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

Percentage Accurate: 79.8% → 92.2%

Time: 23.7s

Alternatives: 19

Speedup: 0.9×

• 37.7% 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: 79.8% 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: 92.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-17} \lor \neg \left(z \leq 1.12 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= z -5e-17) (not (<= z 1.12e-69)))
   (/ (- (+ (* 9.0 (/ (* x y) z)) (/ b z)) (* 4.0 (* a t))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* 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 ((z <= -5e-17) || !(z <= 1.12e-69)) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 ((z <= (-5d-17)) .or. (.not. (z <= 1.12d-69))) then
        tmp = (((9.0d0 * ((x * y) / z)) + (b / z)) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (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 ((z <= -5e-17) || !(z <= 1.12e-69)) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 (z <= -5e-17) or not (z <= 1.12e-69):
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 ((z <= -5e-17) || !(z <= 1.12e-69))
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z)) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(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 ((z <= -5e-17) || ~((z <= 1.12e-69)))
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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[z, -5e-17], N[Not[LessEqual[z, 1.12e-69]], $MachinePrecision]], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $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[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e-17 or 1.12e-69 < z

   1. Initial program 63.9%

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

      1. associate-+l- 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. *-commutative 66.5%

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

      7. associate-*r* 63.9%

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

      8. *-commutative 63.9%

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

      9. associate-*l* 64.6%

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

      10. associate-*l* 72.5%

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

   3. Simplified 72.5%

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

      1. associate-+l- 72.5%

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

      2. div-sub 70.4%

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

      3. *-commutative 70.4%

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

      4. associate-*l* 70.5%

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

      5. associate-*l* 70.5%

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

      6. fma-neg 70.5%

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

   6. Applied egg-rr 70.5%

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

      1. associate-*r* 70.4%

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

      2. times-frac 67.2%

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

      3. fma-udef 67.2%

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

      4. unsub-neg 67.2%

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

      5. *-commutative 67.2%

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

      6. *-commutative 67.2%

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

      7. associate-*l* 67.2%

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

      8. *-commutative 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in c around 0 89.4%

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

   if -4.9999999999999999e-17 < z < 1.12e-69

   1. Initial program 96.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-17} \lor \neg \left(z \leq 1.12 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+213}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-135}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (/ a (/ c t)))) (t_2 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= t -5.5e+213)
     (* -4.0 (* t (/ a c)))
     (if (<= t -3.15e+16)
       t_1
       (if (<= t -4e-118)
         t_2
         (if (<= t -1.05e-264)
           (/ (/ b z) c)
           (if (<= t 2.1e-276)
             t_2
             (if (<= t 1.95e-135) (/ b (* c 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 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (t <= -5.5e+213) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= -3.15e+16) {
		tmp = t_1;
	} else if (t <= -4e-118) {
		tmp = t_2;
	} else if (t <= -1.05e-264) {
		tmp = (b / z) / c;
	} else if (t <= 2.1e-276) {
		tmp = t_2;
	} else if (t <= 1.95e-135) {
		tmp = b / (c * 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) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = 9.0d0 * ((y / c) * (x / z))
    if (t <= (-5.5d+213)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= (-3.15d+16)) then
        tmp = t_1
    else if (t <= (-4d-118)) then
        tmp = t_2
    else if (t <= (-1.05d-264)) then
        tmp = (b / z) / c
    else if (t <= 2.1d-276) then
        tmp = t_2
    else if (t <= 1.95d-135) then
        tmp = b / (c * 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 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (t <= -5.5e+213) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= -3.15e+16) {
		tmp = t_1;
	} else if (t <= -4e-118) {
		tmp = t_2;
	} else if (t <= -1.05e-264) {
		tmp = (b / z) / c;
	} else if (t <= 2.1e-276) {
		tmp = t_2;
	} else if (t <= 1.95e-135) {
		tmp = b / (c * 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 = -4.0 * (a / (c / t))
	t_2 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if t <= -5.5e+213:
		tmp = -4.0 * (t * (a / c))
	elif t <= -3.15e+16:
		tmp = t_1
	elif t <= -4e-118:
		tmp = t_2
	elif t <= -1.05e-264:
		tmp = (b / z) / c
	elif t <= 2.1e-276:
		tmp = t_2
	elif t <= 1.95e-135:
		tmp = b / (c * 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(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (t <= -5.5e+213)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= -3.15e+16)
		tmp = t_1;
	elseif (t <= -4e-118)
		tmp = t_2;
	elseif (t <= -1.05e-264)
		tmp = Float64(Float64(b / z) / c);
	elseif (t <= 2.1e-276)
		tmp = t_2;
	elseif (t <= 1.95e-135)
		tmp = Float64(b / Float64(c * 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 = -4.0 * (a / (c / t));
	t_2 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (t <= -5.5e+213)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= -3.15e+16)
		tmp = t_1;
	elseif (t <= -4e-118)
		tmp = t_2;
	elseif (t <= -1.05e-264)
		tmp = (b / z) / c;
	elseif (t <= 2.1e-276)
		tmp = t_2;
	elseif (t <= 1.95e-135)
		tmp = b / (c * 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[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+213], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.15e+16], t$95$1, If[LessEqual[t, -4e-118], t$95$2, If[LessEqual[t, -1.05e-264], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 2.1e-276], t$95$2, If[LessEqual[t, 1.95e-135], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.50000000000000059e213

   1. Initial program 73.3%

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

      1. associate-+l- 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-*r* 93.2%

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

      4. *-commutative 93.2%

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

      5. associate-+l- 93.2%

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

      6. *-commutative 93.2%

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

      7. associate-*r* 73.3%

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

      8. *-commutative 73.3%

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

      9. associate-*l* 73.3%

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

      10. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0 85.5%

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

      1. cancel-sign-sub-inv 85.5%

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

      2. metadata-eval 85.5%

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

      3. +-commutative 85.5%

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

      4. *-commutative 85.5%

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

      5. fma-def 85.5%

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

      6. associate-/l* 58.6%

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

      7. associate-/r/ 84.8%

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

      8. fma-def 84.8%

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

      9. *-commutative 84.8%

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

      10. *-commutative 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in a around inf 78.9%

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

      1. associate-*l/ 78.1%

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

      2. *-commutative 78.1%

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

   10. Simplified 78.1%

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

   if -5.50000000000000059e213 < t < -3.15e16 or 1.95000000000000011e-135 < t

   1. Initial program 70.9%

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

      1. associate-+l- 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 77.7%

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

      4. *-commutative 77.7%

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

      5. associate-+l- 77.7%

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

      6. *-commutative 77.7%

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

      7. associate-*r* 70.9%

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

      8. *-commutative 70.9%

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

      9. associate-*l* 71.6%

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

      10. associate-*l* 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in z around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-/l* 55.0%

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

   7. Simplified 55.0%

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

   if -3.15e16 < t < -3.99999999999999994e-118 or -1.0500000000000001e-264 < t < 2.1e-276

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-+l- 74.1%

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

      6. *-commutative 74.1%

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

      7. associate-*r* 78.8%

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

      8. *-commutative 78.8%

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

      9. associate-*l* 78.8%

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

      10. associate-*l* 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in x around 0 71.3%

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

      1. cancel-sign-sub-inv 71.3%

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

      2. metadata-eval 71.3%

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

      3. +-commutative 71.3%

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

      4. *-commutative 71.3%

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

      5. fma-def 71.3%

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

      6. associate-/l* 71.3%

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

      7. associate-/r/ 69.0%

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

      8. fma-def 69.0%

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

      9. *-commutative 69.0%

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

      10. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in x around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. times-frac 58.6%

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

   10. Simplified 58.6%

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

   if -3.99999999999999994e-118 < t < -1.0500000000000001e-264

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-+l- 83.6%

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

      6. *-commutative 83.6%

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

      7. associate-*r* 91.7%

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

      8. *-commutative 91.7%

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

      9. associate-*l* 91.7%

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

      10. associate-*l* 91.6%

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

   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. Step-by-step derivation

      1. associate-+l- 91.6%

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

      2. div-sub 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-*l* 85.9%

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

      5. associate-*l* 85.9%

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

      6. fma-neg 85.9%

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

   6. Applied egg-rr 85.9%

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

      1. associate-*r* 86.0%

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

      2. times-frac 77.4%

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

      3. fma-udef 77.4%

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

      4. unsub-neg 77.4%

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

      5. *-commutative 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-*l* 77.4%

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

      8. *-commutative 77.4%

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

   8. Simplified 77.4%

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

   9. Taylor expanded in c around 0 94.3%

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

   10. Taylor expanded in b around inf 59.6%

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

   if 2.1e-276 < t < 1.95000000000000011e-135

   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* 82.7%

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

      4. *-commutative 82.7%

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

      5. associate-+l- 82.7%

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

      6. *-commutative 82.7%

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

      7. associate-*r* 91.5%

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

      8. *-commutative 91.5%

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

      9. associate-*l* 91.4%

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

      10. associate-*l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in b around inf 52.4%

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

      1. *-commutative 52.4%

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

   7. Simplified 52.4%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+213}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{+16}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-118}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-135}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x}{\frac{c}{\frac{y}{z}}}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-112}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (/ c (/ y z))))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= a -1.4e-80)
     t_2
     (if (<= a 1.8e-204)
       t_1
       (if (<= a 1.1e-112)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 2.1e-32) t_1 (if (<= a 8.5e+59) (/ (/ b z) c) t_2)))))))

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 / (c / (y / z)));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -1.4e-80) {
		tmp = t_2;
	} else if (a <= 1.8e-204) {
		tmp = t_1;
	} else if (a <= 1.1e-112) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 2.1e-32) {
		tmp = t_1;
	} else if (a <= 8.5e+59) {
		tmp = (b / z) / c;
	} else {
		tmp = t_2;
	}
	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 = 9.0d0 * (x / (c / (y / z)))
    t_2 = (-4.0d0) * (t * (a / c))
    if (a <= (-1.4d-80)) then
        tmp = t_2
    else if (a <= 1.8d-204) then
        tmp = t_1
    else if (a <= 1.1d-112) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 2.1d-32) then
        tmp = t_1
    else if (a <= 8.5d+59) then
        tmp = (b / z) / c
    else
        tmp = t_2
    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 / (c / (y / z)));
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -1.4e-80) {
		tmp = t_2;
	} else if (a <= 1.8e-204) {
		tmp = t_1;
	} else if (a <= 1.1e-112) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 2.1e-32) {
		tmp = t_1;
	} else if (a <= 8.5e+59) {
		tmp = (b / z) / c;
	} else {
		tmp = t_2;
	}
	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 / (c / (y / z)))
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -1.4e-80:
		tmp = t_2
	elif a <= 1.8e-204:
		tmp = t_1
	elif a <= 1.1e-112:
		tmp = (b / z) * (1.0 / c)
	elif a <= 2.1e-32:
		tmp = t_1
	elif a <= 8.5e+59:
		tmp = (b / z) / c
	else:
		tmp = t_2
	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(c / Float64(y / z))))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -1.4e-80)
		tmp = t_2;
	elseif (a <= 1.8e-204)
		tmp = t_1;
	elseif (a <= 1.1e-112)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 2.1e-32)
		tmp = t_1;
	elseif (a <= 8.5e+59)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = t_2;
	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 / (c / (y / z)));
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -1.4e-80)
		tmp = t_2;
	elseif (a <= 1.8e-204)
		tmp = t_1;
	elseif (a <= 1.1e-112)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 2.1e-32)
		tmp = t_1;
	elseif (a <= 8.5e+59)
		tmp = (b / z) / c;
	else
		tmp = t_2;
	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[(c / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e-80], t$95$2, If[LessEqual[a, 1.8e-204], t$95$1, If[LessEqual[a, 1.1e-112], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-32], t$95$1, If[LessEqual[a, 8.5e+59], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.39999999999999995e-80 or 8.4999999999999999e59 < a

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 72.6%

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

      4. *-commutative 72.6%

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

      5. associate-+l- 72.6%

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

      6. *-commutative 72.6%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 78.1%

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

      10. associate-*l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around 0 72.3%

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

      1. cancel-sign-sub-inv 72.3%

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

      2. metadata-eval 72.3%

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

      3. +-commutative 72.3%

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

      4. *-commutative 72.3%

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

      5. fma-def 72.3%

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

      6. associate-/l* 76.2%

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

      7. associate-/r/ 77.1%

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

      8. fma-def 77.1%

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

      9. *-commutative 77.1%

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

      10. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in a around inf 45.7%

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

      1. associate-*l/ 54.2%

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

      2. *-commutative 54.2%

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

   10. Simplified 54.2%

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

   if -1.39999999999999995e-80 < a < 1.79999999999999982e-204 or 1.10000000000000011e-112 < a < 2.0999999999999999e-32

   1. Initial program 77.9%

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

      1. associate-+l- 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-+l- 89.4%

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

      6. *-commutative 89.4%

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

      7. associate-*r* 77.9%

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

      8. *-commutative 77.9%

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

      9. associate-*l* 77.8%

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

      10. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

      1. associate-+l- 90.4%

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

      2. div-sub 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-*l* 86.9%

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

      5. associate-*l* 86.9%

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

      6. fma-neg 86.9%

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

   6. Applied egg-rr 86.9%

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

      1. associate-*r* 86.8%

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

      2. times-frac 82.4%

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

      3. fma-udef 82.4%

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

      4. unsub-neg 82.4%

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

      5. *-commutative 82.4%

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

      6. *-commutative 82.4%

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

      7. associate-*l* 82.4%

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

      8. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in c around 0 90.4%

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

   10. Taylor expanded in x around inf 50.7%

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

       1. associate-*r/ 50.7%

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

       2. *-commutative 50.7%

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

       3. associate-*r/ 50.7%

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

       4. *-commutative 50.7%

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

       5. associate-/l* 49.6%

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

       6. associate-/l* 48.1%

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

   12. Simplified 48.1%

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

   if 1.79999999999999982e-204 < a < 1.10000000000000011e-112

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 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. *-commutative 79.3%

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

      7. associate-*r* 73.0%

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

      8. *-commutative 73.0%

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

      9. associate-*l* 73.0%

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

      10. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

      1. associate-+l- 79.4%

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

      2. div-sub 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*l* 78.9%

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

      5. associate-*l* 78.9%

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

      6. fma-neg 78.9%

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

   6. Applied egg-rr 78.9%

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

      1. associate-*r* 78.9%

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

      2. times-frac 85.2%

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

      3. fma-udef 85.2%

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

      4. unsub-neg 85.2%

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

      5. *-commutative 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*l* 85.2%

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

      8. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in c around 0 87.5%

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

   10. Taylor expanded in b around inf 51.0%

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

       1. div-inv 51.1%

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

   12. Applied egg-rr 51.1%

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

   if 2.0999999999999999e-32 < a < 8.4999999999999999e59

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+l- 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*r* 91.7%

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

      8. *-commutative 91.7%

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

      9. associate-*l* 91.7%

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

      10. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

      1. associate-+l- 91.5%

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

      2. div-sub 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*l* 91.5%

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

      5. associate-*l* 91.5%

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

      6. fma-neg 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. associate-*r* 91.5%

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

      2. times-frac 83.2%

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

      3. fma-udef 83.2%

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

      4. unsub-neg 83.2%

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

      5. *-commutative 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. *-commutative 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in c around 0 91.9%

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

   10. Taylor expanded in b around inf 67.6%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-204}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{c}{\frac{y}{z}}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-112}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{c}{\frac{y}{z}}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-204}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{c}{\frac{y}{z}}}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-113}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-29}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (* t (/ a c)))))
   (if (<= a -2.7e-80)
     t_1
     (if (<= a 7.2e-204)
       (* 9.0 (/ x (/ c (/ y z))))
       (if (<= a 4.3e-113)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 3.4e-29)
           (* 9.0 (/ (* x y) (* c z)))
           (if (<= a 1.75e+61) (/ (/ b 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 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -2.7e-80) {
		tmp = t_1;
	} else if (a <= 7.2e-204) {
		tmp = 9.0 * (x / (c / (y / z)));
	} else if (a <= 4.3e-113) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 3.4e-29) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (a <= 1.75e+61) {
		tmp = (b / 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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (a <= (-2.7d-80)) then
        tmp = t_1
    else if (a <= 7.2d-204) then
        tmp = 9.0d0 * (x / (c / (y / z)))
    else if (a <= 4.3d-113) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 3.4d-29) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else if (a <= 1.75d+61) then
        tmp = (b / 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 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -2.7e-80) {
		tmp = t_1;
	} else if (a <= 7.2e-204) {
		tmp = 9.0 * (x / (c / (y / z)));
	} else if (a <= 4.3e-113) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 3.4e-29) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (a <= 1.75e+61) {
		tmp = (b / 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 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -2.7e-80:
		tmp = t_1
	elif a <= 7.2e-204:
		tmp = 9.0 * (x / (c / (y / z)))
	elif a <= 4.3e-113:
		tmp = (b / z) * (1.0 / c)
	elif a <= 3.4e-29:
		tmp = 9.0 * ((x * y) / (c * z))
	elif a <= 1.75e+61:
		tmp = (b / 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(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -2.7e-80)
		tmp = t_1;
	elseif (a <= 7.2e-204)
		tmp = Float64(9.0 * Float64(x / Float64(c / Float64(y / z))));
	elseif (a <= 4.3e-113)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 3.4e-29)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	elseif (a <= 1.75e+61)
		tmp = Float64(Float64(b / 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 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -2.7e-80)
		tmp = t_1;
	elseif (a <= 7.2e-204)
		tmp = 9.0 * (x / (c / (y / z)));
	elseif (a <= 4.3e-113)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 3.4e-29)
		tmp = 9.0 * ((x * y) / (c * z));
	elseif (a <= 1.75e+61)
		tmp = (b / 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[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-80], t$95$1, If[LessEqual[a, 7.2e-204], N[(9.0 * N[(x / N[(c / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e-113], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-29], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e+61], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.7000000000000002e-80 or 1.75000000000000009e61 < a

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 72.6%

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

      4. *-commutative 72.6%

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

      5. associate-+l- 72.6%

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

      6. *-commutative 72.6%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 78.1%

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

      10. associate-*l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around 0 72.3%

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

      1. cancel-sign-sub-inv 72.3%

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

      2. metadata-eval 72.3%

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

      3. +-commutative 72.3%

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

      4. *-commutative 72.3%

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

      5. fma-def 72.3%

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

      6. associate-/l* 76.2%

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

      7. associate-/r/ 77.1%

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

      8. fma-def 77.1%

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

      9. *-commutative 77.1%

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

      10. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in a around inf 45.7%

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

      1. associate-*l/ 54.2%

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

      2. *-commutative 54.2%

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

   10. Simplified 54.2%

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

   if -2.7000000000000002e-80 < a < 7.1999999999999993e-204

   1. Initial program 76.9%

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

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 87.7%

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

      4. *-commutative 87.7%

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

      5. associate-+l- 87.7%

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

      6. *-commutative 87.7%

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

      7. associate-*r* 76.9%

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

      8. *-commutative 76.9%

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

      9. associate-*l* 76.9%

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

      10. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

      1. associate-+l- 88.9%

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

      2. div-sub 87.5%

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

      3. *-commutative 87.5%

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

      4. associate-*l* 87.6%

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

      5. associate-*l* 87.6%

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

      6. fma-neg 87.6%

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

   6. Applied egg-rr 87.6%

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

      1. associate-*r* 87.5%

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

      2. times-frac 80.9%

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

      3. fma-udef 80.9%

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

      4. unsub-neg 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

      7. associate-*l* 80.9%

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

      8. *-commutative 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in c around 0 90.2%

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

   10. Taylor expanded in x around inf 51.2%

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

       1. associate-*r/ 51.2%

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

       2. *-commutative 51.2%

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

       3. associate-*r/ 51.2%

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

       4. *-commutative 51.2%

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

       5. associate-/l* 48.6%

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

       6. associate-/l* 48.2%

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

   12. Simplified 48.2%

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

   if 7.1999999999999993e-204 < a < 4.3e-113

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 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. *-commutative 79.3%

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

      7. associate-*r* 73.0%

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

      8. *-commutative 73.0%

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

      9. associate-*l* 73.0%

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

      10. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

      1. associate-+l- 79.4%

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

      2. div-sub 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*l* 78.9%

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

      5. associate-*l* 78.9%

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

      6. fma-neg 78.9%

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

   6. Applied egg-rr 78.9%

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

      1. associate-*r* 78.9%

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

      2. times-frac 85.2%

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

      3. fma-udef 85.2%

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

      4. unsub-neg 85.2%

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

      5. *-commutative 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*l* 85.2%

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

      8. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in c around 0 87.5%

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

   10. Taylor expanded in b around inf 51.0%

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

       1. div-inv 51.1%

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

   12. Applied egg-rr 51.1%

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

   if 4.3e-113 < a < 3.39999999999999972e-29

   1. Initial program 83.6%

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

      1. associate-+l- 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r* 83.6%

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

      8. *-commutative 83.6%

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

      9. associate-*l* 83.5%

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

      10. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 47.5%

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

   if 3.39999999999999972e-29 < a < 1.75000000000000009e61

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+l- 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*r* 91.7%

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

      8. *-commutative 91.7%

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

      9. associate-*l* 91.7%

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

      10. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

      1. associate-+l- 91.5%

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

      2. div-sub 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*l* 91.5%

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

      5. associate-*l* 91.5%

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

      6. fma-neg 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. associate-*r* 91.5%

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

      2. times-frac 83.2%

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

      3. fma-udef 83.2%

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

      4. unsub-neg 83.2%

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

      5. *-commutative 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. *-commutative 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in c around 0 91.9%

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

   10. Taylor expanded in b around inf 67.6%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-204}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{c}{\frac{y}{z}}}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-113}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-29}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-204}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (* t (/ a c)))))
   (if (<= a -2.2e-95)
     t_1
     (if (<= a 3.4e-204)
       (* (* x (/ y z)) (/ 9.0 c))
       (if (<= a 4.5e-113)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 1.25e-33)
           (* 9.0 (/ (* x y) (* c z)))
           (if (<= a 1.15e+60) (/ (/ b 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 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -2.2e-95) {
		tmp = t_1;
	} else if (a <= 3.4e-204) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (a <= 4.5e-113) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.25e-33) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (a <= 1.15e+60) {
		tmp = (b / 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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (a <= (-2.2d-95)) then
        tmp = t_1
    else if (a <= 3.4d-204) then
        tmp = (x * (y / z)) * (9.0d0 / c)
    else if (a <= 4.5d-113) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 1.25d-33) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else if (a <= 1.15d+60) then
        tmp = (b / 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 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -2.2e-95) {
		tmp = t_1;
	} else if (a <= 3.4e-204) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (a <= 4.5e-113) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.25e-33) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (a <= 1.15e+60) {
		tmp = (b / 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 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -2.2e-95:
		tmp = t_1
	elif a <= 3.4e-204:
		tmp = (x * (y / z)) * (9.0 / c)
	elif a <= 4.5e-113:
		tmp = (b / z) * (1.0 / c)
	elif a <= 1.25e-33:
		tmp = 9.0 * ((x * y) / (c * z))
	elif a <= 1.15e+60:
		tmp = (b / 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(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -2.2e-95)
		tmp = t_1;
	elseif (a <= 3.4e-204)
		tmp = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c));
	elseif (a <= 4.5e-113)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 1.25e-33)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	elseif (a <= 1.15e+60)
		tmp = Float64(Float64(b / 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 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -2.2e-95)
		tmp = t_1;
	elseif (a <= 3.4e-204)
		tmp = (x * (y / z)) * (9.0 / c);
	elseif (a <= 4.5e-113)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 1.25e-33)
		tmp = 9.0 * ((x * y) / (c * z));
	elseif (a <= 1.15e+60)
		tmp = (b / 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[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-95], t$95$1, If[LessEqual[a, 3.4e-204], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-113], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-33], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+60], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.1999999999999999e-95 or 1.15000000000000008e60 < a

   1. Initial program 77.5%

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

      1. associate-+l- 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r* 72.8%

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

      4. *-commutative 72.8%

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

      5. associate-+l- 72.8%

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

      6. *-commutative 72.8%

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

      7. associate-*r* 77.5%

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

      8. *-commutative 77.5%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around 0 72.5%

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

      1. cancel-sign-sub-inv 72.5%

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

      2. metadata-eval 72.5%

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

      3. +-commutative 72.5%

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

      4. *-commutative 72.5%

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

      5. fma-def 72.5%

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

      6. associate-/l* 76.4%

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

      7. associate-/r/ 77.2%

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

      8. fma-def 77.2%

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

      9. *-commutative 77.2%

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

      10. *-commutative 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in a around inf 45.4%

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

      1. associate-*l/ 53.8%

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

      2. *-commutative 53.8%

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

   10. Simplified 53.8%

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

   if -2.1999999999999999e-95 < a < 3.4000000000000002e-204

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 87.6%

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

      4. *-commutative 87.6%

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

      5. associate-+l- 87.6%

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

      6. *-commutative 87.6%

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

      7. associate-*r* 76.6%

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

      8. *-commutative 76.6%

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

      9. associate-*l* 76.5%

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

      10. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

      1. associate-+l- 88.8%

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

      2. div-sub 87.3%

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

      3. *-commutative 87.3%

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

      4. associate-*l* 87.4%

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

      5. associate-*l* 87.4%

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

      6. fma-neg 87.4%

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

   6. Applied egg-rr 87.4%

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

      1. associate-*r* 87.3%

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

      2. times-frac 80.7%

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

      3. fma-udef 80.7%

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

      4. unsub-neg 80.7%

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

      5. *-commutative 80.7%

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

      6. *-commutative 80.7%

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

      7. associate-*l* 80.7%

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

      8. *-commutative 80.7%

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

   8. Simplified 80.7%

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

   9. Taylor expanded in c around 0 90.1%

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

   10. Taylor expanded in z around -inf 92.9%

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

       1. mul-1-neg 92.9%

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

       2. unsub-neg 92.9%

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

       3. *-commutative 92.9%

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

       4. associate-*l* 92.9%

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

       5. neg-mul-1 92.9%

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

       6. unsub-neg 92.9%

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

       7. *-commutative 92.9%

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

       8. associate-*l* 92.9%

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

   12. Simplified 92.9%

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

   13. Taylor expanded in x around inf 50.5%

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

       1. associate-*r/ 50.5%

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

       2. *-commutative 50.5%

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

       3. *-commutative 50.5%

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

       4. times-frac 49.8%

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

       5. associate-*r/ 49.4%

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

   15. Simplified 49.4%

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

   if 3.4000000000000002e-204 < a < 4.5000000000000001e-113

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 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. *-commutative 79.3%

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

      7. associate-*r* 73.0%

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

      8. *-commutative 73.0%

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

      9. associate-*l* 73.0%

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

      10. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

      1. associate-+l- 79.4%

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

      2. div-sub 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*l* 78.9%

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

      5. associate-*l* 78.9%

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

      6. fma-neg 78.9%

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

   6. Applied egg-rr 78.9%

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

      1. associate-*r* 78.9%

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

      2. times-frac 85.2%

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

      3. fma-udef 85.2%

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

      4. unsub-neg 85.2%

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

      5. *-commutative 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*l* 85.2%

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

      8. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in c around 0 87.5%

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

   10. Taylor expanded in b around inf 51.0%

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

       1. div-inv 51.1%

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

   12. Applied egg-rr 51.1%

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

   if 4.5000000000000001e-113 < a < 1.25000000000000007e-33

   1. Initial program 83.6%

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

      1. associate-+l- 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r* 83.6%

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

      8. *-commutative 83.6%

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

      9. associate-*l* 83.5%

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

      10. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 47.5%

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

   if 1.25000000000000007e-33 < a < 1.15000000000000008e60

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+l- 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*r* 91.7%

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

      8. *-commutative 91.7%

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

      9. associate-*l* 91.7%

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

      10. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

      1. associate-+l- 91.5%

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

      2. div-sub 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*l* 91.5%

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

      5. associate-*l* 91.5%

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

      6. fma-neg 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. associate-*r* 91.5%

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

      2. times-frac 83.2%

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

      3. fma-udef 83.2%

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

      4. unsub-neg 83.2%

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

      5. *-commutative 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. *-commutative 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in c around 0 91.9%

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

   10. Taylor expanded in b around inf 67.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-95}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-204}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-202}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-24}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (* t (/ a c)))))
   (if (<= a -6.1e-80)
     t_1
     (if (<= a 1.75e-202)
       (* 9.0 (* (/ x c) (/ y z)))
       (if (<= a 5.5e-113)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 1.42e-24)
           (* 9.0 (/ (* x y) (* c z)))
           (if (<= a 1.6e+60) (/ (/ b 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 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -6.1e-80) {
		tmp = t_1;
	} else if (a <= 1.75e-202) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 5.5e-113) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.42e-24) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (a <= 1.6e+60) {
		tmp = (b / 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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (a <= (-6.1d-80)) then
        tmp = t_1
    else if (a <= 1.75d-202) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (a <= 5.5d-113) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 1.42d-24) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else if (a <= 1.6d+60) then
        tmp = (b / 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 = -4.0 * (t * (a / c));
	double tmp;
	if (a <= -6.1e-80) {
		tmp = t_1;
	} else if (a <= 1.75e-202) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (a <= 5.5e-113) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.42e-24) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (a <= 1.6e+60) {
		tmp = (b / 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 = -4.0 * (t * (a / c))
	tmp = 0
	if a <= -6.1e-80:
		tmp = t_1
	elif a <= 1.75e-202:
		tmp = 9.0 * ((x / c) * (y / z))
	elif a <= 5.5e-113:
		tmp = (b / z) * (1.0 / c)
	elif a <= 1.42e-24:
		tmp = 9.0 * ((x * y) / (c * z))
	elif a <= 1.6e+60:
		tmp = (b / 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(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (a <= -6.1e-80)
		tmp = t_1;
	elseif (a <= 1.75e-202)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (a <= 5.5e-113)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 1.42e-24)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	elseif (a <= 1.6e+60)
		tmp = Float64(Float64(b / 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 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (a <= -6.1e-80)
		tmp = t_1;
	elseif (a <= 1.75e-202)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (a <= 5.5e-113)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 1.42e-24)
		tmp = 9.0 * ((x * y) / (c * z));
	elseif (a <= 1.6e+60)
		tmp = (b / 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[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.1e-80], t$95$1, If[LessEqual[a, 1.75e-202], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-113], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.42e-24], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+60], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.1000000000000002e-80 or 1.59999999999999995e60 < a

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 72.6%

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

      4. *-commutative 72.6%

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

      5. associate-+l- 72.6%

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

      6. *-commutative 72.6%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 78.1%

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

      10. associate-*l* 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around 0 72.3%

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

      1. cancel-sign-sub-inv 72.3%

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

      2. metadata-eval 72.3%

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

      3. +-commutative 72.3%

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

      4. *-commutative 72.3%

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

      5. fma-def 72.3%

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

      6. associate-/l* 76.2%

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

      7. associate-/r/ 77.1%

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

      8. fma-def 77.1%

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

      9. *-commutative 77.1%

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

      10. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in a around inf 45.7%

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

      1. associate-*l/ 54.2%

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

      2. *-commutative 54.2%

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

   10. Simplified 54.2%

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

   if -6.1000000000000002e-80 < a < 1.75e-202

   1. Initial program 76.9%

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

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 87.7%

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

      4. *-commutative 87.7%

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

      5. associate-+l- 87.7%

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

      6. *-commutative 87.7%

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

      7. associate-*r* 76.9%

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

      8. *-commutative 76.9%

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

      9. associate-*l* 76.9%

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

      10. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around 0 91.5%

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

      1. cancel-sign-sub-inv 91.5%

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

      2. metadata-eval 91.5%

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

      3. +-commutative 91.5%

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

      4. *-commutative 91.5%

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

      5. fma-def 91.5%

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

      6. associate-/l* 81.0%

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

      7. associate-/r/ 89.0%

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

      8. fma-def 89.0%

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

      9. *-commutative 89.0%

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

      10. *-commutative 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in x around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. times-frac 48.7%

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

   10. Simplified 48.7%

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

   if 1.75e-202 < a < 5.50000000000000053e-113

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 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. *-commutative 79.3%

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

      7. associate-*r* 73.0%

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

      8. *-commutative 73.0%

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

      9. associate-*l* 73.0%

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

      10. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

      1. associate-+l- 79.4%

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

      2. div-sub 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*l* 78.9%

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

      5. associate-*l* 78.9%

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

      6. fma-neg 78.9%

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

   6. Applied egg-rr 78.9%

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

      1. associate-*r* 78.9%

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

      2. times-frac 85.2%

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

      3. fma-udef 85.2%

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

      4. unsub-neg 85.2%

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

      5. *-commutative 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*l* 85.2%

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

      8. *-commutative 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in c around 0 87.5%

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

   10. Taylor expanded in b around inf 51.0%

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

       1. div-inv 51.1%

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

   12. Applied egg-rr 51.1%

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

   if 5.50000000000000053e-113 < a < 1.42e-24

   1. Initial program 83.6%

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

      1. associate-+l- 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*r* 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-+l- 99.6%

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

      6. *-commutative 99.6%

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

      7. associate-*r* 83.6%

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

      8. *-commutative 83.6%

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

      9. associate-*l* 83.5%

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

      10. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 47.5%

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

   if 1.42e-24 < a < 1.59999999999999995e60

   1. Initial program 91.7%

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

      1. associate-+l- 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+l- 91.5%

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

      6. *-commutative 91.5%

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

      7. associate-*r* 91.7%

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

      8. *-commutative 91.7%

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

      9. associate-*l* 91.7%

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

      10. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

      1. associate-+l- 91.5%

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

      2. div-sub 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*l* 91.5%

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

      5. associate-*l* 91.5%

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

      6. fma-neg 91.5%

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

   6. Applied egg-rr 91.5%

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

      1. associate-*r* 91.5%

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

      2. times-frac 83.2%

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

      3. fma-udef 83.2%

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

      4. unsub-neg 83.2%

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

      5. *-commutative 83.2%

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

      6. *-commutative 83.2%

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

      7. associate-*l* 83.2%

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

      8. *-commutative 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in c around 0 91.9%

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

   10. Taylor expanded in b around inf 67.6%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-202}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-24}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) - \frac{x}{\frac{z}{y \cdot -9}}}{c}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} - t \cdot \left(4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

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 (<= z -2.2e+56)
   (/ (- (* t (* a -4.0)) (/ x (/ z (* y -9.0)))) c)
   (if (<= z 3.9e-135)
     (/ (+ b (* 9.0 (* x y))) (* c z))
     (if (<= z 1.8e-36)
       (/ (- b (* 4.0 (* a (* z t)))) (* c z))
       (- (* (/ (* 9.0 y) z) (/ x c)) (* t (* 4.0 (/ 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 <= -2.2e+56) {
		tmp = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c;
	} else if (z <= 3.9e-135) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (z <= 1.8e-36) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z);
	} else {
		tmp = (((9.0 * y) / z) * (x / c)) - (t * (4.0 * (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 <= (-2.2d+56)) then
        tmp = ((t * (a * (-4.0d0))) - (x / (z / (y * (-9.0d0))))) / c
    else if (z <= 3.9d-135) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else if (z <= 1.8d-36) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c * z)
    else
        tmp = (((9.0d0 * y) / z) * (x / c)) - (t * (4.0d0 * (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 <= -2.2e+56) {
		tmp = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c;
	} else if (z <= 3.9e-135) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (z <= 1.8e-36) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z);
	} else {
		tmp = (((9.0 * y) / z) * (x / c)) - (t * (4.0 * (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 <= -2.2e+56:
		tmp = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c
	elif z <= 3.9e-135:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	elif z <= 1.8e-36:
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z)
	else:
		tmp = (((9.0 * y) / z) * (x / c)) - (t * (4.0 * (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 <= -2.2e+56)
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) - Float64(x / Float64(z / Float64(y * -9.0)))) / c);
	elseif (z <= 3.9e-135)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	elseif (z <= 1.8e-36)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c)) - Float64(t * Float64(4.0 * Float64(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 <= -2.2e+56)
		tmp = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c;
	elseif (z <= 3.9e-135)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	elseif (z <= 1.8e-36)
		tmp = (b - (4.0 * (a * (z * t)))) / (c * z);
	else
		tmp = (((9.0 * y) / z) * (x / c)) - (t * (4.0 * (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, -2.2e+56], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z / N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.9e-135], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-36], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.20000000000000016e56

   1. Initial program 57.9%

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

      1. associate-+l- 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-*r* 65.1%

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

      4. *-commutative 65.1%

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

      5. associate-+l- 65.1%

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

      6. *-commutative 65.1%

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

      7. associate-*r* 57.9%

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

      8. *-commutative 57.9%

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

      9. associate-*l* 57.9%

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

      10. associate-*l* 70.5%

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

   3. Simplified 70.5%

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

      1. associate-+l- 70.5%

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

      2. div-sub 70.5%

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

      3. *-commutative 70.5%

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

      4. associate-*l* 70.4%

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

      5. associate-*l* 70.4%

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

      6. fma-neg 70.4%

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

   6. Applied egg-rr 70.4%

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

      1. associate-*r* 70.5%

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

      2. times-frac 61.4%

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

      3. fma-udef 61.4%

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

      4. unsub-neg 61.4%

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

      5. *-commutative 61.4%

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

      6. *-commutative 61.4%

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

      7. associate-*l* 61.4%

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

      8. *-commutative 61.4%

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

   8. Simplified 61.4%

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

   9. Taylor expanded in c around 0 92.8%

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

   10. Taylor expanded in z around -inf 92.8%

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

       1. mul-1-neg 92.8%

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

       2. unsub-neg 92.8%

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

       3. *-commutative 92.8%

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

       4. associate-*l* 92.8%

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

       5. neg-mul-1 92.8%

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

       6. unsub-neg 92.8%

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

       7. *-commutative 92.8%

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

       8. associate-*l* 92.8%

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

   12. Simplified 92.8%

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

   13. Taylor expanded in b around 0 78.7%

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

       1. associate-*r* 78.7%

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

       2. associate-*r/ 78.8%

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

       3. *-commutative 78.8%

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

       4. associate-*r* 78.8%

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

       5. associate-/l* 82.4%

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

       6. *-commutative 82.4%

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

   15. Simplified 82.4%

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

   if -2.20000000000000016e56 < z < 3.90000000000000022e-135

   1. Initial program 94.7%

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

      1. associate-+l- 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-*r* 96.4%

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

      4. *-commutative 96.4%

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

      5. associate-+l- 96.4%

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

      6. *-commutative 96.4%

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

      7. associate-*r* 94.7%

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

      8. *-commutative 94.7%

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

      9. associate-*l* 94.7%

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

      10. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around inf 82.2%

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

   if 3.90000000000000022e-135 < z < 1.80000000000000016e-36

   1. Initial program 94.2%

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

      1. associate-+l- 94.2%

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

      2. *-commutative 94.2%

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

      3. associate-*r* 91.1%

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

      4. *-commutative 91.1%

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

      5. associate-+l- 91.1%

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

      6. *-commutative 91.1%

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

      7. associate-*r* 94.2%

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

      8. *-commutative 94.2%

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

      9. associate-*l* 94.2%

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

      10. associate-*l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in x around 0 84.0%

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

   if 1.80000000000000016e-36 < z

   1. Initial program 57.1%

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

      1. associate-+l- 57.1%

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

      2. *-commutative 57.1%

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

      3. associate-*r* 55.5%

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

      4. *-commutative 55.5%

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

      5. associate-+l- 55.5%

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

      6. *-commutative 55.5%

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

      7. associate-*r* 57.1%

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

      8. *-commutative 57.1%

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

      9. associate-*l* 58.7%

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

      10. associate-*l* 65.2%

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

   3. Simplified 65.2%

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

      1. associate-+l- 65.2%

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

      2. div-sub 61.9%

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

      3. *-commutative 61.9%

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

      4. associate-*l* 61.9%

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

      5. associate-*l* 61.9%

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

      6. fma-neg 61.9%

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

   6. Applied egg-rr 61.9%

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

      1. associate-*r* 61.9%

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

      2. times-frac 66.6%

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

      3. fma-udef 66.6%

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

      4. unsub-neg 66.6%

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

      5. *-commutative 66.6%

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

      6. *-commutative 66.6%

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

      7. associate-*l* 66.6%

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

      8. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in z around inf 76.6%

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

       1. associate-*l/ 76.4%

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

       2. *-commutative 76.4%

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

       3. *-commutative 76.4%

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

       4. associate-*l* 76.4%

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

   11. Simplified 76.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) - \frac{x}{\frac{z}{y \cdot -9}}}{c}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} - t \cdot \left(4 \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+212}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+184} \lor \neg \left(t \leq -2.7 \cdot 10^{+104}\right) \land t \leq 3.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

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 (<= t -9.5e+212)
   (* -4.0 (* t (/ a c)))
   (if (or (<= t -1.05e+184) (and (not (<= t -2.7e+104)) (<= t 3.2e-135)))
     (/ (+ b (* 9.0 (* x y))) (* c z))
     (* -4.0 (/ a (/ c t))))))

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 (t <= -9.5e+212) {
		tmp = -4.0 * (t * (a / c));
	} else if ((t <= -1.05e+184) || (!(t <= -2.7e+104) && (t <= 3.2e-135))) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 (t <= (-9.5d+212)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if ((t <= (-1.05d+184)) .or. (.not. (t <= (-2.7d+104))) .and. (t <= 3.2d-135)) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = (-4.0d0) * (a / (c / t))
    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 (t <= -9.5e+212) {
		tmp = -4.0 * (t * (a / c));
	} else if ((t <= -1.05e+184) || (!(t <= -2.7e+104) && (t <= 3.2e-135))) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 t <= -9.5e+212:
		tmp = -4.0 * (t * (a / c))
	elif (t <= -1.05e+184) or (not (t <= -2.7e+104) and (t <= 3.2e-135)):
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = -4.0 * (a / (c / t))
	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 (t <= -9.5e+212)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif ((t <= -1.05e+184) || (!(t <= -2.7e+104) && (t <= 3.2e-135)))
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	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 (t <= -9.5e+212)
		tmp = -4.0 * (t * (a / c));
	elseif ((t <= -1.05e+184) || (~((t <= -2.7e+104)) && (t <= 3.2e-135)))
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = -4.0 * (a / (c / t));
	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[t, -9.5e+212], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.05e+184], And[N[Not[LessEqual[t, -2.7e+104]], $MachinePrecision], LessEqual[t, 3.2e-135]]], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999993e212

   1. Initial program 73.3%

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

      1. associate-+l- 73.3%

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

      2. *-commutative 73.3%

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

      3. associate-*r* 93.2%

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

      4. *-commutative 93.2%

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

      5. associate-+l- 93.2%

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

      6. *-commutative 93.2%

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

      7. associate-*r* 73.3%

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

      8. *-commutative 73.3%

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

      9. associate-*l* 73.3%

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

      10. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0 85.5%

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

      1. cancel-sign-sub-inv 85.5%

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

      2. metadata-eval 85.5%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 85.5%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 85.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 58.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 84.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 84.8%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 84.8%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in a around inf 78.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 78.1%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 78.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   10. Simplified 78.1%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -9.4999999999999993e212 < t < -1.05e184 or -2.69999999999999985e104 < t < 3.2e-135

   1. Initial program 84.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 85.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 72.5%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if -1.05e184 < t < -2.69999999999999985e104 or 3.2e-135 < t

   1. Initial program 69.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 69.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 69.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 69.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 46.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 54.3%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 54.3%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+212}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+184} \lor \neg \left(t \leq -2.7 \cdot 10^{+104}\right) \land t \leq 3.2 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-29}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) (* 4.0 (* a t))) c)))
   (if (<= z -7.5e+58)
     t_1
     (if (<= z 3.9e-135)
       (/ (+ b (* 9.0 (* x y))) (* c z))
       (if (<= z 1.26e-29) (/ (- b (* 4.0 (* a (* z t)))) (* c 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)) - (4.0 * (a * t))) / c;
	double tmp;
	if (z <= -7.5e+58) {
		tmp = t_1;
	} else if (z <= 3.9e-135) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (z <= 1.26e-29) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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)) - (4.0d0 * (a * t))) / c
    if (z <= (-7.5d+58)) then
        tmp = t_1
    else if (z <= 3.9d-135) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else if (z <= 1.26d-29) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c * 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)) - (4.0 * (a * t))) / c;
	double tmp;
	if (z <= -7.5e+58) {
		tmp = t_1;
	} else if (z <= 3.9e-135) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (z <= 1.26e-29) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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)) - (4.0 * (a * t))) / c
	tmp = 0
	if z <= -7.5e+58:
		tmp = t_1
	elif z <= 3.9e-135:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	elif z <= 1.26e-29:
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(4.0 * Float64(a * t))) / c)
	tmp = 0.0
	if (z <= -7.5e+58)
		tmp = t_1;
	elseif (z <= 3.9e-135)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	elseif (z <= 1.26e-29)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c * 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)) - (4.0 * (a * t))) / c;
	tmp = 0.0;
	if (z <= -7.5e+58)
		tmp = t_1;
	elseif (z <= 3.9e-135)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	elseif (z <= 1.26e-29)
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -7.5e+58], t$95$1, If[LessEqual[z, 3.9e-135], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e-29], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000001e58 or 1.25999999999999996e-29 < z

   1. Initial program 57.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 57.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 57.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 60.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 57.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 57.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 58.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 67.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 67.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 65.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 65.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 65.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 65.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 65.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 65.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 64.1%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 64.1%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 89.0%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in b around 0 76.1%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -7.5000000000000001e58 < z < 3.90000000000000022e-135

   1. Initial program 94.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 96.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.2%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 3.90000000000000022e-135 < z < 1.25999999999999996e-29

   1. Initial program 94.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 91.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-29}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) - \frac{x}{\frac{z}{y \cdot -9}}}{c}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (- (* t (* a -4.0)) (/ x (/ z (* y -9.0)))) c)))
   (if (<= z -1.2e+56)
     t_1
     (if (<= z 3.9e-135)
       (/ (+ b (* 9.0 (* x y))) (* c z))
       (if (<= z 1.35e-36) (/ (- b (* 4.0 (* a (* z t)))) (* c 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 = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c;
	double tmp;
	if (z <= -1.2e+56) {
		tmp = t_1;
	} else if (z <= 3.9e-135) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (z <= 1.35e-36) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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 = ((t * (a * (-4.0d0))) - (x / (z / (y * (-9.0d0))))) / c
    if (z <= (-1.2d+56)) then
        tmp = t_1
    else if (z <= 3.9d-135) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else if (z <= 1.35d-36) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c * 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 = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c;
	double tmp;
	if (z <= -1.2e+56) {
		tmp = t_1;
	} else if (z <= 3.9e-135) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (z <= 1.35e-36) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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 = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c
	tmp = 0
	if z <= -1.2e+56:
		tmp = t_1
	elif z <= 3.9e-135:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	elif z <= 1.35e-36:
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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(Float64(Float64(t * Float64(a * -4.0)) - Float64(x / Float64(z / Float64(y * -9.0)))) / c)
	tmp = 0.0
	if (z <= -1.2e+56)
		tmp = t_1;
	elseif (z <= 3.9e-135)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	elseif (z <= 1.35e-36)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c * 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 = ((t * (a * -4.0)) - (x / (z / (y * -9.0)))) / c;
	tmp = 0.0;
	if (z <= -1.2e+56)
		tmp = t_1;
	elseif (z <= 3.9e-135)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	elseif (z <= 1.35e-36)
		tmp = (b - (4.0 * (a * (z * t)))) / (c * 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[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z / N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.2e+56], t$95$1, If[LessEqual[z, 3.9e-135], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-36], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000007e56 or 1.35000000000000004e-36 < z

   1. Initial program 57.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 57.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 57.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 60.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 57.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 57.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 58.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 67.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 67.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 65.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 65.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 65.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 65.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 65.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 65.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 64.1%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 64.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 64.1%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 89.0%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in z around -inf 88.9%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 88.9%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 88.9%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 88.9%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 88.9%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. neg-mul-1 88.9%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       6. unsub-neg 88.9%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       7. *-commutative 88.9%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       8. associate-*l* 88.9%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 88.9%

       \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right) - \frac{x \cdot \left(y \cdot -9\right) - b}{z}}}{c} \]

   13. Taylor expanded in b around 0 76.1%

       \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - -9 \cdot \frac{x \cdot y}{z}}{c}} \]
   14. Step-by-step derivation

       1. associate-*r* 76.1%

          \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t} - -9 \cdot \frac{x \cdot y}{z}}{c} \]

       2. associate-*r/ 76.0%

          \[\leadsto \frac{\left(-4 \cdot a\right) \cdot t - \color{blue}{\frac{-9 \cdot \left(x \cdot y\right)}{z}}}{c} \]

       3. *-commutative 76.0%

          \[\leadsto \frac{\left(-4 \cdot a\right) \cdot t - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9}}{z}}{c} \]

       4. associate-*r* 76.0%

          \[\leadsto \frac{\left(-4 \cdot a\right) \cdot t - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)}}{z}}{c} \]

       5. associate-/l* 79.5%

          \[\leadsto \frac{\left(-4 \cdot a\right) \cdot t - \color{blue}{\frac{x}{\frac{z}{y \cdot -9}}}}{c} \]

       6. *-commutative 79.5%

          \[\leadsto \frac{\left(-4 \cdot a\right) \cdot t - \frac{x}{\frac{z}{\color{blue}{-9 \cdot y}}}}{c} \]

   15. Simplified 79.5%

       \[\leadsto \color{blue}{\frac{\left(-4 \cdot a\right) \cdot t - \frac{x}{\frac{z}{-9 \cdot y}}}{c}} \]

   if -1.20000000000000007e56 < z < 3.90000000000000022e-135

   1. Initial program 94.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 96.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 91.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.2%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 3.90000000000000022e-135 < z < 1.35000000000000004e-36

   1. Initial program 94.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 91.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 94.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 94.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 94.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.0%

      \[\leadsto \color{blue}{\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) - \frac{x}{\frac{z}{y \cdot -9}}}{c}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) - \frac{x}{\frac{z}{y \cdot -9}}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+63} \lor \neg \left(z \leq 4 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= z -3.2e+63) (not (<= z 4e-71)))
   (/ (+ (* a (* t -4.0)) (/ (- b (* x (* y -9.0))) z)) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* 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 ((z <= -3.2e+63) || !(z <= 4e-71)) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 ((z <= (-3.2d+63)) .or. (.not. (z <= 4d-71))) then
        tmp = ((a * (t * (-4.0d0))) + ((b - (x * (y * (-9.0d0)))) / z)) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (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 ((z <= -3.2e+63) || !(z <= 4e-71)) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 (z <= -3.2e+63) or not (z <= 4e-71):
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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 ((z <= -3.2e+63) || !(z <= 4e-71))
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(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 ((z <= -3.2e+63) || ~((z <= 4e-71)))
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (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[z, -3.2e+63], N[Not[LessEqual[z, 4e-71]], $MachinePrecision]], N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $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[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000011e63 or 3.9999999999999997e-71 < z

   1. Initial program 60.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 63.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 63.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 63.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 63.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 60.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 60.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 61.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 69.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 69.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 68.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 68.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 68.3%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 68.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 68.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 68.3%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 68.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 66.0%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 66.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 66.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 66.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 66.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 66.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 66.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 89.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in z around -inf 89.2%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 89.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 89.2%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 89.2%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 89.2%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. neg-mul-1 89.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       6. unsub-neg 89.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       7. *-commutative 89.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       8. associate-*l* 89.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 89.2%

       \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right) - \frac{x \cdot \left(y \cdot -9\right) - b}{z}}}{c} \]

   if -3.20000000000000011e63 < z < 3.9999999999999997e-71

   1. Initial program 94.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+63} \lor \neg \left(z \leq 4 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+68}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+122}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{9}{\frac{z}{y}}}{c} - t \cdot \left(4 \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

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 (<= z -5e+68)
   (/ (+ (* a (* t -4.0)) (/ (- b (* x (* y -9.0))) z)) c)
   (if (<= z 9.6e+122)
     (/ (- b (- (* (* a t) (* z 4.0)) (* x (* 9.0 y)))) (* c z))
     (- (/ (* x (/ 9.0 (/ z y))) c) (* t (* 4.0 (/ 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 <= -5e+68) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else if (z <= 9.6e+122) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = ((x * (9.0 / (z / y))) / c) - (t * (4.0 * (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 <= (-5d+68)) then
        tmp = ((a * (t * (-4.0d0))) + ((b - (x * (y * (-9.0d0)))) / z)) / c
    else if (z <= 9.6d+122) then
        tmp = (b - (((a * t) * (z * 4.0d0)) - (x * (9.0d0 * y)))) / (c * z)
    else
        tmp = ((x * (9.0d0 / (z / y))) / c) - (t * (4.0d0 * (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 <= -5e+68) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else if (z <= 9.6e+122) {
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (c * z);
	} else {
		tmp = ((x * (9.0 / (z / y))) / c) - (t * (4.0 * (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 <= -5e+68:
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c
	elif z <= 9.6e+122:
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (c * z)
	else:
		tmp = ((x * (9.0 / (z / y))) / c) - (t * (4.0 * (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 <= -5e+68)
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	elseif (z <= 9.6e+122)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(9.0 * y)))) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(x * Float64(9.0 / Float64(z / y))) / c) - Float64(t * Float64(4.0 * Float64(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 <= -5e+68)
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	elseif (z <= 9.6e+122)
		tmp = (b - (((a * t) * (z * 4.0)) - (x * (9.0 * y)))) / (c * z);
	else
		tmp = ((x * (9.0 / (z / y))) / c) - (t * (4.0 * (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, -5e+68], N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 9.6e+122], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(9.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] - N[(t * N[(4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000004e68

   1. Initial program 57.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 57.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 57.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 63.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 63.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 63.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 63.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 57.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 57.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 57.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 68.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 68.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 68.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 68.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 68.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 68.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 68.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 68.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 68.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 59.1%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 59.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 59.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 59.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 59.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 59.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 59.1%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 92.4%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in z around -inf 92.4%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 92.4%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 92.4%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 92.4%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 92.4%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. neg-mul-1 92.4%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       6. unsub-neg 92.4%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       7. *-commutative 92.4%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       8. associate-*l* 92.4%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 92.4%

       \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right) - \frac{x \cdot \left(y \cdot -9\right) - b}{z}}}{c} \]

   if -5.0000000000000004e68 < z < 9.6000000000000007e122

   1. Initial program 92.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 92.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 92.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 93.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 92.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 92.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 92.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   if 9.6000000000000007e122 < z

   1. Initial program 34.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 34.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 34.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 32.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 32.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 32.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 32.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 34.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 34.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 37.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 46.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 46.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 43.6%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 43.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 43.6%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 43.6%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 43.6%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 43.6%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 49.2%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 49.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 49.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 49.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 49.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 49.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 49.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]
   9. Step-by-step derivation

      1. associate-*r/ 54.8%

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot y}{z} \cdot x}{c}} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c} \]

      2. associate-/l* 54.8%

         \[\leadsto \frac{\color{blue}{\frac{9}{\frac{z}{y}}} \cdot x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c} \]

   10. Applied egg-rr 54.8%

       \[\leadsto \color{blue}{\frac{\frac{9}{\frac{z}{y}} \cdot x}{c}} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c} \]

   11. Taylor expanded in z around inf 82.8%

       \[\leadsto \frac{\frac{9}{\frac{z}{y}} \cdot x}{c} - \color{blue}{4 \cdot \frac{a \cdot t}{c}} \]
   12. Step-by-step derivation

       1. associate-*l/ 79.6%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

       2. *-commutative 79.6%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\left(\frac{a}{c} \cdot t\right) \cdot 4} \]

       3. *-commutative 79.6%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot 4 \]

       4. associate-*l* 79.6%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{t \cdot \left(\frac{a}{c} \cdot 4\right)} \]

   13. Simplified 79.8%

       \[\leadsto \frac{\frac{9}{\frac{z}{y}} \cdot x}{c} - \color{blue}{t \cdot \left(\frac{a}{c} \cdot 4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+68}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+122}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{9}{\frac{z}{y}}}{c} - t \cdot \left(4 \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4500000:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-46} \lor \neg \left(t \leq 1.45 \cdot 10^{-135}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= t -1.26e+37)
     t_1
     (if (<= t -4500000.0)
       (/ b (* c z))
       (if (or (<= t -3.6e-46) (not (<= t 1.45e-135))) t_1 (/ (/ 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) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -1.26e+37) {
		tmp = t_1;
	} else if (t <= -4500000.0) {
		tmp = b / (c * z);
	} else if ((t <= -3.6e-46) || !(t <= 1.45e-135)) {
		tmp = t_1;
	} else {
		tmp = (b / 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (t <= (-1.26d+37)) then
        tmp = t_1
    else if (t <= (-4500000.0d0)) then
        tmp = b / (c * z)
    else if ((t <= (-3.6d-46)) .or. (.not. (t <= 1.45d-135))) then
        tmp = t_1
    else
        tmp = (b / 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 t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -1.26e+37) {
		tmp = t_1;
	} else if (t <= -4500000.0) {
		tmp = b / (c * z);
	} else if ((t <= -3.6e-46) || !(t <= 1.45e-135)) {
		tmp = t_1;
	} else {
		tmp = (b / 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):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -1.26e+37:
		tmp = t_1
	elif t <= -4500000.0:
		tmp = b / (c * z)
	elif (t <= -3.6e-46) or not (t <= 1.45e-135):
		tmp = t_1
	else:
		tmp = (b / 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)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -1.26e+37)
		tmp = t_1;
	elseif (t <= -4500000.0)
		tmp = Float64(b / Float64(c * z));
	elseif ((t <= -3.6e-46) || !(t <= 1.45e-135))
		tmp = t_1;
	else
		tmp = Float64(Float64(b / 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)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -1.26e+37)
		tmp = t_1;
	elseif (t <= -4500000.0)
		tmp = b / (c * z);
	elseif ((t <= -3.6e-46) || ~((t <= 1.45e-135)))
		tmp = t_1;
	else
		tmp = (b / 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_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+37], t$95$1, If[LessEqual[t, -4500000.0], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.6e-46], N[Not[LessEqual[t, 1.45e-135]], $MachinePrecision]], t$95$1, N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.26e37 or -4.5e6 < t < -3.6e-46 or 1.4500000000000001e-135 < t

   1. Initial program 72.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 78.1%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 78.1%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 78.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 78.1%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 78.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 78.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 84.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 84.1%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in a around inf 49.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 57.2%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 57.2%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   10. Simplified 57.2%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.26e37 < t < -4.5e6

   1. Initial program 66.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 67.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 66.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 66.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 67.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 4.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 4.9%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 4.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -3.6e-46 < t < 1.4500000000000001e-135

   1. Initial program 87.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 87.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 87.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 79.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 79.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 79.3%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 79.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 79.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 79.3%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 75.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 86.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in b around inf 47.6%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+37}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -4500000:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-46} \lor \neg \left(t \leq 1.45 \cdot 10^{-135}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -215000:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-46}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* -4.0 (* t (/ a c)))))
   (if (<= t -1.2e+37)
     t_1
     (if (<= t -215000.0)
       (/ b (* c z))
       (if (<= t -3.8e-46)
         (* -4.0 (/ (* a t) c))
         (if (<= t 1.9e-135) (/ (/ b 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 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -1.2e+37) {
		tmp = t_1;
	} else if (t <= -215000.0) {
		tmp = b / (c * z);
	} else if (t <= -3.8e-46) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t <= 1.9e-135) {
		tmp = (b / 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) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (t <= (-1.2d+37)) then
        tmp = t_1
    else if (t <= (-215000.0d0)) then
        tmp = b / (c * z)
    else if (t <= (-3.8d-46)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (t <= 1.9d-135) then
        tmp = (b / 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 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -1.2e+37) {
		tmp = t_1;
	} else if (t <= -215000.0) {
		tmp = b / (c * z);
	} else if (t <= -3.8e-46) {
		tmp = -4.0 * ((a * t) / c);
	} else if (t <= 1.9e-135) {
		tmp = (b / 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 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -1.2e+37:
		tmp = t_1
	elif t <= -215000.0:
		tmp = b / (c * z)
	elif t <= -3.8e-46:
		tmp = -4.0 * ((a * t) / c)
	elif t <= 1.9e-135:
		tmp = (b / 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(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -1.2e+37)
		tmp = t_1;
	elseif (t <= -215000.0)
		tmp = Float64(b / Float64(c * z));
	elseif (t <= -3.8e-46)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (t <= 1.9e-135)
		tmp = Float64(Float64(b / 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 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -1.2e+37)
		tmp = t_1;
	elseif (t <= -215000.0)
		tmp = b / (c * z);
	elseif (t <= -3.8e-46)
		tmp = -4.0 * ((a * t) / c);
	elseif (t <= 1.9e-135)
		tmp = (b / 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[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+37], t$95$1, If[LessEqual[t, -215000.0], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-46], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-135], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2e37 or 1.9000000000000001e-135 < t

   1. Initial program 70.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 70.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 70.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 74.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.8%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 76.8%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 76.8%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 76.8%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 76.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 76.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 76.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 83.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 83.1%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 83.1%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in a around inf 50.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 58.0%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 58.0%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   10. Simplified 58.0%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.2e37 < t < -215000

   1. Initial program 66.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 67.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 66.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 66.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 67.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 4.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 4.9%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 4.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -215000 < t < -3.7999999999999997e-46

   1. Initial program 88.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 88.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 88.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 88.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 88.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 88.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 88.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 88.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 88.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 45.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -3.7999999999999997e-46 < t < 1.9000000000000001e-135

   1. Initial program 87.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 87.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 87.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 79.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 79.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 79.3%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 79.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 79.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 79.3%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 75.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 86.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in b around inf 47.6%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+37}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -215000:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-46}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 2.3 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 2.3e-41)
   (/ (- (+ (* 9.0 (/ (* x y) z)) (/ b z)) (* 4.0 (* a t))) c)
   (+ (* -4.0 (* t (/ a c))) (/ (- (/ b c) (* -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 (c <= 2.3e-41) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c;
	} else {
		tmp = (-4.0 * (t * (a / c))) + (((b / c) - (-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 (c <= 2.3d-41) then
        tmp = (((9.0d0 * ((x * y) / z)) + (b / z)) - (4.0d0 * (a * t))) / c
    else
        tmp = ((-4.0d0) * (t * (a / c))) + (((b / c) - ((-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 (c <= 2.3e-41) {
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c;
	} else {
		tmp = (-4.0 * (t * (a / c))) + (((b / c) - (-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 c <= 2.3e-41:
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c
	else:
		tmp = (-4.0 * (t * (a / c))) + (((b / c) - (-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 (c <= 2.3e-41)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z)) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c))) + Float64(Float64(Float64(b / c) - Float64(-9.0 * 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 (c <= 2.3e-41)
		tmp = (((9.0 * ((x * y) / z)) + (b / z)) - (4.0 * (a * t))) / c;
	else
		tmp = (-4.0 * (t * (a / c))) + (((b / c) - (-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[c, 2.3e-41], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(-9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 2.3000000000000001e-41

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 84.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 77.4%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 77.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 77.4%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 77.4%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 77.4%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 77.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 71.0%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 71.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 71.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 71.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 71.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 71.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 71.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 88.6%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if 2.3000000000000001e-41 < c

   1. Initial program 74.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 74.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 68.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 78.5%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 78.5%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 78.5%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 78.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 86.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 85.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 85.6%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 85.6%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 85.6%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in z around -inf 82.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 82.8%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}\right)} \]

      2. unsub-neg 82.8%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]

      3. associate-*l/ 89.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      4. *-commutative 89.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      5. mul-1-neg 89.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{-9 \cdot \frac{x \cdot y}{c} + \color{blue}{\left(-\frac{b}{c}\right)}}{z} \]

      6. sub-neg 89.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{-9 \cdot \frac{x \cdot y}{c} - \frac{b}{c}}}{z} \]

      7. associate-*r/ 88.3%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{-9 \cdot \color{blue}{\left(x \cdot \frac{y}{c}\right)} - \frac{b}{c}}{z} \]

   10. Simplified 88.3%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{-9 \cdot \left(x \cdot \frac{y}{c}\right) - \frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.3 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;9 \cdot x \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;9 \cdot x \leq 5 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

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 (<= (* 9.0 x) -2e-21)
   (/ (+ b (* 9.0 (* x y))) (* c z))
   (if (<= (* 9.0 x) 5e+94)
     (/ (- (/ b z) (* a (* 4.0 t))) c)
     (* 9.0 (* (/ y c) (/ x 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 ((9.0 * x) <= -2e-21) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if ((9.0 * x) <= 5e+94) {
		tmp = ((b / z) - (a * (4.0 * t))) / c;
	} else {
		tmp = 9.0 * ((y / c) * (x / 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 ((9.0d0 * x) <= (-2d-21)) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else if ((9.0d0 * x) <= 5d+94) then
        tmp = ((b / z) - (a * (4.0d0 * t))) / c
    else
        tmp = 9.0d0 * ((y / c) * (x / 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 ((9.0 * x) <= -2e-21) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if ((9.0 * x) <= 5e+94) {
		tmp = ((b / z) - (a * (4.0 * t))) / c;
	} else {
		tmp = 9.0 * ((y / c) * (x / 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 (9.0 * x) <= -2e-21:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	elif (9.0 * x) <= 5e+94:
		tmp = ((b / z) - (a * (4.0 * t))) / c
	else:
		tmp = 9.0 * ((y / c) * (x / 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 (Float64(9.0 * x) <= -2e-21)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	elseif (Float64(9.0 * x) <= 5e+94)
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c);
	else
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / 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 ((9.0 * x) <= -2e-21)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	elseif ((9.0 * x) <= 5e+94)
		tmp = ((b / z) - (a * (4.0 * t))) / c;
	else
		tmp = 9.0 * ((y / c) * (x / 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[N[(9.0 * x), $MachinePrecision], -2e-21], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(9.0 * x), $MachinePrecision], 5e+94], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 9) < -1.99999999999999982e-21

   1. Initial program 77.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 78.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 72.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 64.5%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if -1.99999999999999982e-21 < (*.f64 x 9) < 5.0000000000000001e94

   1. Initial program 80.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 83.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 83.1%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 75.8%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 75.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.8%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 71.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 71.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 71.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 71.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 71.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 71.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 89.5%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 75.9%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   11. Step-by-step derivation

       1. associate-*r* 75.9%

          \[\leadsto \frac{\frac{b}{z} - \color{blue}{\left(4 \cdot a\right) \cdot t}}{c} \]

       2. *-commutative 75.9%

          \[\leadsto \frac{\frac{b}{z} - \color{blue}{t \cdot \left(4 \cdot a\right)}}{c} \]

       3. associate-*r* 75.9%

          \[\leadsto \frac{\frac{b}{z} - \color{blue}{\left(t \cdot 4\right) \cdot a}}{c} \]

   12. Simplified 75.9%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - \left(t \cdot 4\right) \cdot a}{c}} \]

   if 5.0000000000000001e94 < (*.f64 x 9)

   1. Initial program 71.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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. *-commutative 75.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 81.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 81.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 81.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 81.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 81.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 78.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 79.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 79.4%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in x around inf 53.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   9. Step-by-step derivation

      1. *-commutative 53.3%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

      2. times-frac 58.6%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]

   10. Simplified 58.6%

       \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;9 \cdot x \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;9 \cdot x \leq 5 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+214}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-46} \lor \neg \left(t \leq 1.95 \cdot 10^{-135}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.02e+214)
   (* -4.0 (* t (/ a c)))
   (if (or (<= t -3.35e-46) (not (<= t 1.95e-135)))
     (* -4.0 (/ a (/ c t)))
     (/ (/ 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) {
	double tmp;
	if (t <= -1.02e+214) {
		tmp = -4.0 * (t * (a / c));
	} else if ((t <= -3.35e-46) || !(t <= 1.95e-135)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / 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 (t <= (-1.02d+214)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if ((t <= (-3.35d-46)) .or. (.not. (t <= 1.95d-135))) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / 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 (t <= -1.02e+214) {
		tmp = -4.0 * (t * (a / c));
	} else if ((t <= -3.35e-46) || !(t <= 1.95e-135)) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / 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 t <= -1.02e+214:
		tmp = -4.0 * (t * (a / c))
	elif (t <= -3.35e-46) or not (t <= 1.95e-135):
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / 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 (t <= -1.02e+214)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif ((t <= -3.35e-46) || !(t <= 1.95e-135))
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / 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 (t <= -1.02e+214)
		tmp = -4.0 * (t * (a / c));
	elseif ((t <= -3.35e-46) || ~((t <= 1.95e-135)))
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / 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[LessEqual[t, -1.02e+214], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.35e-46], N[Not[LessEqual[t, 1.95e-135]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e214

   1. Initial program 73.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 93.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 73.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 73.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 93.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.5%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 85.5%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 85.5%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 85.5%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 85.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 58.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 84.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 84.8%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 84.8%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in a around inf 78.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 78.1%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 78.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   10. Simplified 78.1%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.02e214 < t < -3.35e-46 or 1.95000000000000011e-135 < t

   1. Initial program 71.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 78.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 73.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 46.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 46.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 53.7%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 53.7%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -3.35e-46 < t < 1.95000000000000011e-135

   1. Initial program 87.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 87.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 87.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 87.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 79.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 79.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 79.3%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 79.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 79.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 79.3%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 79.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 75.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 75.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 86.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in b around inf 47.6%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+214}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-46} \lor \neg \left(t \leq 1.95 \cdot 10^{-135}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.25 \cdot 10^{+63}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

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 (<= t 3.25e+63)
   (/ (+ (* a (* t -4.0)) (/ (- b (* x (* y -9.0))) 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 (t <= 3.25e+63) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / 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 (t <= 3.25d+63) then
        tmp = ((a * (t * (-4.0d0))) + ((b - (x * (y * (-9.0d0)))) / 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 (t <= 3.25e+63) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / 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 t <= 3.25e+63:
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / 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 (t <= 3.25e+63)
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(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 (t <= 3.25e+63)
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / 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[t, 3.25e+63], N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.24999999999999996e63

   1. Initial program 81.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 82.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 82.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 77.5%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 77.5%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 77.4%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 77.4%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 77.4%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 77.5%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 72.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 72.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 72.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 72.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 72.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 72.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 72.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 72.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 85.8%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in z around -inf 87.2%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 87.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 87.2%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 87.2%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 87.2%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. neg-mul-1 87.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       6. unsub-neg 87.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       7. *-commutative 87.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       8. associate-*l* 87.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 87.2%

       \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right) - \frac{x \cdot \left(y \cdot -9\right) - b}{z}}}{c} \]

   if 3.24999999999999996e63 < t

   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* 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 75.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 62.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 62.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 62.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 66.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 68.7%

         \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \left(-4\right) \cdot \frac{a \cdot t}{c}} \]

      2. metadata-eval 68.7%

         \[\leadsto \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) + \color{blue}{-4} \cdot \frac{a \cdot t}{c} \]

      3. +-commutative 68.7%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      4. *-commutative 68.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + \left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      5. fma-def 68.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a \cdot t}{c}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right)} \]

      6. associate-/l* 70.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{c}{t}}}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      7. associate-/r/ 72.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{a}{c} \cdot t}, -4, 9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) \]

      8. fma-def 72.9%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)}\right) \]

      9. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{\color{blue}{z \cdot c}}, \frac{b}{c \cdot z}\right)\right) \]

      10. *-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{\color{blue}{z \cdot c}}\right)\right) \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{c} \cdot t, -4, \mathsf{fma}\left(9, \frac{x \cdot y}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)} \]

   8. Taylor expanded in a around inf 54.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*l/ 60.4%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 60.4%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   10. Simplified 60.4%

       \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.25 \cdot 10^{+63}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

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 (* 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) {
	return b / (c * z);
}

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 / (c * z)
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 / (c * z);
}

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 / (c * z)

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(c * z))
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 / (c * z);
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[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.9%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 77.9%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 77.9%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.5%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 79.5%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 77.9%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 77.9%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 78.3%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 79.9%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 79.9%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 32.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 32.3%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 32.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 32.3%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer target: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (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)))