59.0%

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

Alternative 15: 34.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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
    code = (b / c) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

   3. *-lowering-*.f64 35.5%

      \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

5. Simplified 35.5%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{b}{c \cdot \color{blue}{z}} \]

   2. associate-/r* N/A

      \[\leadsto \frac{\frac{b}{c}}{\color{blue}{z}} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{b}{c}\right), \color{blue}{z}\right) \]

   4. /-lowering-/.f64 36.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(b, c\right), z\right) \]

7. Applied egg-rr 36.6%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
8. Add Preprocessing

Alternative 16: 34.9% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(b, \color{blue}{\left(c \cdot z\right)}\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(b, \left(z \cdot \color{blue}{c}\right)\right) \]

   3. *-lowering-*.f64 35.5%

      \[\leadsto \mathsf{/.f64}\left(b, \mathsf{*.f64}\left(z, \color{blue}{c}\right)\right) \]

5. Simplified 35.5%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Add Preprocessing

Developer Target 1: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))