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

Percentage Accurate: 80.3% → 88.4%

Time: 14.7s

Alternatives: 19

Speedup: 0.7×

• 38.1% 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: 80.3% 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: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+179} \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\frac{y \cdot \left(9 \cdot \frac{x}{z} + \frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{y}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.5e+179) (not (<= z 0.065)))
   (/ (* y (+ (* 9.0 (/ x z)) (/ (* t (+ (* -4.0 a) (/ b (* z t)))) y))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

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 ((z <= -2.5e+179) || !(z <= 0.065)) {
		tmp = (y * ((9.0 * (x / z)) + ((t * ((-4.0 * a) + (b / (z * t)))) / y))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

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 ((z <= (-2.5d+179)) .or. (.not. (z <= 0.065d0))) then
        tmp = (y * ((9.0d0 * (x / z)) + ((t * (((-4.0d0) * a) + (b / (z * t)))) / y))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

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 ((z <= -2.5e+179) || !(z <= 0.065)) {
		tmp = (y * ((9.0 * (x / z)) + ((t * ((-4.0 * a) + (b / (z * t)))) / y))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[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 (z <= -2.5e+179) or not (z <= 0.065):
		tmp = (y * ((9.0 * (x / z)) + ((t * ((-4.0 * a) + (b / (z * t)))) / y))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

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 ((z <= -2.5e+179) || !(z <= 0.065))
		tmp = Float64(Float64(y * Float64(Float64(9.0 * Float64(x / z)) + Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(b / Float64(z * t)))) / y))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

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 ((z <= -2.5e+179) || ~((z <= 0.065)))
		tmp = (y * ((9.0 * (x / z)) + ((t * ((-4.0 * a) + (b / (z * t)))) / y))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.5e+179], N[Not[LessEqual[z, 0.065]], $MachinePrecision]], N[(N[(y * N[(N[(9.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(b / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e179 or 0.065000000000000002 < z

   1. Initial program 46.3%

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

      1. associate-+l- 46.3%

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

      2. *-commutative 46.3%

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

      3. associate-*r* 48.4%

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

      4. *-commutative 48.4%

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

      5. associate-+l- 48.4%

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

      6. associate-*l* 48.4%

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

      7. associate-*l* 53.4%

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

      8. *-commutative 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in t around inf 66.4%

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

   6. Taylor expanded in c around 0 77.3%

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

   7. Taylor expanded in y around inf 86.6%

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

   if -2.5e179 < z < 0.065000000000000002

   1. Initial program 94.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+179} \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\frac{y \cdot \left(9 \cdot \frac{x}{z} + \frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{y}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+90}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{c}\\ \mathbf{elif}\;z \leq -530000000000:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{z \cdot c} + \frac{b}{c \cdot \left(z \cdot y\right)}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{\left(z \cdot t\right) \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-35}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2e+90)
   (/ (* t (+ (* -4.0 a) (/ b (* z t)))) c)
   (if (<= z -530000000000.0)
     (* y (+ (* 9.0 (/ x (* z c))) (/ b (* c (* z y)))))
     (if (<= z -7.8e-91)
       (* t (+ (* -4.0 (/ a c)) (/ b (* (* z t) c))))
       (if (<= z 1.95e-35)
         (/ (+ b (* 9.0 (* y x))) (* z c))
         (- (/ b (* z c)) (* 4.0 (/ (* t a) c))))))))

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 (z <= -2e+90) {
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	} else if (z <= -530000000000.0) {
		tmp = y * ((9.0 * (x / (z * c))) + (b / (c * (z * y))));
	} else if (z <= -7.8e-91) {
		tmp = t * ((-4.0 * (a / c)) + (b / ((z * t) * c)));
	} else if (z <= 1.95e-35) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	}
	return tmp;
}

Fortran

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 (z <= (-2d+90)) then
        tmp = (t * (((-4.0d0) * a) + (b / (z * t)))) / c
    else if (z <= (-530000000000.0d0)) then
        tmp = y * ((9.0d0 * (x / (z * c))) + (b / (c * (z * y))))
    else if (z <= (-7.8d-91)) then
        tmp = t * (((-4.0d0) * (a / c)) + (b / ((z * t) * c)))
    else if (z <= 1.95d-35) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (b / (z * c)) - (4.0d0 * ((t * a) / c))
    end if
    code = tmp
end function

Java

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 (z <= -2e+90) {
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	} else if (z <= -530000000000.0) {
		tmp = y * ((9.0 * (x / (z * c))) + (b / (c * (z * y))));
	} else if (z <= -7.8e-91) {
		tmp = t * ((-4.0 * (a / c)) + (b / ((z * t) * c)));
	} else if (z <= 1.95e-35) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	}
	return tmp;
}

Python

[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 z <= -2e+90:
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c
	elif z <= -530000000000.0:
		tmp = y * ((9.0 * (x / (z * c))) + (b / (c * (z * y))))
	elif z <= -7.8e-91:
		tmp = t * ((-4.0 * (a / c)) + (b / ((z * t) * c)))
	elif z <= 1.95e-35:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c))
	return tmp

Julia

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 (z <= -2e+90)
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(b / Float64(z * t)))) / c);
	elseif (z <= -530000000000.0)
		tmp = Float64(y * Float64(Float64(9.0 * Float64(x / Float64(z * c))) + Float64(b / Float64(c * Float64(z * y)))));
	elseif (z <= -7.8e-91)
		tmp = Float64(t * Float64(Float64(-4.0 * Float64(a / c)) + Float64(b / Float64(Float64(z * t) * c))));
	elseif (z <= 1.95e-35)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(t * a) / c)));
	end
	return tmp
end

MATLAB

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 (z <= -2e+90)
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	elseif (z <= -530000000000.0)
		tmp = y * ((9.0 * (x / (z * c))) + (b / (c * (z * y))));
	elseif (z <= -7.8e-91)
		tmp = t * ((-4.0 * (a / c)) + (b / ((z * t) * c)));
	elseif (z <= 1.95e-35)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = (b / (z * c)) - (4.0 * ((t * a) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2e+90], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(b / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -530000000000.0], N[(y * N[(N[(9.0 * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-91], N[(t * N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-35], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999993e90

   1. Initial program 56.5%

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

      1. associate-+l- 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-*r* 49.4%

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

      4. *-commutative 49.4%

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

      5. associate-+l- 49.4%

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

      6. associate-*l* 49.4%

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

      7. associate-*l* 58.9%

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

      8. *-commutative 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in t around inf 75.0%

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

   6. Taylor expanded in c around 0 81.5%

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

   7. Taylor expanded in x around 0 75.1%

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

   if -1.99999999999999993e90 < z < -5.3e11

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r* 91.6%

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

      4. *-commutative 91.6%

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

      5. associate-+l- 91.6%

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

      6. associate-*l* 91.7%

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

      7. associate-*l* 91.6%

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

      8. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in z around 0 83.7%

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

   6. Taylor expanded in a around 0 61.7%

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

   7. Taylor expanded in y around inf 46.3%

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

   if -5.3e11 < z < -7.79999999999999987e-91

   1. Initial program 88.1%

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

      1. associate-+l- 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*r* 89.6%

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

      4. *-commutative 89.6%

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

      5. associate-+l- 89.6%

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

      6. associate-*l* 89.7%

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

      7. associate-*l* 89.8%

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

      8. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in t around inf 81.5%

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

   6. Taylor expanded in x around 0 66.3%

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

   if -7.79999999999999987e-91 < z < 1.9499999999999999e-35

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

      6. associate-*l* 95.7%

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

      7. associate-*l* 92.4%

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

      8. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

   7. Simplified 86.2%

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

   if 1.9499999999999999e-35 < z

   1. Initial program 55.8%

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

      1. associate-+l- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

      5. associate-+l- 60.3%

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

      6. associate-*l* 60.3%

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

      7. associate-*l* 63.6%

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

      8. *-commutative 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in x around 0 77.6%

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

   6. Taylor expanded in x around 0 70.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+90}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{c}\\ \mathbf{elif}\;z \leq -530000000000:\\ \;\;\;\;y \cdot \left(9 \cdot \frac{x}{z \cdot c} + \frac{b}{c \cdot \left(z \cdot y\right)}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{\left(z \cdot t\right) \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-35}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ t_2 := 9 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-89}:\\ \;\;\;\;\frac{t\_2 - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-36}:\\ \;\;\;\;\frac{b + t\_2}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x (* (/ 9.0 c) (/ y z))) (* 4.0 (/ (* t a) c))))
        (t_2 (* 9.0 (* y x))))
   (if (<= z -1e+129)
     t_1
     (if (<= z -2.3e-89)
       (/ (- t_2 (* 4.0 (* a (* z t)))) (* z c))
       (if (<= z 1.55e-36) (/ (+ b t_2) (* z c)) t_1)))))

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 = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	double t_2 = 9.0 * (y * x);
	double tmp;
	if (z <= -1e+129) {
		tmp = t_1;
	} else if (z <= -2.3e-89) {
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 1.55e-36) {
		tmp = (b + t_2) / (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.
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 = (x * ((9.0d0 / c) * (y / z))) - (4.0d0 * ((t * a) / c))
    t_2 = 9.0d0 * (y * x)
    if (z <= (-1d+129)) then
        tmp = t_1
    else if (z <= (-2.3d-89)) then
        tmp = (t_2 - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (z <= 1.55d-36) then
        tmp = (b + t_2) / (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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	double t_2 = 9.0 * (y * x);
	double tmp;
	if (z <= -1e+129) {
		tmp = t_1;
	} else if (z <= -2.3e-89) {
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 1.55e-36) {
		tmp = (b + t_2) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[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 = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c))
	t_2 = 9.0 * (y * x)
	tmp = 0
	if z <= -1e+129:
		tmp = t_1
	elif z <= -2.3e-89:
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c)
	elif z <= 1.55e-36:
		tmp = (b + t_2) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

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(x * Float64(Float64(9.0 / c) * Float64(y / z))) - Float64(4.0 * Float64(Float64(t * a) / c)))
	t_2 = Float64(9.0 * Float64(y * x))
	tmp = 0.0
	if (z <= -1e+129)
		tmp = t_1;
	elseif (z <= -2.3e-89)
		tmp = Float64(Float64(t_2 - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (z <= 1.55e-36)
		tmp = Float64(Float64(b + t_2) / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	t_2 = 9.0 * (y * x);
	tmp = 0.0;
	if (z <= -1e+129)
		tmp = t_1;
	elseif (z <= -2.3e-89)
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c);
	elseif (z <= 1.55e-36)
		tmp = (b + t_2) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(N[(9.0 / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+129], t$95$1, If[LessEqual[z, -2.3e-89], N[(N[(t$95$2 - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-36], N[(N[(b + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e129 or 1.5499999999999999e-36 < z

   1. Initial program 52.9%

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

      1. associate-+l- 52.9%

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

      2. *-commutative 52.9%

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

      3. associate-*r* 53.7%

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

      4. *-commutative 53.7%

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

      5. associate-+l- 53.7%

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

      6. associate-*l* 53.7%

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

      7. associate-*l* 59.0%

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

      8. *-commutative 59.0%

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

   3. Simplified 59.0%

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

   5. Taylor expanded in x around 0 75.4%

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

   6. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]
   7. Step-by-step derivation

      1. associate-*r/ 63.2%

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

      2. associate-*r* 63.2%

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

      3. *-commutative 63.2%

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

      4. associate-*r/ 68.9%

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

      5. associate-*l* 68.9%

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

      6. associate-*r/ 68.9%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

      7. times-frac 77.1%

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

   8. Simplified 77.1%

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

   if -1e129 < z < -2.3e-89

   1. Initial program 91.3%

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

      1. associate-+l- 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-*r* 89.5%

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

      4. *-commutative 89.5%

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

      5. associate-+l- 89.5%

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

      6. associate-*l* 89.6%

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

      7. associate-*l* 92.1%

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

      8. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in b around 0 79.6%

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

   if -2.3e-89 < z < 1.5499999999999999e-36

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

      6. associate-*l* 95.7%

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

      7. associate-*l* 92.4%

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

      8. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

   7. Simplified 86.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-89}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+180}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-20} \lor \neg \left(z \leq -1.6 \cdot 10^{-55}\right) \land z \leq 9.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.8e+180)
   (* (* t (* -4.0 a)) (/ 1.0 c))
   (if (or (<= z -1.15e-20) (and (not (<= z -1.6e-55)) (<= z 9.8e+36)))
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (* -4.0 (/ (* t a) c)))))

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 (z <= -3.8e+180) {
		tmp = (t * (-4.0 * a)) * (1.0 / c);
	} else if ((z <= -1.15e-20) || (!(z <= -1.6e-55) && (z <= 9.8e+36))) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Fortran

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 (z <= (-3.8d+180)) then
        tmp = (t * ((-4.0d0) * a)) * (1.0d0 / c)
    else if ((z <= (-1.15d-20)) .or. (.not. (z <= (-1.6d-55))) .and. (z <= 9.8d+36)) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * ((t * a) / c)
    end if
    code = tmp
end function

Java

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 (z <= -3.8e+180) {
		tmp = (t * (-4.0 * a)) * (1.0 / c);
	} else if ((z <= -1.15e-20) || (!(z <= -1.6e-55) && (z <= 9.8e+36))) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Python

[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 z <= -3.8e+180:
		tmp = (t * (-4.0 * a)) * (1.0 / c)
	elif (z <= -1.15e-20) or (not (z <= -1.6e-55) and (z <= 9.8e+36)):
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * ((t * a) / c)
	return tmp

Julia

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 (z <= -3.8e+180)
		tmp = Float64(Float64(t * Float64(-4.0 * a)) * Float64(1.0 / c));
	elseif ((z <= -1.15e-20) || (!(z <= -1.6e-55) && (z <= 9.8e+36)))
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	end
	return tmp
end

MATLAB

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 (z <= -3.8e+180)
		tmp = (t * (-4.0 * a)) * (1.0 / c);
	elseif ((z <= -1.15e-20) || (~((z <= -1.6e-55)) && (z <= 9.8e+36)))
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * ((t * a) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.8e+180], N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.15e-20], And[N[Not[LessEqual[z, -1.6e-55]], $MachinePrecision], LessEqual[z, 9.8e+36]]], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e180

   1. Initial program 36.2%

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

      1. associate-+l- 36.2%

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

      2. *-commutative 36.2%

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

      3. associate-*r* 32.3%

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

      4. *-commutative 32.3%

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

      5. associate-+l- 32.3%

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

      6. associate-*l* 32.3%

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

      7. associate-*l* 39.9%

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

      8. *-commutative 39.9%

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

   3. Simplified 39.9%

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

   5. Taylor expanded in t around inf 68.6%

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

   6. Taylor expanded in c around 0 80.5%

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

   7. Taylor expanded in t around inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

   9. Simplified 67.8%

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

       1. div-inv 67.9%

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

       2. *-commutative 67.9%

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

   11. Applied egg-rr 67.9%

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

   if -3.8e180 < z < -1.15e-20 or -1.6000000000000001e-55 < z < 9.79999999999999962e36

   1. Initial program 93.7%

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

      1. associate-+l- 93.7%

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

      2. *-commutative 93.7%

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

      3. associate-*r* 93.1%

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

      4. *-commutative 93.1%

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

      5. associate-+l- 93.1%

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

      6. associate-*l* 93.0%

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

      7. associate-*l* 91.9%

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

      8. *-commutative 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if -1.15e-20 < z < -1.6000000000000001e-55 or 9.79999999999999962e36 < z

   1. Initial program 52.2%

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

      1. associate-+l- 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-*r* 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-+l- 57.7%

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

      6. associate-*l* 57.7%

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

      7. associate-*l* 61.4%

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

      8. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in z around inf 63.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 63.3%

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

   7. Simplified 63.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+180}:\\ \;\;\;\;\left(t \cdot \left(-4 \cdot a\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-20} \lor \neg \left(z \leq -1.6 \cdot 10^{-55}\right) \land z \leq 9.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+179} \lor \neg \left(z \leq 1.2 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.5e+179) (not (<= z 1.2e+28)))
   (- (* x (* (/ 9.0 c) (/ y z))) (* 4.0 (/ (* t a) c)))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

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 ((z <= -2.5e+179) || !(z <= 1.2e+28)) {
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

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 ((z <= (-2.5d+179)) .or. (.not. (z <= 1.2d+28))) then
        tmp = (x * ((9.0d0 / c) * (y / z))) - (4.0d0 * ((t * a) / c))
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

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 ((z <= -2.5e+179) || !(z <= 1.2e+28)) {
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[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 (z <= -2.5e+179) or not (z <= 1.2e+28):
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c))
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

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 ((z <= -2.5e+179) || !(z <= 1.2e+28))
		tmp = Float64(Float64(x * Float64(Float64(9.0 / c) * Float64(y / z))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

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 ((z <= -2.5e+179) || ~((z <= 1.2e+28)))
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.5e+179], N[Not[LessEqual[z, 1.2e+28]], $MachinePrecision]], N[(N[(x * N[(N[(9.0 / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e179 or 1.19999999999999991e28 < z

   1. Initial program 43.3%

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

      1. associate-+l- 43.3%

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

      2. *-commutative 43.3%

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

      3. associate-*r* 45.6%

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

      4. *-commutative 45.6%

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

      5. associate-+l- 45.6%

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

      6. associate-*l* 45.6%

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

      7. associate-*l* 51.0%

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

      8. *-commutative 51.0%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in x around 0 71.7%

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

   6. Taylor expanded in x around inf 63.8%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]
   7. Step-by-step derivation

      1. associate-*r/ 63.8%

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

      2. associate-*r* 63.8%

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

      3. *-commutative 63.8%

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

      4. associate-*r/ 70.9%

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

      5. associate-*l* 70.9%

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

      6. associate-*r/ 70.9%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

      7. times-frac 80.0%

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

   8. Simplified 80.0%

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

   if -2.5e179 < z < 1.19999999999999991e28

   1. Initial program 93.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+179} \lor \neg \left(z \leq 1.2 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+179} \lor \neg \left(z \leq 9 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.5e+179) (not (<= z 9e+28)))
   (- (* x (* (/ 9.0 c) (/ y z))) (* 4.0 (/ (* t a) c)))
   (/ (+ b (- (* x (* y 9.0)) (* (* z 4.0) (* t a)))) (* z c))))

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 ((z <= -2.5e+179) || !(z <= 9e+28)) {
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Fortran

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 ((z <= (-2.5d+179)) .or. (.not. (z <= 9d+28))) then
        tmp = (x * ((9.0d0 / c) * (y / z))) - (4.0d0 * ((t * a) / c))
    else
        tmp = (b + ((x * (y * 9.0d0)) - ((z * 4.0d0) * (t * a)))) / (z * c)
    end if
    code = tmp
end function

Java

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 ((z <= -2.5e+179) || !(z <= 9e+28)) {
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Python

[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 (z <= -2.5e+179) or not (z <= 9e+28):
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c))
	else:
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (t * a)))) / (z * c)
	return tmp

Julia

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 ((z <= -2.5e+179) || !(z <= 9e+28))
		tmp = Float64(Float64(x * Float64(Float64(9.0 / c) * Float64(y / z))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

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 ((z <= -2.5e+179) || ~((z <= 9e+28)))
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	else
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (t * a)))) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.5e+179], N[Not[LessEqual[z, 9e+28]], $MachinePrecision]], N[(N[(x * N[(N[(9.0 / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e179 or 8.9999999999999994e28 < z

   1. Initial program 43.3%

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

      1. associate-+l- 43.3%

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

      2. *-commutative 43.3%

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

      3. associate-*r* 45.6%

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

      4. *-commutative 45.6%

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

      5. associate-+l- 45.6%

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

      6. associate-*l* 45.6%

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

      7. associate-*l* 51.0%

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

      8. *-commutative 51.0%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in x around 0 71.7%

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

   6. Taylor expanded in x around inf 63.8%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]
   7. Step-by-step derivation

      1. associate-*r/ 63.8%

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

      2. associate-*r* 63.8%

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

      3. *-commutative 63.8%

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

      4. associate-*r/ 70.9%

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

      5. associate-*l* 70.9%

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

      6. associate-*r/ 70.9%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

      7. times-frac 80.0%

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

   8. Simplified 80.0%

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

   if -2.5e179 < z < 8.9999999999999994e28

   1. Initial program 93.7%

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

      1. associate-+l- 93.7%

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

      2. *-commutative 93.7%

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

      3. associate-*r* 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-+l- 93.3%

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

      6. associate-*l* 93.2%

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

      7. associate-*l* 92.1%

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

      8. *-commutative 92.1%

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

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+179} \lor \neg \left(z \leq 9 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{c}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+116}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{c}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-90}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c} + -4 \cdot t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* t a) c)))
   (if (<= z -1.4e+116)
     (/ (* t (+ (* -4.0 a) (/ b (* z t)))) c)
     (if (<= z -2.4e-90)
       (+ (* 9.0 (/ (* y x) (* z c))) (* -4.0 t_1))
       (if (<= z 4.4e-35)
         (/ (+ b (* 9.0 (* y x))) (* z c))
         (- (/ b (* z c)) (* 4.0 t_1)))))))

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) / c;
	double tmp;
	if (z <= -1.4e+116) {
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	} else if (z <= -2.4e-90) {
		tmp = (9.0 * ((y * x) / (z * c))) + (-4.0 * t_1);
	} else if (z <= 4.4e-35) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * t_1);
	}
	return tmp;
}

Fortran

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) / c
    if (z <= (-1.4d+116)) then
        tmp = (t * (((-4.0d0) * a) + (b / (z * t)))) / c
    else if (z <= (-2.4d-90)) then
        tmp = (9.0d0 * ((y * x) / (z * c))) + ((-4.0d0) * t_1)
    else if (z <= 4.4d-35) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (b / (z * c)) - (4.0d0 * t_1)
    end if
    code = tmp
end function

Java

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) / c;
	double tmp;
	if (z <= -1.4e+116) {
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	} else if (z <= -2.4e-90) {
		tmp = (9.0 * ((y * x) / (z * c))) + (-4.0 * t_1);
	} else if (z <= 4.4e-35) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * t_1);
	}
	return tmp;
}

Python

[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) / c
	tmp = 0
	if z <= -1.4e+116:
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c
	elif z <= -2.4e-90:
		tmp = (9.0 * ((y * x) / (z * c))) + (-4.0 * t_1)
	elif z <= 4.4e-35:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = (b / (z * c)) - (4.0 * t_1)
	return tmp

Julia

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(t * a) / c)
	tmp = 0.0
	if (z <= -1.4e+116)
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(b / Float64(z * t)))) / c);
	elseif (z <= -2.4e-90)
		tmp = Float64(Float64(9.0 * Float64(Float64(y * x) / Float64(z * c))) + Float64(-4.0 * t_1));
	elseif (z <= 4.4e-35)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * t_1));
	end
	return tmp
end

MATLAB

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) / c;
	tmp = 0.0;
	if (z <= -1.4e+116)
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	elseif (z <= -2.4e-90)
		tmp = (9.0 * ((y * x) / (z * c))) + (-4.0 * t_1);
	elseif (z <= 4.4e-35)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = (b / (z * c)) - (4.0 * 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.4e+116], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(b / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -2.4e-90], N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-35], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.40000000000000002e116

   1. Initial program 50.7%

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

      1. associate-+l- 50.7%

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

      2. *-commutative 50.7%

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

      3. associate-*r* 45.2%

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

      4. *-commutative 45.2%

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

      5. associate-+l- 45.2%

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

      6. associate-*l* 45.2%

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

      7. associate-*l* 53.4%

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

      8. *-commutative 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in t around inf 71.7%

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

   6. Taylor expanded in c around 0 79.1%

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

   7. Taylor expanded in x around 0 74.4%

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

   if -1.40000000000000002e116 < z < -2.4000000000000002e-90

   1. Initial program 90.8%

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

      1. associate-+l- 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*r* 89.0%

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

      4. *-commutative 89.0%

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

      5. associate-+l- 89.0%

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

      6. associate-*l* 89.0%

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

      7. associate-*l* 91.7%

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

      8. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in b around 0 83.6%

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

   6. Taylor expanded in x around 0 76.2%

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

   if -2.4000000000000002e-90 < z < 4.39999999999999987e-35

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

      6. associate-*l* 95.7%

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

      7. associate-*l* 92.4%

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

      8. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

   7. Simplified 86.2%

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

   if 4.39999999999999987e-35 < z

   1. Initial program 55.8%

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

      1. associate-+l- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

      5. associate-+l- 60.3%

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

      6. associate-*l* 60.3%

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

      7. associate-*l* 63.6%

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

      8. *-commutative 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in x around 0 77.6%

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

   6. Taylor expanded in x around 0 70.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+116}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{c}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-90}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-89} \lor \neg \left(z \leq 6.6 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.3e-89) (not (<= z 6.6e-37)))
   (- (* x (* (/ 9.0 c) (/ y z))) (* 4.0 (/ (* t a) c)))
   (/ (+ b (* 9.0 (* y x))) (* z c))))

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 ((z <= -2.3e-89) || !(z <= 6.6e-37)) {
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Fortran

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 ((z <= (-2.3d-89)) .or. (.not. (z <= 6.6d-37))) then
        tmp = (x * ((9.0d0 / c) * (y / z))) - (4.0d0 * ((t * a) / c))
    else
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    end if
    code = tmp
end function

Java

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 ((z <= -2.3e-89) || !(z <= 6.6e-37)) {
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Python

[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 (z <= -2.3e-89) or not (z <= 6.6e-37):
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c))
	else:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	return tmp

Julia

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 ((z <= -2.3e-89) || !(z <= 6.6e-37))
		tmp = Float64(Float64(x * Float64(Float64(9.0 / c) * Float64(y / z))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

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 ((z <= -2.3e-89) || ~((z <= 6.6e-37)))
		tmp = (x * ((9.0 / c) * (y / z))) - (4.0 * ((t * a) / c));
	else
		tmp = (b + (9.0 * (y * x))) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.3e-89], N[Not[LessEqual[z, 6.6e-37]], $MachinePrecision]], N[(N[(x * N[(N[(9.0 / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e-89 or 6.59999999999999964e-37 < z

   1. Initial program 63.7%

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

      1. associate-+l- 63.7%

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

      2. *-commutative 63.7%

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

      3. associate-*r* 63.8%

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

      4. *-commutative 63.8%

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

      5. associate-+l- 63.8%

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

      6. associate-*l* 63.8%

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

      7. associate-*l* 68.3%

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

      8. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in x around 0 77.9%

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

   6. Taylor expanded in x around inf 65.9%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]
   7. Step-by-step derivation

      1. associate-*r/ 65.9%

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

      2. associate-*r* 65.9%

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

      3. *-commutative 65.9%

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

      4. associate-*r/ 70.7%

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

      5. associate-*l* 70.7%

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

      6. associate-*r/ 70.7%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} - 4 \cdot \frac{a \cdot t}{c} \]

      7. times-frac 75.9%

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

   8. Simplified 75.9%

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

   if -2.3e-89 < z < 6.59999999999999964e-37

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

      6. associate-*l* 95.7%

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

      7. associate-*l* 92.4%

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

      8. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

   7. Simplified 86.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-89} \lor \neg \left(z \leq 6.6 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(\frac{9}{c} \cdot \frac{y}{z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-303}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.5e+101)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= x -2.6e-303)
     (* -4.0 (* t (/ a c)))
     (if (<= x 2.4e-120) (* (/ b c) (/ 1.0 z)) (* 9.0 (/ (* x (/ y c)) z))))))

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 (x <= -1.5e+101) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -2.6e-303) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.4e-120) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Fortran

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 (x <= (-1.5d+101)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-2.6d-303)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= 2.4d-120) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = 9.0d0 * ((x * (y / c)) / z)
    end if
    code = tmp
end function

Java

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 (x <= -1.5e+101) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -2.6e-303) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.4e-120) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Python

[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 x <= -1.5e+101:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -2.6e-303:
		tmp = -4.0 * (t * (a / c))
	elif x <= 2.4e-120:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = 9.0 * ((x * (y / c)) / z)
	return tmp

Julia

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 (x <= -1.5e+101)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -2.6e-303)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= 2.4e-120)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(9.0 * Float64(Float64(x * Float64(y / c)) / z));
	end
	return tmp
end

MATLAB

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 (x <= -1.5e+101)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -2.6e-303)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= 2.4e-120)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = 9.0 * ((x * (y / c)) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.5e+101], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-303], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-120], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.49999999999999997e101

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 79.4%

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

      4. *-commutative 79.4%

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

      5. associate-+l- 79.4%

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

      6. associate-*l* 79.3%

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

      7. associate-*l* 76.5%

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

      8. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in z around 0 76.9%

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

      1. associate-/l* 82.3%

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

   7. Applied egg-rr 82.3%

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

   8. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 61.5%

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

      2. associate-*r* 61.6%

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

   10. Simplified 61.6%

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

       1. associate-*l* 61.5%

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

       2. associate-*r/ 61.4%

          \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

       3. *-commutative 61.4%

          \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

       4. times-frac 77.0%

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

   12. Applied egg-rr 77.0%

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

   if -1.49999999999999997e101 < x < -2.60000000000000005e-303

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 73.0%

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

      4. *-commutative 73.0%

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

      5. associate-+l- 73.0%

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

      6. associate-*l* 73.0%

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

      7. associate-*l* 78.3%

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

      8. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 76.3%

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

   6. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 51.6%

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

      2. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -2.60000000000000005e-303 < x < 2.3999999999999999e-120

   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. Step-by-step derivation

      1. associate-+l- 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 55.8%

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

      1. associate-/r* 59.3%

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

   7. Simplified 59.3%

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

      1. div-inv 59.3%

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

   9. Applied egg-rr 59.3%

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

   if 2.3999999999999999e-120 < x

   1. Initial program 79.4%

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

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

      6. associate-*l* 80.5%

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

      7. associate-*l* 79.5%

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

      8. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 47.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 47.6%

         \[\leadsto 9 \cdot \color{blue}{\frac{\frac{x \cdot y}{c}}{z}} \]

      2. associate-/l* 48.3%

         \[\leadsto 9 \cdot \frac{\color{blue}{x \cdot \frac{y}{c}}}{z} \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot \frac{y}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-303}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-296}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.5e+101)
   (* 9.0 (* y (/ (/ x c) z)))
   (if (<= x -4.2e-296)
     (* -4.0 (* t (/ a c)))
     (if (<= x 2.1e-116) (* (/ b c) (/ 1.0 z)) (* 9.0 (/ (* x (/ y c)) z))))))

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 (x <= -1.5e+101) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (x <= -4.2e-296) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.1e-116) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Fortran

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 (x <= (-1.5d+101)) then
        tmp = 9.0d0 * (y * ((x / c) / z))
    else if (x <= (-4.2d-296)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= 2.1d-116) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = 9.0d0 * ((x * (y / c)) / z)
    end if
    code = tmp
end function

Java

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 (x <= -1.5e+101) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (x <= -4.2e-296) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.1e-116) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = 9.0 * ((x * (y / c)) / z);
	}
	return tmp;
}

Python

[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 x <= -1.5e+101:
		tmp = 9.0 * (y * ((x / c) / z))
	elif x <= -4.2e-296:
		tmp = -4.0 * (t * (a / c))
	elif x <= 2.1e-116:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = 9.0 * ((x * (y / c)) / z)
	return tmp

Julia

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 (x <= -1.5e+101)
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / c) / z)));
	elseif (x <= -4.2e-296)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= 2.1e-116)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(9.0 * Float64(Float64(x * Float64(y / c)) / z));
	end
	return tmp
end

MATLAB

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 (x <= -1.5e+101)
		tmp = 9.0 * (y * ((x / c) / z));
	elseif (x <= -4.2e-296)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= 2.1e-116)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = 9.0 * ((x * (y / c)) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.5e+101], N[(9.0 * N[(y * N[(N[(x / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-296], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-116], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.49999999999999997e101

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 79.4%

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

      4. *-commutative 79.4%

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

      5. associate-+l- 79.4%

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

      6. associate-*l* 79.3%

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

      7. associate-*l* 76.5%

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

      8. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in z around 0 76.9%

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

   6. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 61.5%

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

      2. associate-*r* 61.6%

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

      3. associate-*l/ 64.2%

         \[\leadsto \color{blue}{\frac{9 \cdot x}{c \cdot z} \cdot y} \]

      4. associate-*r/ 64.3%

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

      5. associate-*l* 64.2%

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

      6. *-commutative 64.2%

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

      7. associate-/r* 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in x around 0 64.2%

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

       1. associate-/r* 78.2%

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

   11. Simplified 78.2%

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

   if -1.49999999999999997e101 < x < -4.1999999999999999e-296

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r* 72.7%

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

      4. *-commutative 72.7%

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

      5. associate-+l- 72.7%

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

      6. associate-*l* 72.7%

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

      7. associate-*l* 78.1%

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

      8. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in z around 0 77.2%

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

   6. Taylor expanded in a around inf 52.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 52.2%

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

      2. associate-/l* 52.0%

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

   8. Simplified 52.0%

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

   if -4.1999999999999999e-296 < x < 2.0999999999999999e-116

   1. Initial program 85.9%

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

      1. associate-+l- 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r* 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-+l- 85.6%

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

      6. associate-*l* 85.6%

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

      7. associate-*l* 85.9%

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

      8. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in b around inf 56.8%

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

      1. associate-/r* 58.0%

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

   7. Simplified 58.0%

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

      1. div-inv 58.1%

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

   9. Applied egg-rr 58.1%

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

   if 2.0999999999999999e-116 < x

   1. Initial program 79.4%

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

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

      6. associate-*l* 80.5%

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

      7. associate-*l* 79.5%

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

      8. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 47.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 47.6%

         \[\leadsto 9 \cdot \color{blue}{\frac{\frac{x \cdot y}{c}}{z}} \]

      2. associate-/l* 48.3%

         \[\leadsto 9 \cdot \frac{\color{blue}{x \cdot \frac{y}{c}}}{z} \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot \frac{y}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-296}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+101}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-298}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

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 (<= x -2.75e+101)
   (* 9.0 (* y (/ (/ x c) z)))
   (if (<= x -1.35e-298)
     (* -4.0 (* t (/ a c)))
     (if (<= x 2.1e-116) (* (/ b c) (/ 1.0 z)) (* 9.0 (* x (/ (/ y c) z)))))))

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 (x <= -2.75e+101) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (x <= -1.35e-298) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.1e-116) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = 9.0 * (x * ((y / c) / z));
	}
	return tmp;
}

Fortran

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 (x <= (-2.75d+101)) then
        tmp = 9.0d0 * (y * ((x / c) / z))
    else if (x <= (-1.35d-298)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= 2.1d-116) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = 9.0d0 * (x * ((y / c) / z))
    end if
    code = tmp
end function

Java

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 (x <= -2.75e+101) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (x <= -1.35e-298) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.1e-116) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = 9.0 * (x * ((y / c) / z));
	}
	return tmp;
}

Python

[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 x <= -2.75e+101:
		tmp = 9.0 * (y * ((x / c) / z))
	elif x <= -1.35e-298:
		tmp = -4.0 * (t * (a / c))
	elif x <= 2.1e-116:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = 9.0 * (x * ((y / c) / z))
	return tmp

Julia

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 (x <= -2.75e+101)
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / c) / z)));
	elseif (x <= -1.35e-298)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= 2.1e-116)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / c) / z)));
	end
	return tmp
end

MATLAB

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 (x <= -2.75e+101)
		tmp = 9.0 * (y * ((x / c) / z));
	elseif (x <= -1.35e-298)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= 2.1e-116)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = 9.0 * (x * ((y / c) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -2.75e+101], N[(9.0 * N[(y * N[(N[(x / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-298], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-116], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.75000000000000009e101

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 79.4%

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

      4. *-commutative 79.4%

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

      5. associate-+l- 79.4%

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

      6. associate-*l* 79.3%

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

      7. associate-*l* 76.5%

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

      8. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in z around 0 76.9%

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

   6. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 61.5%

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

      2. associate-*r* 61.6%

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

      3. associate-*l/ 64.2%

         \[\leadsto \color{blue}{\frac{9 \cdot x}{c \cdot z} \cdot y} \]

      4. associate-*r/ 64.3%

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

      5. associate-*l* 64.2%

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

      6. *-commutative 64.2%

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

      7. associate-/r* 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in x around 0 64.2%

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

       1. associate-/r* 78.2%

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

   11. Simplified 78.2%

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

   if -2.75000000000000009e101 < x < -1.3500000000000001e-298

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 73.0%

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

      4. *-commutative 73.0%

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

      5. associate-+l- 73.0%

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

      6. associate-*l* 73.0%

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

      7. associate-*l* 78.3%

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

      8. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 76.3%

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

   6. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 51.6%

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

      2. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -1.3500000000000001e-298 < x < 2.0999999999999999e-116

   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. Step-by-step derivation

      1. associate-+l- 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 55.8%

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

      1. associate-/r* 59.3%

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

   7. Simplified 59.3%

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

      1. div-inv 59.3%

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

   9. Applied egg-rr 59.3%

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

   if 2.0999999999999999e-116 < x

   1. Initial program 79.4%

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

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

      6. associate-*l* 80.5%

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

      7. associate-*l* 79.5%

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

      8. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 47.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 50.9%

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

      2. associate-/r* 50.9%

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

   7. Simplified 50.9%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+101}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-298}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{-305}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-116}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* x (/ (/ y c) z)))))
   (if (<= x -1.5e+101)
     t_1
     (if (<= x -8.4e-305)
       (* -4.0 (* t (/ a c)))
       (if (<= x 1.08e-116) (* (/ b c) (/ 1.0 z)) t_1)))))

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 = 9.0 * (x * ((y / c) / z));
	double tmp;
	if (x <= -1.5e+101) {
		tmp = t_1;
	} else if (x <= -8.4e-305) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 1.08e-116) {
		tmp = (b / c) * (1.0 / 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.
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 = 9.0d0 * (x * ((y / c) / z))
    if (x <= (-1.5d+101)) then
        tmp = t_1
    else if (x <= (-8.4d-305)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= 1.08d-116) then
        tmp = (b / c) * (1.0d0 / 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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (x * ((y / c) / z));
	double tmp;
	if (x <= -1.5e+101) {
		tmp = t_1;
	} else if (x <= -8.4e-305) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 1.08e-116) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[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 = 9.0 * (x * ((y / c) / z))
	tmp = 0
	if x <= -1.5e+101:
		tmp = t_1
	elif x <= -8.4e-305:
		tmp = -4.0 * (t * (a / c))
	elif x <= 1.08e-116:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

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(9.0 * Float64(x * Float64(Float64(y / c) / z)))
	tmp = 0.0
	if (x <= -1.5e+101)
		tmp = t_1;
	elseif (x <= -8.4e-305)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= 1.08e-116)
		tmp = Float64(Float64(b / c) * Float64(1.0 / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * (x * ((y / c) / z));
	tmp = 0.0;
	if (x <= -1.5e+101)
		tmp = t_1;
	elseif (x <= -8.4e-305)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= 1.08e-116)
		tmp = (b / c) * (1.0 / 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(x * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+101], t$95$1, If[LessEqual[x, -8.4e-305], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e-116], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.49999999999999997e101 or 1.08000000000000001e-116 < x

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 80.2%

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

      4. *-commutative 80.2%

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

      5. associate-+l- 80.2%

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

      6. associate-*l* 80.2%

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

      7. associate-*l* 78.7%

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

      8. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x around inf 51.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 55.8%

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

      2. associate-/r* 56.8%

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

   7. Simplified 56.8%

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

   if -1.49999999999999997e101 < x < -8.3999999999999999e-305

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 73.0%

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

      4. *-commutative 73.0%

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

      5. associate-+l- 73.0%

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

      6. associate-*l* 73.0%

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

      7. associate-*l* 78.3%

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

      8. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 76.3%

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

   6. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 51.6%

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

      2. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -8.3999999999999999e-305 < x < 1.08000000000000001e-116

   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. Step-by-step derivation

      1. associate-+l- 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 55.8%

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

      1. associate-/r* 59.3%

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

   7. Simplified 59.3%

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

      1. div-inv 59.3%

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

   9. Applied egg-rr 59.3%

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

Alternative 13: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-297}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-117}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* x (/ y (* z c))))))
   (if (<= x -2.6e+102)
     t_1
     (if (<= x -1.7e-297)
       (* -4.0 (* t (/ a c)))
       (if (<= x 2.7e-117) (* (/ b c) (/ 1.0 z)) t_1)))))

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 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (x <= -2.6e+102) {
		tmp = t_1;
	} else if (x <= -1.7e-297) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.7e-117) {
		tmp = (b / c) * (1.0 / 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.
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 = 9.0d0 * (x * (y / (z * c)))
    if (x <= (-2.6d+102)) then
        tmp = t_1
    else if (x <= (-1.7d-297)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (x <= 2.7d-117) then
        tmp = (b / c) * (1.0d0 / 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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (x <= -2.6e+102) {
		tmp = t_1;
	} else if (x <= -1.7e-297) {
		tmp = -4.0 * (t * (a / c));
	} else if (x <= 2.7e-117) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[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 = 9.0 * (x * (y / (z * c)))
	tmp = 0
	if x <= -2.6e+102:
		tmp = t_1
	elif x <= -1.7e-297:
		tmp = -4.0 * (t * (a / c))
	elif x <= 2.7e-117:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

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(9.0 * Float64(x * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (x <= -2.6e+102)
		tmp = t_1;
	elseif (x <= -1.7e-297)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (x <= 2.7e-117)
		tmp = Float64(Float64(b / c) * Float64(1.0 / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * (x * (y / (z * c)));
	tmp = 0.0;
	if (x <= -2.6e+102)
		tmp = t_1;
	elseif (x <= -1.7e-297)
		tmp = -4.0 * (t * (a / c));
	elseif (x <= 2.7e-117)
		tmp = (b / c) * (1.0 / 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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+102], t$95$1, If[LessEqual[x, -1.7e-297], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-117], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.60000000000000006e102 or 2.70000000000000003e-117 < x

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 80.2%

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

      4. *-commutative 80.2%

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

      5. associate-+l- 80.2%

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

      6. associate-*l* 80.2%

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

      7. associate-*l* 78.7%

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

      8. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x around inf 51.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/l* 55.8%

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

      2. associate-/r* 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in y around 0 55.8%

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

   if -2.60000000000000006e102 < x < -1.69999999999999991e-297

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 73.0%

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

      4. *-commutative 73.0%

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

      5. associate-+l- 73.0%

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

      6. associate-*l* 73.0%

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

      7. associate-*l* 78.3%

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

      8. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around 0 76.3%

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

   6. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 51.6%

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

      2. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -1.69999999999999991e-297 < x < 2.70000000000000003e-117

   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. Step-by-step derivation

      1. associate-+l- 85.6%

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

      2. *-commutative 85.6%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 55.8%

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

      1. associate-/r* 59.3%

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

   7. Simplified 59.3%

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

      1. div-inv 59.3%

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

   9. Applied egg-rr 59.3%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+102}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-297}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-117}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-62} \lor \neg \left(z \leq 1.4 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.3e-62) (not (<= z 1.4e-36)))
   (- (/ b (* z c)) (* 4.0 (/ (* t a) c)))
   (/ (+ b (* 9.0 (* y x))) (* z c))))

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 ((z <= -1.3e-62) || !(z <= 1.4e-36)) {
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Fortran

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 ((z <= (-1.3d-62)) .or. (.not. (z <= 1.4d-36))) then
        tmp = (b / (z * c)) - (4.0d0 * ((t * a) / c))
    else
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    end if
    code = tmp
end function

Java

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 ((z <= -1.3e-62) || !(z <= 1.4e-36)) {
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Python

[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 (z <= -1.3e-62) or not (z <= 1.4e-36):
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c))
	else:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	return tmp

Julia

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 ((z <= -1.3e-62) || !(z <= 1.4e-36))
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

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 ((z <= -1.3e-62) || ~((z <= 1.4e-36)))
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	else
		tmp = (b + (9.0 * (y * x))) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.3e-62], N[Not[LessEqual[z, 1.4e-36]], $MachinePrecision]], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-62 or 1.4000000000000001e-36 < z

   1. Initial program 62.0%

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

      1. associate-+l- 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-*r* 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-+l- 62.1%

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

      6. associate-*l* 62.2%

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

      7. associate-*l* 66.8%

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

      8. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in x around 0 76.9%

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

   6. Taylor expanded in x around 0 67.4%

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

   if -1.3e-62 < z < 1.4000000000000001e-36

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*r* 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-+l- 96.0%

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

      6. associate-*l* 95.9%

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

      7. associate-*l* 92.8%

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

      8. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. *-commutative 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-62} \lor \neg \left(z \leq 1.4 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{c}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.2e-90)
   (/ (* t (+ (* -4.0 a) (/ b (* z t)))) c)
   (if (<= z 2.95e-36)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (- (/ b (* z c)) (* 4.0 (/ (* t a) c))))))

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 (z <= -7.2e-90) {
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	} else if (z <= 2.95e-36) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	}
	return tmp;
}

Fortran

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 (z <= (-7.2d-90)) then
        tmp = (t * (((-4.0d0) * a) + (b / (z * t)))) / c
    else if (z <= 2.95d-36) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (b / (z * c)) - (4.0d0 * ((t * a) / c))
    end if
    code = tmp
end function

Java

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 (z <= -7.2e-90) {
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	} else if (z <= 2.95e-36) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c));
	}
	return tmp;
}

Python

[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 z <= -7.2e-90:
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c
	elif z <= 2.95e-36:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = (b / (z * c)) - (4.0 * ((t * a) / c))
	return tmp

Julia

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 (z <= -7.2e-90)
		tmp = Float64(Float64(t * Float64(Float64(-4.0 * a) + Float64(b / Float64(z * t)))) / c);
	elseif (z <= 2.95e-36)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(Float64(t * a) / c)));
	end
	return tmp
end

MATLAB

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 (z <= -7.2e-90)
		tmp = (t * ((-4.0 * a) + (b / (z * t)))) / c;
	elseif (z <= 2.95e-36)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = (b / (z * c)) - (4.0 * ((t * a) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.2e-90], N[(N[(t * N[(N[(-4.0 * a), $MachinePrecision] + N[(b / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.95e-36], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999961e-90

   1. Initial program 70.5%

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

      1. associate-+l- 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-*r* 66.8%

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

      4. *-commutative 66.8%

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

      5. associate-+l- 66.8%

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

      6. associate-*l* 66.8%

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

      7. associate-*l* 72.3%

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

      8. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in t around inf 75.4%

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

   6. Taylor expanded in c around 0 80.0%

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

   7. Taylor expanded in x around 0 68.5%

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

   if -7.19999999999999961e-90 < z < 2.94999999999999998e-36

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

      6. associate-*l* 95.7%

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

      7. associate-*l* 92.4%

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

      8. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. *-commutative 86.2%

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

   7. Simplified 86.2%

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

   if 2.94999999999999998e-36 < z

   1. Initial program 55.8%

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

      1. associate-+l- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

      5. associate-+l- 60.3%

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

      6. associate-*l* 60.3%

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

      7. associate-*l* 63.6%

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

      8. *-commutative 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in x around 0 77.6%

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

   6. Taylor expanded in x around 0 70.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a + \frac{b}{z \cdot t}\right)}{c}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-16} \lor \neg \left(a \leq 3.9\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -6.2e-16) (not (<= a 3.9)))
   (* -4.0 (* t (/ a c)))
   (/ (/ b c) z)))

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 ((a <= -6.2e-16) || !(a <= 3.9)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

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 ((a <= (-6.2d-16)) .or. (.not. (a <= 3.9d0))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

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 ((a <= -6.2e-16) || !(a <= 3.9)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[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 (a <= -6.2e-16) or not (a <= 3.9):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

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 ((a <= -6.2e-16) || !(a <= 3.9))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

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 ((a <= -6.2e-16) || ~((a <= 3.9)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b / c) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -6.2e-16], N[Not[LessEqual[a, 3.9]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2000000000000002e-16 or 3.89999999999999991 < a

   1. Initial program 82.9%

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

      1. associate-+l- 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*r* 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-+l- 79.0%

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

      6. associate-*l* 79.0%

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

      7. associate-*l* 80.6%

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

      8. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in z around 0 80.4%

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

   6. Taylor expanded in a around inf 54.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 54.9%

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

      2. associate-/l* 56.3%

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

   8. Simplified 56.3%

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

   if -6.2000000000000002e-16 < a < 3.89999999999999991

   1. Initial program 74.3%

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

      1. associate-+l- 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*r* 78.9%

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

      4. *-commutative 78.9%

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

      5. associate-+l- 78.9%

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

      6. associate-*l* 78.9%

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

      7. associate-*l* 78.9%

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

      8. *-commutative 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in b around inf 44.7%

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

      1. associate-/r* 46.1%

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

   7. Simplified 46.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-16} \lor \neg \left(a \leq 3.9\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+66} \lor \neg \left(b \leq 3.8 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

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 (or (<= b -2.9e+66) (not (<= b 3.8e+86)))
   (/ (/ b c) z)
   (* -4.0 (* a (/ t c)))))

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 <= -2.9e+66) || !(b <= 3.8e+86)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

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 <= (-2.9d+66)) .or. (.not. (b <= 3.8d+86))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

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 <= -2.9e+66) || !(b <= 3.8e+86)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[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 <= -2.9e+66) or not (b <= 3.8e+86):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

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 <= -2.9e+66) || !(b <= 3.8e+86))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

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 <= -2.9e+66) || ~((b <= 3.8e+86)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (a * (t / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -2.9e+66], N[Not[LessEqual[b, 3.8e+86]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.89999999999999986e66 or 3.79999999999999978e86 < b

   1. Initial program 75.0%

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

      1. associate-+l- 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*r* 75.0%

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

      4. *-commutative 75.0%

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

      5. associate-+l- 75.0%

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

      6. associate-*l* 75.0%

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

      7. associate-*l* 74.9%

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

      8. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in b around inf 51.9%

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

      1. associate-/r* 58.9%

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

   7. Simplified 58.9%

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

   if -2.89999999999999986e66 < b < 3.79999999999999978e86

   1. Initial program 80.5%

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

      1. associate-+l- 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*r* 81.2%

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

      4. *-commutative 81.2%

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

      5. associate-+l- 81.2%

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

      6. associate-*l* 81.2%

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

      7. associate-*l* 82.5%

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

      8. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in z around 0 83.8%

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

   6. Taylor expanded in a around inf 47.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-/l* 42.1%

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

   8. Simplified 42.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+66} \lor \neg \left(b \leq 3.8 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-110}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 1.25e-110) (/ b (* z c)) (/ (/ b c) z)))

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 (y <= 1.25e-110) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

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 (y <= 1.25d-110) then
        tmp = b / (z * c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

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 (y <= 1.25e-110) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[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 y <= 1.25e-110:
		tmp = b / (z * c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

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 (y <= 1.25e-110)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

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 (y <= 1.25e-110)
		tmp = b / (z * c);
	else
		tmp = (b / c) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 1.25e-110], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.25e-110

   1. Initial program 79.2%

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

      1. associate-+l- 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

      6. associate-*l* 79.3%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in b around inf 36.1%

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

      1. *-commutative 36.1%

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

   7. Simplified 36.1%

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

   if 1.25e-110 < y

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-+l- 78.3%

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

      6. associate-*l* 78.3%

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

      7. associate-*l* 77.2%

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

      8. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in b around inf 22.7%

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

      1. associate-/r* 25.8%

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

   7. Simplified 25.8%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 35.8% accurate, 3.8× speedup

Math

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

FPCore

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

Derivation

1. Initial program 78.5%

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

   1. associate-+l- 78.5%

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

   2. *-commutative 78.5%

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

   3. associate-*r* 78.9%

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

   4. *-commutative 78.9%

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

   5. associate-+l- 78.9%

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

   6. associate-*l* 78.9%

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

   7. associate-*l* 79.7%

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

   8. *-commutative 79.7%

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

3. Simplified 79.7%

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

5. Taylor expanded in b around inf 31.4%

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

   1. *-commutative 31.4%

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

7. Simplified 31.4%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer target: 81.2% 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 2024106 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))