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

Percentage Accurate: 79.5% → 92.6%

Time: 27.3s

Alternatives: 24

Speedup: 0.9×

• 37.6% 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: 79.5% 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: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+48} \lor \neg \left(z \leq 1.9 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{\left(9 \cdot \left(y \cdot \frac{x}{z}\right) + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.95e+48) (not (<= z 1.9e-149)))
   (/ (- (+ (* 9.0 (* y (/ x z))) (/ b z)) (* 4.0 (* a t))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.95e+48) || !(z <= 1.9e-149)) {
		tmp = (((9.0 * (y * (x / z))) + (b / z)) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.95d+48)) .or. (.not. (z <= 1.9d-149))) then
        tmp = (((9.0d0 * (y * (x / z))) + (b / z)) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.95e+48) || !(z <= 1.9e-149)) {
		tmp = (((9.0 * (y * (x / z))) + (b / z)) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.95e+48) or not (z <= 1.9e-149):
		tmp = (((9.0 * (y * (x / z))) + (b / z)) - (4.0 * (a * t))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.95e+48) || !(z <= 1.9e-149))
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y * Float64(x / 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(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.95e+48) || ~((z <= 1.9e-149)))
		tmp = (((9.0 * (y * (x / z))) + (b / z)) - (4.0 * (a * t))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.95e+48], N[Not[LessEqual[z, 1.9e-149]], $MachinePrecision]], N[(N[(N[(N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $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[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e48 or 1.90000000000000003e-149 < z

   1. Initial program 67.1%

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

      1. associate-+l- 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*r* 67.7%

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

      4. *-commutative 67.7%

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

      5. associate-+l- 67.7%

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

      6. *-commutative 67.7%

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

      7. associate-*r* 67.1%

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

      8. *-commutative 67.1%

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

      9. associate-*l* 67.1%

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

      10. associate-*l* 71.8%

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

   3. Simplified 71.8%

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

      1. associate-+l- 71.8%

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

      2. div-sub 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* 70.5%

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

      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* 70.5%

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

      2. times-frac 71.1%

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

      3. fma-udef 71.1%

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

      4. unsub-neg 71.1%

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

      5. *-commutative 71.1%

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

      6. *-commutative 71.1%

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

      7. associate-*l* 71.1%

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

      8. *-commutative 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in c around 0 91.2%

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

       1. *-commutative 91.2%

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

       2. *-un-lft-identity 91.2%

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

       3. times-frac 93.5%

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

   11. Applied egg-rr 93.5%

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

   12. Taylor expanded in y around 0 91.2%

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

       1. *-commutative 91.2%

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

       2. associate-*r/ 93.5%

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

   14. Simplified 93.5%

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

   if -1.95e48 < z < 1.90000000000000003e-149

   1. Initial program 94.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+48} \lor \neg \left(z \leq 1.9 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{\left(9 \cdot \left(y \cdot \frac{x}{z}\right) + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-306}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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)))))
   (if (<= a -9.2e-120)
     (* -4.0 (/ a (/ c t)))
     (if (<= a -2.1e-203)
       t_1
       (if (<= a 4.9e-306)
         (/ 1.0 (/ c (/ b z)))
         (if (<= a 4.7e-212)
           t_1
           (if (<= a 7e-47)
             (* b (/ (/ 1.0 c) z))
             (if (<= a 2.3e-12) t_1 (* -4.0 (* t (/ a c)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double tmp;
	if (a <= -9.2e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -2.1e-203) {
		tmp = t_1;
	} else if (a <= 4.9e-306) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 4.7e-212) {
		tmp = t_1;
	} else if (a <= 7e-47) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.3e-12) {
		tmp = t_1;
	} 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.
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 / c) * (y / z))
    if (a <= (-9.2d-120)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-2.1d-203)) then
        tmp = t_1
    else if (a <= 4.9d-306) then
        tmp = 1.0d0 / (c / (b / z))
    else if (a <= 4.7d-212) then
        tmp = t_1
    else if (a <= 7d-47) then
        tmp = b * ((1.0d0 / c) / z)
    else if (a <= 2.3d-12) then
        tmp = t_1
    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;
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 tmp;
	if (a <= -9.2e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -2.1e-203) {
		tmp = t_1;
	} else if (a <= 4.9e-306) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 4.7e-212) {
		tmp = t_1;
	} else if (a <= 7e-47) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.3e-12) {
		tmp = t_1;
	} 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])
[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))
	tmp = 0
	if a <= -9.2e-120:
		tmp = -4.0 * (a / (c / t))
	elif a <= -2.1e-203:
		tmp = t_1
	elif a <= 4.9e-306:
		tmp = 1.0 / (c / (b / z))
	elif a <= 4.7e-212:
		tmp = t_1
	elif a <= 7e-47:
		tmp = b * ((1.0 / c) / z)
	elif a <= 2.3e-12:
		tmp = t_1
	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])
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(Float64(x / c) * Float64(y / z)))
	tmp = 0.0
	if (a <= -9.2e-120)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -2.1e-203)
		tmp = t_1;
	elseif (a <= 4.9e-306)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (a <= 4.7e-212)
		tmp = t_1;
	elseif (a <= 7e-47)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (a <= 2.3e-12)
		tmp = t_1;
	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])){:}
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));
	tmp = 0.0;
	if (a <= -9.2e-120)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -2.1e-203)
		tmp = t_1;
	elseif (a <= 4.9e-306)
		tmp = 1.0 / (c / (b / z));
	elseif (a <= 4.7e-212)
		tmp = t_1;
	elseif (a <= 7e-47)
		tmp = b * ((1.0 / c) / z);
	elseif (a <= 2.3e-12)
		tmp = t_1;
	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.
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[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e-120], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-203], t$95$1, If[LessEqual[a, 4.9e-306], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-212], t$95$1, If[LessEqual[a, 7e-47], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-12], t$95$1, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.19999999999999946e-120

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. *-commutative 76.2%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   if -9.19999999999999946e-120 < a < -2.10000000000000002e-203 or 4.90000000000000025e-306 < a < 4.69999999999999998e-212 or 6.9999999999999996e-47 < a < 2.29999999999999989e-12

   1. Initial program 75.5%

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

      1. associate-+l- 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-*r* 83.7%

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

      4. *-commutative 83.7%

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

      5. associate-+l- 83.7%

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

      6. *-commutative 83.7%

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

      7. associate-*r* 75.5%

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

      8. *-commutative 75.5%

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

      9. associate-*l* 75.5%

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

      10. associate-*l* 83.8%

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

   3. Simplified 83.8%

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

      1. associate-+l- 83.8%

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

      2. div-sub 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* 77.6%

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

      5. associate-*l* 77.6%

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

      6. fma-neg 77.6%

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

   6. Applied egg-rr 77.6%

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

      1. associate-*r* 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 65.2%

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

      3. fma-udef 65.2%

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

      4. unsub-neg 65.2%

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

      5. *-commutative 65.2%

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

      6. *-commutative 65.2%

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

      7. associate-*l* 65.2%

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

      8. *-commutative 65.2%

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

   8. Simplified 65.2%

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

   9. Taylor expanded in c around 0 85.7%

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

   10. Taylor expanded in x around inf 48.0%

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

       1. times-frac 43.8%

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

   12. Simplified 43.8%

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

   if -2.10000000000000002e-203 < a < 4.90000000000000025e-306

   1. Initial program 85.7%

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

      1. associate-+l- 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-+l- 99.7%

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

      6. *-commutative 99.7%

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

      7. associate-*r* 85.7%

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

      8. *-commutative 85.7%

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

      9. associate-*l* 85.7%

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

      10. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around inf 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

      1. clear-num 61.3%

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

      2. inv-pow 61.3%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

      3. *-commutative 61.3%

         \[\leadsto {\left(\frac{\color{blue}{c \cdot z}}{b}\right)}^{-1} \]

   9. Applied egg-rr 61.3%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 61.3%

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

       2. associate-/l* 57.0%

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

   11. Simplified 57.0%

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

   if 4.69999999999999998e-212 < a < 6.9999999999999996e-47

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-+l- 82.6%

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

      6. *-commutative 82.6%

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

      7. associate-*r* 82.5%

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

      8. *-commutative 82.5%

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

      9. associate-*l* 82.5%

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

      10. associate-*l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in b around inf 54.9%

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

      1. *-commutative 54.9%

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

   7. Simplified 54.9%

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

      1. div-inv 55.0%

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

      2. *-commutative 55.0%

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

   9. Applied egg-rr 55.0%

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

       1. expm1-log1p-u 40.1%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 26.0%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 26.0%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 26.0%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 40.1%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 55.0%

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

       3. *-commutative 55.0%

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

       4. associate-/r* 56.8%

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

   13. Simplified 56.8%

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

   if 2.29999999999999989e-12 < 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* 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-+l- 70.8%

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

      6. *-commutative 70.8%

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

      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* 77.6%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

      1. associate-+l- 77.6%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 69.1%

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

      6. fma-neg 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. associate-*r* 69.1%

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

      2. times-frac 66.4%

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

      3. fma-udef 66.4%

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

      4. unsub-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in z around inf 43.5%

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

       1. *-commutative 43.5%

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

       2. associate-*l/ 56.0%

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

       3. *-commutative 56.0%

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

   11. Simplified 56.0%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-203}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-306}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-212}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-304}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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)))))
   (if (<= a -9.2e-120)
     (* -4.0 (/ a (/ c t)))
     (if (<= a -7.5e-215)
       t_1
       (if (<= a 2.2e-304)
         (/ 1.0 (/ c (/ b z)))
         (if (<= a 2.25e-185)
           (* 9.0 (* (/ x z) (/ y c)))
           (if (<= a 1.06e-47)
             (* b (/ (/ 1.0 c) z))
             (if (<= a 2.25e-12) t_1 (* -4.0 (* t (/ a c)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double tmp;
	if (a <= -9.2e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -7.5e-215) {
		tmp = t_1;
	} else if (a <= 2.2e-304) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 2.25e-185) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 1.06e-47) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.25e-12) {
		tmp = t_1;
	} 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.
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 / c) * (y / z))
    if (a <= (-9.2d-120)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-7.5d-215)) then
        tmp = t_1
    else if (a <= 2.2d-304) then
        tmp = 1.0d0 / (c / (b / z))
    else if (a <= 2.25d-185) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (a <= 1.06d-47) then
        tmp = b * ((1.0d0 / c) / z)
    else if (a <= 2.25d-12) then
        tmp = t_1
    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;
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 tmp;
	if (a <= -9.2e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -7.5e-215) {
		tmp = t_1;
	} else if (a <= 2.2e-304) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 2.25e-185) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 1.06e-47) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.25e-12) {
		tmp = t_1;
	} 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])
[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))
	tmp = 0
	if a <= -9.2e-120:
		tmp = -4.0 * (a / (c / t))
	elif a <= -7.5e-215:
		tmp = t_1
	elif a <= 2.2e-304:
		tmp = 1.0 / (c / (b / z))
	elif a <= 2.25e-185:
		tmp = 9.0 * ((x / z) * (y / c))
	elif a <= 1.06e-47:
		tmp = b * ((1.0 / c) / z)
	elif a <= 2.25e-12:
		tmp = t_1
	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])
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(Float64(x / c) * Float64(y / z)))
	tmp = 0.0
	if (a <= -9.2e-120)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -7.5e-215)
		tmp = t_1;
	elseif (a <= 2.2e-304)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (a <= 2.25e-185)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (a <= 1.06e-47)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (a <= 2.25e-12)
		tmp = t_1;
	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])){:}
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));
	tmp = 0.0;
	if (a <= -9.2e-120)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -7.5e-215)
		tmp = t_1;
	elseif (a <= 2.2e-304)
		tmp = 1.0 / (c / (b / z));
	elseif (a <= 2.25e-185)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (a <= 1.06e-47)
		tmp = b * ((1.0 / c) / z);
	elseif (a <= 2.25e-12)
		tmp = t_1;
	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.
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[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e-120], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-215], t$95$1, If[LessEqual[a, 2.2e-304], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-185], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e-47], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-12], t$95$1, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -9.19999999999999946e-120

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. *-commutative 76.2%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   if -9.19999999999999946e-120 < a < -7.49999999999999986e-215 or 1.06e-47 < a < 2.2499999999999999e-12

   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* 79.8%

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

      4. *-commutative 79.8%

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

      5. associate-+l- 79.8%

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

      6. *-commutative 79.8%

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

      7. associate-*r* 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* 76.6%

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

      10. associate-*l* 79.8%

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

   3. Simplified 79.8%

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

      1. associate-+l- 79.8%

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

      2. div-sub 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-*l* 69.5%

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

      5. associate-*l* 69.5%

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

      6. fma-neg 69.5%

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

   6. Applied egg-rr 69.5%

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

      1. associate-*r* 69.5%

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

      2. times-frac 59.4%

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

      3. fma-udef 59.4%

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

      4. unsub-neg 59.4%

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

      5. *-commutative 59.4%

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

      6. *-commutative 59.4%

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

      7. associate-*l* 59.4%

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

      8. *-commutative 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in c around 0 76.4%

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

   10. Taylor expanded in x around inf 40.6%

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

       1. times-frac 33.7%

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

   12. Simplified 33.7%

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

   if -7.49999999999999986e-215 < a < 2.2e-304

   1. Initial program 84.2%

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

      1. associate-+l- 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-*r* 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* 84.2%

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

      8. *-commutative 84.2%

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

      9. associate-*l* 84.2%

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

      10. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 62.5%

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

      1. *-commutative 62.5%

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

   7. Simplified 62.5%

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

      1. clear-num 62.3%

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

      2. inv-pow 62.3%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

      3. *-commutative 62.3%

         \[\leadsto {\left(\frac{\color{blue}{c \cdot z}}{b}\right)}^{-1} \]

   9. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 62.3%

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

       2. associate-/l* 57.5%

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

   11. Simplified 57.5%

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

   if 2.2e-304 < a < 2.2500000000000001e-185

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 91.9%

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

      4. *-commutative 91.9%

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

      5. associate-+l- 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 79.9%

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

      10. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l* 88.1%

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

      5. associate-*l* 88.1%

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

      6. fma-neg 88.1%

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

   6. Applied egg-rr 88.1%

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

      1. associate-*r* 88.0%

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

      2. times-frac 80.2%

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

      3. fma-udef 80.2%

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

      4. unsub-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-*l* 80.2%

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

      8. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in c around 0 99.8%

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

       1. *-commutative 99.8%

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

       2. *-un-lft-identity 99.8%

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

       3. times-frac 95.9%

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

   11. Applied egg-rr 95.9%

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

   12. Taylor expanded in y around inf 57.3%

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

       1. *-commutative 57.3%

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

       2. times-frac 53.5%

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

   14. Simplified 53.5%

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

   if 2.2500000000000001e-185 < a < 1.06e-47

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 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* 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 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

      1. div-inv 51.8%

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

      2. *-commutative 51.8%

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

   9. Applied egg-rr 51.8%

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

       1. expm1-log1p-u 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 26.1%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 26.1%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 26.1%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 51.8%

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

       3. *-commutative 51.8%

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

       4. associate-/r* 53.8%

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

   13. Simplified 53.8%

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

   if 2.2499999999999999e-12 < 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* 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-+l- 70.8%

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

      6. *-commutative 70.8%

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

      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* 77.6%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

      1. associate-+l- 77.6%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 69.1%

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

      6. fma-neg 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. associate-*r* 69.1%

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

      2. times-frac 66.4%

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

      3. fma-udef 66.4%

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

      4. unsub-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in z around inf 43.5%

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

       1. *-commutative 43.5%

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

       2. associate-*l/ 56.0%

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

       3. *-commutative 56.0%

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

   11. Simplified 56.0%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-215}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-304}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-218}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-180}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= a -1e-119)
   (* -4.0 (/ a (/ c t)))
   (if (<= a -8.8e-218)
     (* 9.0 (/ (* y x) (* z c)))
     (if (<= a -5e-309)
       (/ 1.0 (/ c (/ b z)))
       (if (<= a 1.5e-180)
         (* 9.0 (* (/ x z) (/ y c)))
         (if (<= a 5e-46)
           (* b (/ (/ 1.0 c) z))
           (if (<= a 2.25e-12)
             (* 9.0 (* (/ x c) (/ y z)))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -8.8e-218) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= -5e-309) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 1.5e-180) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 5e-46) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.25e-12) {
		tmp = 9.0 * ((x / c) * (y / z));
	} 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1d-119)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-8.8d-218)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= (-5d-309)) then
        tmp = 1.0d0 / (c / (b / z))
    else if (a <= 1.5d-180) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (a <= 5d-46) then
        tmp = b * ((1.0d0 / c) / z)
    else if (a <= 2.25d-12) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -8.8e-218) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= -5e-309) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 1.5e-180) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 5e-46) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.25e-12) {
		tmp = 9.0 * ((x / c) * (y / z));
	} 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])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1e-119:
		tmp = -4.0 * (a / (c / t))
	elif a <= -8.8e-218:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= -5e-309:
		tmp = 1.0 / (c / (b / z))
	elif a <= 1.5e-180:
		tmp = 9.0 * ((x / z) * (y / c))
	elif a <= 5e-46:
		tmp = b * ((1.0 / c) / z)
	elif a <= 2.25e-12:
		tmp = 9.0 * ((x / c) * (y / z))
	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])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1e-119)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -8.8e-218)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= -5e-309)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (a <= 1.5e-180)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (a <= 5e-46)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (a <= 2.25e-12)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	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])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1e-119)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -8.8e-218)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= -5e-309)
		tmp = 1.0 / (c / (b / z));
	elseif (a <= 1.5e-180)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (a <= 5e-46)
		tmp = b * ((1.0 / c) / z);
	elseif (a <= 2.25e-12)
		tmp = 9.0 * ((x / c) * (y / z));
	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.
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[a, -1e-119], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.8e-218], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-309], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-180], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-46], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-12], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.00000000000000001e-119

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. *-commutative 76.2%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   if -1.00000000000000001e-119 < a < -8.80000000000000028e-218

   1. Initial program 89.5%

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

      1. associate-+l- 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*r* 94.5%

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

      4. *-commutative 94.5%

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

      5. associate-+l- 94.5%

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

      6. *-commutative 94.5%

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

      7. associate-*r* 89.5%

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

      8. *-commutative 89.5%

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

      9. associate-*l* 89.5%

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

      10. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around inf 48.5%

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

   if -8.80000000000000028e-218 < a < -4.9999999999999995e-309

   1. Initial program 83.3%

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

      1. associate-+l- 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*r* 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* 83.3%

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

      8. *-commutative 83.3%

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

      9. associate-*l* 83.3%

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

      10. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 60.4%

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

      1. *-commutative 60.4%

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

   7. Simplified 60.4%

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

      1. clear-num 60.3%

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

      2. inv-pow 60.3%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

      3. *-commutative 60.3%

         \[\leadsto {\left(\frac{\color{blue}{c \cdot z}}{b}\right)}^{-1} \]

   9. Applied egg-rr 60.3%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 60.3%

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

       2. associate-/l* 55.1%

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

   11. Simplified 55.1%

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

   if -4.9999999999999995e-309 < a < 1.5e-180

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 91.9%

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

      4. *-commutative 91.9%

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

      5. associate-+l- 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 79.9%

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

      10. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l* 88.1%

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

      5. associate-*l* 88.1%

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

      6. fma-neg 88.1%

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

   6. Applied egg-rr 88.1%

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

      1. associate-*r* 88.0%

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

      2. times-frac 80.2%

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

      3. fma-udef 80.2%

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

      4. unsub-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-*l* 80.2%

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

      8. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in c around 0 99.8%

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

       1. *-commutative 99.8%

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

       2. *-un-lft-identity 99.8%

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

       3. times-frac 95.9%

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

   11. Applied egg-rr 95.9%

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

   12. Taylor expanded in y around inf 57.3%

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

       1. *-commutative 57.3%

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

       2. times-frac 53.5%

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

   14. Simplified 53.5%

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

   if 1.5e-180 < a < 4.99999999999999992e-46

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 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* 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 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

      1. div-inv 51.8%

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

      2. *-commutative 51.8%

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

   9. Applied egg-rr 51.8%

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

       1. expm1-log1p-u 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 26.1%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 26.1%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 26.1%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 51.8%

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

       3. *-commutative 51.8%

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

       4. associate-/r* 53.8%

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

   13. Simplified 53.8%

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

   if 4.99999999999999992e-46 < a < 2.2499999999999999e-12

   1. Initial program 56.4%

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

      1. associate-+l- 56.4%

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

      2. *-commutative 56.4%

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

      3. associate-*r* 56.4%

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

      4. *-commutative 56.4%

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

      5. associate-+l- 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-*r* 56.4%

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

      8. *-commutative 56.4%

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

      9. associate-*l* 56.4%

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

      10. associate-*l* 56.4%

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

   3. Simplified 56.4%

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

      1. associate-+l- 56.4%

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

      2. div-sub 56.4%

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

      3. *-commutative 56.4%

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

      4. associate-*l* 56.3%

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

      5. associate-*l* 56.3%

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

      6. fma-neg 56.3%

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

   6. Applied egg-rr 56.3%

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

      1. associate-*r* 56.4%

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

      2. times-frac 65.1%

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

      3. fma-udef 65.1%

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

      4. unsub-neg 65.1%

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

      5. *-commutative 65.1%

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

      6. *-commutative 65.1%

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

      7. associate-*l* 65.1%

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

      8. *-commutative 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in c around 0 82.4%

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

   10. Taylor expanded in x around inf 23.5%

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

       1. times-frac 32.1%

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

   12. Simplified 32.1%

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

   if 2.2499999999999999e-12 < 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* 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-+l- 70.8%

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

      6. *-commutative 70.8%

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

      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* 77.6%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

      1. associate-+l- 77.6%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 69.1%

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

      6. fma-neg 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. associate-*r* 69.1%

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

      2. times-frac 66.4%

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

      3. fma-udef 66.4%

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

      4. unsub-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in z around inf 43.5%

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

       1. *-commutative 43.5%

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

       2. associate-*l/ 56.0%

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

       3. *-commutative 56.0%

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

   11. Simplified 56.0%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-218}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-180}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-209}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= a -1.45e-119)
   (* -4.0 (/ a (/ c t)))
   (if (<= a -7e-209)
     (* 9.0 (/ (* y x) (* z c)))
     (if (<= a 2.4e-303)
       (/ 1.0 (/ c (/ b z)))
       (if (<= a 5.8e-183)
         (* 9.0 (* (/ x z) (/ y c)))
         (if (<= a 2.9e-46)
           (* b (/ (/ 1.0 c) z))
           (if (<= a 2.25e-12)
             (* (/ (* 9.0 y) z) (/ x c))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.45e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -7e-209) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 2.4e-303) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 5.8e-183) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 2.9e-46) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.25e-12) {
		tmp = ((9.0 * y) / z) * (x / 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1.45d-119)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-7d-209)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= 2.4d-303) then
        tmp = 1.0d0 / (c / (b / z))
    else if (a <= 5.8d-183) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (a <= 2.9d-46) then
        tmp = b * ((1.0d0 / c) / z)
    else if (a <= 2.25d-12) then
        tmp = ((9.0d0 * y) / z) * (x / 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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.45e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -7e-209) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 2.4e-303) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 5.8e-183) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (a <= 2.9e-46) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.25e-12) {
		tmp = ((9.0 * y) / z) * (x / 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])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.45e-119:
		tmp = -4.0 * (a / (c / t))
	elif a <= -7e-209:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= 2.4e-303:
		tmp = 1.0 / (c / (b / z))
	elif a <= 5.8e-183:
		tmp = 9.0 * ((x / z) * (y / c))
	elif a <= 2.9e-46:
		tmp = b * ((1.0 / c) / z)
	elif a <= 2.25e-12:
		tmp = ((9.0 * y) / z) * (x / 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])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.45e-119)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -7e-209)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= 2.4e-303)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (a <= 5.8e-183)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (a <= 2.9e-46)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (a <= 2.25e-12)
		tmp = Float64(Float64(Float64(9.0 * y) / z) * Float64(x / 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])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.45e-119)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -7e-209)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= 2.4e-303)
		tmp = 1.0 / (c / (b / z));
	elseif (a <= 5.8e-183)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (a <= 2.9e-46)
		tmp = b * ((1.0 / c) / z);
	elseif (a <= 2.25e-12)
		tmp = ((9.0 * y) / z) * (x / 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.
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[a, -1.45e-119], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-209], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-303], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-183], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-46], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-12], N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.45e-119

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. *-commutative 76.2%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   if -1.45e-119 < a < -7.00000000000000004e-209

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-*r* 93.8%

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

      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* 88.3%

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

      8. *-commutative 88.3%

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

      9. associate-*l* 88.3%

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

      10. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf 48.2%

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

   if -7.00000000000000004e-209 < a < 2.4000000000000001e-303

   1. Initial program 85.0%

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

      1. associate-+l- 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-*r* 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* 85.0%

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

      8. *-commutative 85.0%

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

      9. associate-*l* 85.0%

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

      10. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 59.5%

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

      1. *-commutative 59.5%

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

   7. Simplified 59.5%

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

      1. clear-num 59.4%

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

      2. inv-pow 59.4%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

      3. *-commutative 59.4%

         \[\leadsto {\left(\frac{\color{blue}{c \cdot z}}{b}\right)}^{-1} \]

   9. Applied egg-rr 59.4%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 59.4%

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

       2. associate-/l* 54.8%

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

   11. Simplified 54.8%

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

   if 2.4000000000000001e-303 < a < 5.8000000000000001e-183

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 91.9%

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

      4. *-commutative 91.9%

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

      5. associate-+l- 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 79.9%

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

      10. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l* 88.1%

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

      5. associate-*l* 88.1%

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

      6. fma-neg 88.1%

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

   6. Applied egg-rr 88.1%

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

      1. associate-*r* 88.0%

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

      2. times-frac 80.2%

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

      3. fma-udef 80.2%

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

      4. unsub-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-*l* 80.2%

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

      8. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in c around 0 99.8%

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

       1. *-commutative 99.8%

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

       2. *-un-lft-identity 99.8%

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

       3. times-frac 95.9%

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

   11. Applied egg-rr 95.9%

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

   12. Taylor expanded in y around inf 57.3%

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

       1. *-commutative 57.3%

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

       2. times-frac 53.5%

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

   14. Simplified 53.5%

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

   if 5.8000000000000001e-183 < a < 2.90000000000000005e-46

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 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* 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 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

      1. div-inv 51.8%

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

      2. *-commutative 51.8%

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

   9. Applied egg-rr 51.8%

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

       1. expm1-log1p-u 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 26.1%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 26.1%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 26.1%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 51.8%

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

       3. *-commutative 51.8%

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

       4. associate-/r* 53.8%

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

   13. Simplified 53.8%

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

   if 2.90000000000000005e-46 < a < 2.2499999999999999e-12

   1. Initial program 56.4%

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

      1. associate-+l- 56.4%

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

      2. *-commutative 56.4%

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

      3. associate-*r* 56.4%

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

      4. *-commutative 56.4%

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

      5. associate-+l- 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-*r* 56.4%

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

      8. *-commutative 56.4%

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

      9. associate-*l* 56.4%

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

      10. associate-*l* 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in x around inf 23.5%

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

      1. associate-*r/ 23.5%

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

      2. *-commutative 23.5%

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

      3. associate-*r* 23.5%

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

      4. *-commutative 23.5%

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

      5. times-frac 32.1%

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

   7. Simplified 32.1%

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

   if 2.2499999999999999e-12 < 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* 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-+l- 70.8%

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

      6. *-commutative 70.8%

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

      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* 77.6%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

      1. associate-+l- 77.6%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 69.1%

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

      6. fma-neg 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. associate-*r* 69.1%

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

      2. times-frac 66.4%

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

      3. fma-udef 66.4%

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

      4. unsub-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in z around inf 43.5%

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

       1. *-commutative 43.5%

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

       2. associate-*l/ 56.0%

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

       3. *-commutative 56.0%

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

   11. Simplified 56.0%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-209}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-12}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-208}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= a -1.4e-119)
   (* -4.0 (/ a (/ c t)))
   (if (<= a -1.35e-208)
     (* 9.0 (/ (* y x) (* z c)))
     (if (<= a 2.8e-306)
       (/ 1.0 (/ c (/ b z)))
       (if (<= a 1.66e-183)
         (/ (* 9.0 (/ (* y x) z)) c)
         (if (<= a 9.5e-46)
           (* b (/ (/ 1.0 c) z))
           (if (<= a 2.4e-12)
             (* (/ (* 9.0 y) z) (/ x c))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.4e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -1.35e-208) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 2.8e-306) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 1.66e-183) {
		tmp = (9.0 * ((y * x) / z)) / c;
	} else if (a <= 9.5e-46) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.4e-12) {
		tmp = ((9.0 * y) / z) * (x / 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1.4d-119)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-1.35d-208)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= 2.8d-306) then
        tmp = 1.0d0 / (c / (b / z))
    else if (a <= 1.66d-183) then
        tmp = (9.0d0 * ((y * x) / z)) / c
    else if (a <= 9.5d-46) then
        tmp = b * ((1.0d0 / c) / z)
    else if (a <= 2.4d-12) then
        tmp = ((9.0d0 * y) / z) * (x / 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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.4e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -1.35e-208) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 2.8e-306) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 1.66e-183) {
		tmp = (9.0 * ((y * x) / z)) / c;
	} else if (a <= 9.5e-46) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.4e-12) {
		tmp = ((9.0 * y) / z) * (x / 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])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.4e-119:
		tmp = -4.0 * (a / (c / t))
	elif a <= -1.35e-208:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= 2.8e-306:
		tmp = 1.0 / (c / (b / z))
	elif a <= 1.66e-183:
		tmp = (9.0 * ((y * x) / z)) / c
	elif a <= 9.5e-46:
		tmp = b * ((1.0 / c) / z)
	elif a <= 2.4e-12:
		tmp = ((9.0 * y) / z) * (x / 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])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.4e-119)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -1.35e-208)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= 2.8e-306)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (a <= 1.66e-183)
		tmp = Float64(Float64(9.0 * Float64(Float64(y * x) / z)) / c);
	elseif (a <= 9.5e-46)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (a <= 2.4e-12)
		tmp = Float64(Float64(Float64(9.0 * y) / z) * Float64(x / 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])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.4e-119)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -1.35e-208)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= 2.8e-306)
		tmp = 1.0 / (c / (b / z));
	elseif (a <= 1.66e-183)
		tmp = (9.0 * ((y * x) / z)) / c;
	elseif (a <= 9.5e-46)
		tmp = b * ((1.0 / c) / z);
	elseif (a <= 2.4e-12)
		tmp = ((9.0 * y) / z) * (x / 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.
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[a, -1.4e-119], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e-208], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-306], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.66e-183], N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 9.5e-46], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-12], N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.4e-119

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. *-commutative 76.2%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   if -1.4e-119 < a < -1.35e-208

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-*r* 93.8%

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

      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* 88.3%

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

      8. *-commutative 88.3%

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

      9. associate-*l* 88.3%

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

      10. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf 48.2%

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

   if -1.35e-208 < a < 2.8000000000000001e-306

   1. Initial program 85.0%

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

      1. associate-+l- 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-*r* 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* 85.0%

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

      8. *-commutative 85.0%

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

      9. associate-*l* 85.0%

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

      10. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 59.5%

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

      1. *-commutative 59.5%

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

   7. Simplified 59.5%

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

      1. clear-num 59.4%

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

      2. inv-pow 59.4%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

      3. *-commutative 59.4%

         \[\leadsto {\left(\frac{\color{blue}{c \cdot z}}{b}\right)}^{-1} \]

   9. Applied egg-rr 59.4%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 59.4%

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

       2. associate-/l* 54.8%

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

   11. Simplified 54.8%

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

   if 2.8000000000000001e-306 < a < 1.66e-183

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 91.9%

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

      4. *-commutative 91.9%

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

      5. associate-+l- 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 79.9%

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

      10. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l* 88.1%

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

      5. associate-*l* 88.1%

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

      6. fma-neg 88.1%

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

   6. Applied egg-rr 88.1%

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

      1. associate-*r* 88.0%

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

      2. times-frac 80.2%

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

      3. fma-udef 80.2%

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

      4. unsub-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-*l* 80.2%

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

      8. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in c around 0 99.8%

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

   10. Taylor expanded in x around inf 61.3%

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

   if 1.66e-183 < a < 9.49999999999999993e-46

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 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* 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 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

      1. div-inv 51.8%

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

      2. *-commutative 51.8%

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

   9. Applied egg-rr 51.8%

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

       1. expm1-log1p-u 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 26.1%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 26.1%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 26.1%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 51.8%

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

       3. *-commutative 51.8%

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

       4. associate-/r* 53.8%

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

   13. Simplified 53.8%

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

   if 9.49999999999999993e-46 < a < 2.39999999999999987e-12

   1. Initial program 56.4%

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

      1. associate-+l- 56.4%

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

      2. *-commutative 56.4%

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

      3. associate-*r* 56.4%

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

      4. *-commutative 56.4%

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

      5. associate-+l- 56.4%

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

      6. *-commutative 56.4%

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

      7. associate-*r* 56.4%

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

      8. *-commutative 56.4%

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

      9. associate-*l* 56.4%

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

      10. associate-*l* 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in x around inf 23.5%

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

      1. associate-*r/ 23.5%

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

      2. *-commutative 23.5%

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

      3. associate-*r* 23.5%

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

      4. *-commutative 23.5%

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

      5. times-frac 32.1%

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

   7. Simplified 32.1%

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

   if 2.39999999999999987e-12 < 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* 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-+l- 70.8%

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

      6. *-commutative 70.8%

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

      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* 77.6%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

      1. associate-+l- 77.6%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 69.1%

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

      6. fma-neg 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. associate-*r* 69.1%

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

      2. times-frac 66.4%

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

      3. fma-udef 66.4%

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

      4. unsub-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

      7. associate-*l* 66.4%

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

      8. *-commutative 66.4%

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

   8. Simplified 66.4%

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

   9. Taylor expanded in z around inf 43.5%

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

       1. *-commutative 43.5%

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

       2. associate-*l/ 56.0%

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

       3. *-commutative 56.0%

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

   11. Simplified 56.0%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-208}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-213}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-309}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= a -1.5e-120)
   (* -4.0 (/ a (/ c t)))
   (if (<= a -1.22e-213)
     (* 9.0 (/ (* y x) (* z c)))
     (if (<= a 5e-309)
       (/ 1.0 (/ c (/ b z)))
       (if (<= a 1.2e-185)
         (/ (/ (* y (* 9.0 x)) z) c)
         (if (<= a 4.1e-47)
           (* b (/ (/ 1.0 c) z))
           (if (<= a 2.5e-12)
             (* (/ (* 9.0 y) z) (/ x c))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.5e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -1.22e-213) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 5e-309) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 1.2e-185) {
		tmp = ((y * (9.0 * x)) / z) / c;
	} else if (a <= 4.1e-47) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.5e-12) {
		tmp = ((9.0 * y) / z) * (x / 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1.5d-120)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-1.22d-213)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= 5d-309) then
        tmp = 1.0d0 / (c / (b / z))
    else if (a <= 1.2d-185) then
        tmp = ((y * (9.0d0 * x)) / z) / c
    else if (a <= 4.1d-47) then
        tmp = b * ((1.0d0 / c) / z)
    else if (a <= 2.5d-12) then
        tmp = ((9.0d0 * y) / z) * (x / 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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.5e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -1.22e-213) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 5e-309) {
		tmp = 1.0 / (c / (b / z));
	} else if (a <= 1.2e-185) {
		tmp = ((y * (9.0 * x)) / z) / c;
	} else if (a <= 4.1e-47) {
		tmp = b * ((1.0 / c) / z);
	} else if (a <= 2.5e-12) {
		tmp = ((9.0 * y) / z) * (x / 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])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.5e-120:
		tmp = -4.0 * (a / (c / t))
	elif a <= -1.22e-213:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= 5e-309:
		tmp = 1.0 / (c / (b / z))
	elif a <= 1.2e-185:
		tmp = ((y * (9.0 * x)) / z) / c
	elif a <= 4.1e-47:
		tmp = b * ((1.0 / c) / z)
	elif a <= 2.5e-12:
		tmp = ((9.0 * y) / z) * (x / 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])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.5e-120)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -1.22e-213)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= 5e-309)
		tmp = Float64(1.0 / Float64(c / Float64(b / z)));
	elseif (a <= 1.2e-185)
		tmp = Float64(Float64(Float64(y * Float64(9.0 * x)) / z) / c);
	elseif (a <= 4.1e-47)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	elseif (a <= 2.5e-12)
		tmp = Float64(Float64(Float64(9.0 * y) / z) * Float64(x / 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])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.5e-120)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -1.22e-213)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= 5e-309)
		tmp = 1.0 / (c / (b / z));
	elseif (a <= 1.2e-185)
		tmp = ((y * (9.0 * x)) / z) / c;
	elseif (a <= 4.1e-47)
		tmp = b * ((1.0 / c) / z);
	elseif (a <= 2.5e-12)
		tmp = ((9.0 * y) / z) * (x / 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.
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[a, -1.5e-120], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.22e-213], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-309], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-185], N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 4.1e-47], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-12], N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.50000000000000005e-120

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. *-commutative 76.2%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 78.2%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   if -1.50000000000000005e-120 < a < -1.22e-213

   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* 94.2%

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

      4. *-commutative 94.2%

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

      5. associate-+l- 94.2%

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

      6. *-commutative 94.2%

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

      7. associate-*r* 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* 88.9%

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

      10. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in x around inf 51.0%

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

   if -1.22e-213 < a < 4.9999999999999995e-309

   1. Initial program 84.2%

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

      1. associate-+l- 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-*r* 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* 84.2%

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

      8. *-commutative 84.2%

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

      9. associate-*l* 84.2%

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

      10. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 62.5%

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

      1. *-commutative 62.5%

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

   7. Simplified 62.5%

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

      1. clear-num 62.3%

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

      2. inv-pow 62.3%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

      3. *-commutative 62.3%

         \[\leadsto {\left(\frac{\color{blue}{c \cdot z}}{b}\right)}^{-1} \]

   9. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{{\left(\frac{c \cdot z}{b}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 62.3%

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

       2. associate-/l* 57.5%

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

   11. Simplified 57.5%

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

   if 4.9999999999999995e-309 < a < 1.2000000000000001e-185

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. associate-*r* 91.9%

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

      4. *-commutative 91.9%

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

      5. associate-+l- 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*l* 79.9%

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

      10. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*l* 88.1%

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

      5. associate-*l* 88.1%

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

      6. fma-neg 88.1%

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

   6. Applied egg-rr 88.1%

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

      1. associate-*r* 88.0%

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

      2. times-frac 80.2%

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

      3. fma-udef 80.2%

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

      4. unsub-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. *-commutative 80.2%

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

      7. associate-*l* 80.2%

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

      8. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in c around 0 99.8%

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

   10. Taylor expanded in x around inf 61.3%

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

       1. associate-*r/ 61.3%

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

       2. associate-*r* 61.2%

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

   12. Simplified 61.2%

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

   if 1.2000000000000001e-185 < a < 4.10000000000000002e-47

   1. Initial program 79.9%

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

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 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* 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 51.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 51.8%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      2. *-commutative 51.8%

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

   9. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 26.1%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 26.1%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 26.1%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 38.5%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 51.8%

          \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

       3. *-commutative 51.8%

          \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

       4. associate-/r* 53.8%

          \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]

   13. Simplified 53.8%

       \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]

   if 4.10000000000000002e-47 < a < 2.49999999999999985e-12

   1. Initial program 56.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 56.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 56.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 56.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 56.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 56.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 56.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 23.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 23.5%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 23.5%

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* 23.5%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. *-commutative 23.5%

         \[\leadsto \frac{\left(9 \cdot y\right) \cdot x}{\color{blue}{z \cdot c}} \]

      5. times-frac 32.1%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   7. Simplified 32.1%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} \]

   if 2.49999999999999985e-12 < 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* 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 70.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      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* 77.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 77.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 77.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 69.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 69.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 69.1%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 69.1%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 69.1%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 69.1%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 69.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 66.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 66.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 66.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 66.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 66.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 66.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 66.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 66.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 43.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 43.5%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 56.0%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 56.0%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 56.0%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-213}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-309}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+178}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 68000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (/ z y))) (* t (* a -4.0))) c)))
   (if (<= t -7.8e+210)
     t_1
     (if (<= t -1.05e+178)
       (/ (/ (+ b (* y (* 9.0 x))) z) c)
       (if (<= t -2e+87)
         t_1
         (if (<= t -2.15e-122)
           (/ (- (/ b z) (* 4.0 (* a t))) c)
           (if (<= t 68000000000.0)
             (/ (+ b (* 9.0 (* y x))) (* z c))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
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 / (z / y))) + (t * (a * -4.0))) / c;
	double tmp;
	if (t <= -7.8e+210) {
		tmp = t_1;
	} else if (t <= -1.05e+178) {
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	} else if (t <= -2e+87) {
		tmp = t_1;
	} else if (t <= -2.15e-122) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 68000000000.0) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 / (z / y))) + (t * (a * (-4.0d0)))) / c
    if (t <= (-7.8d+210)) then
        tmp = t_1
    else if (t <= (-1.05d+178)) then
        tmp = ((b + (y * (9.0d0 * x))) / z) / c
    else if (t <= (-2d+87)) then
        tmp = t_1
    else if (t <= (-2.15d-122)) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else if (t <= 68000000000.0d0) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 / (z / y))) + (t * (a * -4.0))) / c;
	double tmp;
	if (t <= -7.8e+210) {
		tmp = t_1;
	} else if (t <= -1.05e+178) {
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	} else if (t <= -2e+87) {
		tmp = t_1;
	} else if (t <= -2.15e-122) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 68000000000.0) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 / (z / y))) + (t * (a * -4.0))) / c
	tmp = 0
	if t <= -7.8e+210:
		tmp = t_1
	elif t <= -1.05e+178:
		tmp = ((b + (y * (9.0 * x))) / z) / c
	elif t <= -2e+87:
		tmp = t_1
	elif t <= -2.15e-122:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	elif t <= 68000000000.0:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(x / Float64(z / y))) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (t <= -7.8e+210)
		tmp = t_1;
	elseif (t <= -1.05e+178)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(9.0 * x))) / z) / c);
	elseif (t <= -2e+87)
		tmp = t_1;
	elseif (t <= -2.15e-122)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	elseif (t <= 68000000000.0)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(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])){:}
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 / (z / y))) + (t * (a * -4.0))) / c;
	tmp = 0.0;
	if (t <= -7.8e+210)
		tmp = t_1;
	elseif (t <= -1.05e+178)
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	elseif (t <= -2e+87)
		tmp = t_1;
	elseif (t <= -2.15e-122)
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	elseif (t <= 68000000000.0)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t, -7.8e+210], t$95$1, If[LessEqual[t, -1.05e+178], N[(N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -2e+87], t$95$1, If[LessEqual[t, -2.15e-122], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 68000000000.0], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.8e210 or -1.0499999999999999e178 < t < -1.9999999999999999e87

   1. Initial program 62.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 62.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 62.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 67.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 62.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 62.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 62.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 67.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 67.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 65.0%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 65.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 65.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 65.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 65.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 65.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 60.5%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 60.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 60.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 60.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 60.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 60.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 60.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 83.5%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 83.5%

          \[\leadsto \frac{\left(9 \cdot \frac{\color{blue}{y \cdot x}}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       2. *-un-lft-identity 83.5%

          \[\leadsto \frac{\left(9 \cdot \frac{y \cdot x}{\color{blue}{1 \cdot z}} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       3. times-frac 86.1%

          \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   11. Applied egg-rr 86.1%

       \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   12. Taylor expanded in b around 0 79.0%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv 79.0%

          \[\leadsto \frac{\color{blue}{9 \cdot \frac{x \cdot y}{z} + \left(-4\right) \cdot \left(a \cdot t\right)}}{c} \]

       2. associate-/l* 81.5%

          \[\leadsto \frac{9 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \left(-4\right) \cdot \left(a \cdot t\right)}{c} \]

       3. metadata-eval 81.5%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

       4. associate-*r* 81.5%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

       5. *-commutative 81.5%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(a \cdot -4\right)} \cdot t}{c} \]

       6. *-commutative 81.5%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{t \cdot \left(a \cdot -4\right)}}{c} \]

   14. Simplified 81.5%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}} \]

   if -7.8e210 < t < -1.0499999999999999e178

   1. Initial program 71.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 85.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 85.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 71.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 71.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 71.2%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 71.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 71.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 71.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 85.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 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 z around 0 71.9%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
   11. Step-by-step derivation

       1. associate-*r* 71.9%

          \[\leadsto \frac{\frac{b + \color{blue}{\left(9 \cdot x\right) \cdot y}}{z}}{c} \]

   12. Simplified 71.9%

       \[\leadsto \frac{\color{blue}{\frac{b + \left(9 \cdot x\right) \cdot y}{z}}}{c} \]

   if -1.9999999999999999e87 < t < -2.15000000000000009e-122

   1. Initial program 74.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 74.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 74.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 74.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 74.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 74.4%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 74.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 74.5%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 74.5%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 74.5%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 74.5%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 74.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 75.3%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 84.7%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 82.5%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -2.15000000000000009e-122 < t < 6.8e10

   1. Initial program 87.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 87.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 87.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.3%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 6.8e10 < t

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+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* 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 83.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      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* 77.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 82.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 72.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 72.8%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 72.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 72.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 69.8%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 50.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 50.4%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 53.3%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 53.3%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 53.3%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+210}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+178}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 68000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -2.52 \cdot 10^{+213}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+178}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} - t\_1}{c}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{b}{z} - t\_1}{c}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 t))))
   (if (<= t -2.52e+213)
     (/ (+ (* 9.0 (/ x (/ z y))) (* t (* a -4.0))) c)
     (if (<= t -1.05e+178)
       (/ (/ (+ b (* y (* 9.0 x))) z) c)
       (if (<= t -2.8e+87)
         (/ (- (* 9.0 (/ (* y x) z)) t_1) c)
         (if (<= t -3.9e-118)
           (/ (- (/ b z) t_1) c)
           (if (<= t 1.16e+24)
             (/ (+ b (* 9.0 (* y x))) (* z c))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
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 * t);
	double tmp;
	if (t <= -2.52e+213) {
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	} else if (t <= -1.05e+178) {
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	} else if (t <= -2.8e+87) {
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c;
	} else if (t <= -3.9e-118) {
		tmp = ((b / z) - t_1) / c;
	} else if (t <= 1.16e+24) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 * (a * t)
    if (t <= (-2.52d+213)) then
        tmp = ((9.0d0 * (x / (z / y))) + (t * (a * (-4.0d0)))) / c
    else if (t <= (-1.05d+178)) then
        tmp = ((b + (y * (9.0d0 * x))) / z) / c
    else if (t <= (-2.8d+87)) then
        tmp = ((9.0d0 * ((y * x) / z)) - t_1) / c
    else if (t <= (-3.9d-118)) then
        tmp = ((b / z) - t_1) / c
    else if (t <= 1.16d+24) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 * t);
	double tmp;
	if (t <= -2.52e+213) {
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	} else if (t <= -1.05e+178) {
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	} else if (t <= -2.8e+87) {
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c;
	} else if (t <= -3.9e-118) {
		tmp = ((b / z) - t_1) / c;
	} else if (t <= 1.16e+24) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 * t)
	tmp = 0
	if t <= -2.52e+213:
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c
	elif t <= -1.05e+178:
		tmp = ((b + (y * (9.0 * x))) / z) / c
	elif t <= -2.8e+87:
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c
	elif t <= -3.9e-118:
		tmp = ((b / z) - t_1) / c
	elif t <= 1.16e+24:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 * t))
	tmp = 0.0
	if (t <= -2.52e+213)
		tmp = Float64(Float64(Float64(9.0 * Float64(x / Float64(z / y))) + Float64(t * Float64(a * -4.0))) / c);
	elseif (t <= -1.05e+178)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(9.0 * x))) / z) / c);
	elseif (t <= -2.8e+87)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / z)) - t_1) / c);
	elseif (t <= -3.9e-118)
		tmp = Float64(Float64(Float64(b / z) - t_1) / c);
	elseif (t <= 1.16e+24)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(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])){:}
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 * t);
	tmp = 0.0;
	if (t <= -2.52e+213)
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	elseif (t <= -1.05e+178)
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	elseif (t <= -2.8e+87)
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c;
	elseif (t <= -3.9e-118)
		tmp = ((b / z) - t_1) / c;
	elseif (t <= 1.16e+24)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.52e+213], N[(N[(N[(9.0 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -1.05e+178], N[(N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -2.8e+87], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -3.9e-118], N[(N[(N[(b / z), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 1.16e+24], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.5200000000000001e213

   1. Initial program 54.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 54.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 54.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 59.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 59.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 59.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 59.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 54.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 54.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 54.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 59.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 59.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 55.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 55.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 55.1%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 55.1%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 55.1%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 55.1%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 55.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 64.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 64.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 64.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 64.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 64.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 64.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 64.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 64.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 77.4%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 77.4%

          \[\leadsto \frac{\left(9 \cdot \frac{\color{blue}{y \cdot x}}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       2. *-un-lft-identity 77.4%

          \[\leadsto \frac{\left(9 \cdot \frac{y \cdot x}{\color{blue}{1 \cdot z}} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       3. times-frac 82.3%

          \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   11. Applied egg-rr 82.3%

       \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   12. Taylor expanded in b around 0 82.0%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv 82.0%

          \[\leadsto \frac{\color{blue}{9 \cdot \frac{x \cdot y}{z} + \left(-4\right) \cdot \left(a \cdot t\right)}}{c} \]

       2. associate-/l* 86.9%

          \[\leadsto \frac{9 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \left(-4\right) \cdot \left(a \cdot t\right)}{c} \]

       3. metadata-eval 86.9%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

       4. associate-*r* 86.9%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

       5. *-commutative 86.9%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(a \cdot -4\right)} \cdot t}{c} \]

       6. *-commutative 86.9%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{t \cdot \left(a \cdot -4\right)}}{c} \]

   14. Simplified 86.9%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}} \]

   if -2.5200000000000001e213 < t < -1.0499999999999999e178

   1. Initial program 71.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 85.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 85.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 71.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 71.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 71.2%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 71.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 71.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 71.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 85.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 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 z around 0 71.9%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
   11. Step-by-step derivation

       1. associate-*r* 71.9%

          \[\leadsto \frac{\frac{b + \color{blue}{\left(9 \cdot x\right) \cdot y}}{z}}{c} \]

   12. Simplified 71.9%

       \[\leadsto \frac{\color{blue}{\frac{b + \left(9 \cdot x\right) \cdot y}{z}}}{c} \]

   if -1.0499999999999999e178 < t < -2.80000000000000015e87

   1. Initial program 71.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 75.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 75.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 55.9%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   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 b around 0 75.7%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -2.80000000000000015e87 < t < -3.90000000000000001e-118

   1. Initial program 74.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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* 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 74.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 74.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 73.8%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 73.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 73.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 73.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 73.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 73.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 74.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 74.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 84.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 82.0%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -3.90000000000000001e-118 < t < 1.16000000000000005e24

   1. Initial program 88.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 88.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 88.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 88.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 88.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.8%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 1.16000000000000005e24 < t

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 76.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 81.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 81.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 71.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 71.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 71.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 71.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 71.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 71.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 70.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 70.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 51.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 51.9%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 54.9%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 54.9%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 54.9%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.52 \cdot 10^{+213}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+178}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+206}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+177}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} - t\_1}{c}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{b}{z} - t\_1}{c}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 t))))
   (if (<= t -2.7e+206)
     (/ (+ (* 9.0 (/ x (/ z y))) (* t (* a -4.0))) c)
     (if (<= t -7.6e+177)
       (+ (* (/ (* 9.0 y) z) (/ x c)) (/ (/ b c) z))
       (if (<= t -3.9e+87)
         (/ (- (* 9.0 (/ (* y x) z)) t_1) c)
         (if (<= t -2.7e-121)
           (/ (- (/ b z) t_1) c)
           (if (<= t 5.9e+23)
             (/ (+ b (* 9.0 (* y x))) (* z c))
             (* -4.0 (* t (/ a c))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
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 * t);
	double tmp;
	if (t <= -2.7e+206) {
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	} else if (t <= -7.6e+177) {
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z);
	} else if (t <= -3.9e+87) {
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c;
	} else if (t <= -2.7e-121) {
		tmp = ((b / z) - t_1) / c;
	} else if (t <= 5.9e+23) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 * (a * t)
    if (t <= (-2.7d+206)) then
        tmp = ((9.0d0 * (x / (z / y))) + (t * (a * (-4.0d0)))) / c
    else if (t <= (-7.6d+177)) then
        tmp = (((9.0d0 * y) / z) * (x / c)) + ((b / c) / z)
    else if (t <= (-3.9d+87)) then
        tmp = ((9.0d0 * ((y * x) / z)) - t_1) / c
    else if (t <= (-2.7d-121)) then
        tmp = ((b / z) - t_1) / c
    else if (t <= 5.9d+23) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 * t);
	double tmp;
	if (t <= -2.7e+206) {
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	} else if (t <= -7.6e+177) {
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z);
	} else if (t <= -3.9e+87) {
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c;
	} else if (t <= -2.7e-121) {
		tmp = ((b / z) - t_1) / c;
	} else if (t <= 5.9e+23) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 * t)
	tmp = 0
	if t <= -2.7e+206:
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c
	elif t <= -7.6e+177:
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z)
	elif t <= -3.9e+87:
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c
	elif t <= -2.7e-121:
		tmp = ((b / z) - t_1) / c
	elif t <= 5.9e+23:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 * t))
	tmp = 0.0
	if (t <= -2.7e+206)
		tmp = Float64(Float64(Float64(9.0 * Float64(x / Float64(z / y))) + Float64(t * Float64(a * -4.0))) / c);
	elseif (t <= -7.6e+177)
		tmp = Float64(Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c)) + Float64(Float64(b / c) / z));
	elseif (t <= -3.9e+87)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / z)) - t_1) / c);
	elseif (t <= -2.7e-121)
		tmp = Float64(Float64(Float64(b / z) - t_1) / c);
	elseif (t <= 5.9e+23)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(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])){:}
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 * t);
	tmp = 0.0;
	if (t <= -2.7e+206)
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	elseif (t <= -7.6e+177)
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z);
	elseif (t <= -3.9e+87)
		tmp = ((9.0 * ((y * x) / z)) - t_1) / c;
	elseif (t <= -2.7e-121)
		tmp = ((b / z) - t_1) / c;
	elseif (t <= 5.9e+23)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+206], N[(N[(N[(9.0 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -7.6e+177], N[(N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e+87], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -2.7e-121], N[(N[(N[(b / z), $MachinePrecision] - t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 5.9e+23], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.70000000000000003e206

   1. Initial program 56.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 61.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 61.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 61.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 61.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 56.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 56.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 61.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 61.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 57.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 57.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 57.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 57.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 57.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 57.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 57.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 66.3%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 66.3%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 78.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 78.3%

          \[\leadsto \frac{\left(9 \cdot \frac{\color{blue}{y \cdot x}}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       2. *-un-lft-identity 78.3%

          \[\leadsto \frac{\left(9 \cdot \frac{y \cdot x}{\color{blue}{1 \cdot z}} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       3. times-frac 78.9%

          \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   11. Applied egg-rr 78.9%

       \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   12. Taylor expanded in b around 0 80.1%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv 80.1%

          \[\leadsto \frac{\color{blue}{9 \cdot \frac{x \cdot y}{z} + \left(-4\right) \cdot \left(a \cdot t\right)}}{c} \]

       2. associate-/l* 84.8%

          \[\leadsto \frac{9 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \left(-4\right) \cdot \left(a \cdot t\right)}{c} \]

       3. metadata-eval 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

       4. associate-*r* 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

       5. *-commutative 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(a \cdot -4\right)} \cdot t}{c} \]

       6. *-commutative 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{t \cdot \left(a \cdot -4\right)}}{c} \]

   14. Simplified 84.8%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}} \]

   if -2.70000000000000003e206 < t < -7.5999999999999996e177

   1. Initial program 66.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 83.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 66.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 66.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 83.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 66.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 66.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 66.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 66.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 66.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 66.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 83.3%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around 0 67.5%

      \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 67.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 67.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac 67.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\frac{-\frac{b}{c}}{z}} \]

   11. Simplified 67.5%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\frac{-\frac{b}{c}}{z}} \]

   if -7.5999999999999996e177 < t < -3.9000000000000002e87

   1. Initial program 71.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 75.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 75.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 55.9%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   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 b around 0 75.7%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -3.9000000000000002e87 < t < -2.7000000000000002e-121

   1. Initial program 74.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 74.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 74.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 74.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 74.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 74.4%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 74.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 74.5%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 74.5%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 74.5%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 74.5%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 74.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 75.3%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 75.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 84.7%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 82.5%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -2.7000000000000002e-121 < t < 5.89999999999999987e23

   1. Initial program 88.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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* 88.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 88.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 88.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 88.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 5.89999999999999987e23 < t

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 76.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 81.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 81.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 71.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 71.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 71.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 71.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 71.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 71.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 70.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 70.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 51.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 51.9%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 54.9%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 54.9%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 54.9%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+206}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+177}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+87}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+206}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{+175}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 12000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -2.5e+206)
   (/ (+ (* 9.0 (/ x (/ z y))) (* t (* a -4.0))) c)
   (if (<= t -9.8e+175)
     (+ (* (/ (* 9.0 y) z) (/ x c)) (/ (/ b c) z))
     (if (<= t -1.3e+87)
       (- (* 9.0 (/ (* y x) (* z c))) (* 4.0 (/ (* a t) c)))
       (if (<= t -1.9e-118)
         (/ (- (/ b z) (* 4.0 (* a t))) c)
         (if (<= t 12000000000.0)
           (/ (+ b (* 9.0 (* y x))) (* z c))
           (* -4.0 (* t (/ a c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
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 <= -2.5e+206) {
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	} else if (t <= -9.8e+175) {
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z);
	} else if (t <= -1.3e+87) {
		tmp = (9.0 * ((y * x) / (z * c))) - (4.0 * ((a * t) / c));
	} else if (t <= -1.9e-118) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 12000000000.0) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-2.5d+206)) then
        tmp = ((9.0d0 * (x / (z / y))) + (t * (a * (-4.0d0)))) / c
    else if (t <= (-9.8d+175)) then
        tmp = (((9.0d0 * y) / z) * (x / c)) + ((b / c) / z)
    else if (t <= (-1.3d+87)) then
        tmp = (9.0d0 * ((y * x) / (z * c))) - (4.0d0 * ((a * t) / c))
    else if (t <= (-1.9d-118)) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else if (t <= 12000000000.0d0) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -2.5e+206) {
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	} else if (t <= -9.8e+175) {
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z);
	} else if (t <= -1.3e+87) {
		tmp = (9.0 * ((y * x) / (z * c))) - (4.0 * ((a * t) / c));
	} else if (t <= -1.9e-118) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 12000000000.0) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -2.5e+206:
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c
	elif t <= -9.8e+175:
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z)
	elif t <= -1.3e+87:
		tmp = (9.0 * ((y * x) / (z * c))) - (4.0 * ((a * t) / c))
	elif t <= -1.9e-118:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	elif t <= 12000000000.0:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -2.5e+206)
		tmp = Float64(Float64(Float64(9.0 * Float64(x / Float64(z / y))) + Float64(t * Float64(a * -4.0))) / c);
	elseif (t <= -9.8e+175)
		tmp = Float64(Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c)) + Float64(Float64(b / c) / z));
	elseif (t <= -1.3e+87)
		tmp = Float64(Float64(9.0 * Float64(Float64(y * x) / Float64(z * c))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	elseif (t <= -1.9e-118)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	elseif (t <= 12000000000.0)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(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])){:}
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 <= -2.5e+206)
		tmp = ((9.0 * (x / (z / y))) + (t * (a * -4.0))) / c;
	elseif (t <= -9.8e+175)
		tmp = (((9.0 * y) / z) * (x / c)) + ((b / c) / z);
	elseif (t <= -1.3e+87)
		tmp = (9.0 * ((y * x) / (z * c))) - (4.0 * ((a * t) / c));
	elseif (t <= -1.9e-118)
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	elseif (t <= 12000000000.0)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -2.5e+206], N[(N[(N[(9.0 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -9.8e+175], N[(N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e+87], N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-118], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 12000000000.0], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.5000000000000001e206

   1. Initial program 56.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 56.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 56.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 61.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 61.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 61.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 61.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 56.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 56.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 56.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 61.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 61.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 57.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 57.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 57.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 57.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 57.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 57.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 57.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 66.3%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 66.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 66.3%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 78.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 78.3%

          \[\leadsto \frac{\left(9 \cdot \frac{\color{blue}{y \cdot x}}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       2. *-un-lft-identity 78.3%

          \[\leadsto \frac{\left(9 \cdot \frac{y \cdot x}{\color{blue}{1 \cdot z}} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

       3. times-frac 78.9%

          \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   11. Applied egg-rr 78.9%

       \[\leadsto \frac{\left(9 \cdot \color{blue}{\left(\frac{y}{1} \cdot \frac{x}{z}\right)} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c} \]

   12. Taylor expanded in b around 0 80.1%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]
   13. Step-by-step derivation

       1. cancel-sign-sub-inv 80.1%

          \[\leadsto \frac{\color{blue}{9 \cdot \frac{x \cdot y}{z} + \left(-4\right) \cdot \left(a \cdot t\right)}}{c} \]

       2. associate-/l* 84.8%

          \[\leadsto \frac{9 \cdot \color{blue}{\frac{x}{\frac{z}{y}}} + \left(-4\right) \cdot \left(a \cdot t\right)}{c} \]

       3. metadata-eval 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{-4} \cdot \left(a \cdot t\right)}{c} \]

       4. associate-*r* 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

       5. *-commutative 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{\left(a \cdot -4\right)} \cdot t}{c} \]

       6. *-commutative 84.8%

          \[\leadsto \frac{9 \cdot \frac{x}{\frac{z}{y}} + \color{blue}{t \cdot \left(a \cdot -4\right)}}{c} \]

   14. Simplified 84.8%

       \[\leadsto \color{blue}{\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}} \]

   if -2.5000000000000001e206 < t < -9.80000000000000002e175

   1. Initial program 66.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 83.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 66.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 66.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 83.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 83.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 66.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 66.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 66.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 66.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 66.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 66.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 83.3%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 83.3%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around 0 67.5%

      \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 67.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 67.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac 67.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\frac{-\frac{b}{c}}{z}} \]

   11. Simplified 67.5%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\frac{-\frac{b}{c}}{z}} \]

   if -9.80000000000000002e175 < t < -1.29999999999999999e87

   1. Initial program 71.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 75.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 75.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 55.9%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 55.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in b around 0 75.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}} \]

   if -1.29999999999999999e87 < t < -1.9e-118

   1. Initial program 74.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 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* 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 74.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 74.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 74.2%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 73.8%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 73.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 73.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 73.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 73.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 73.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 74.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 74.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 74.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 84.3%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 82.0%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -1.9e-118 < t < 1.2e10

   1. Initial program 87.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 87.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 87.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 88.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 88.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.5%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 1.2e10 < t

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+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* 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 83.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      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* 77.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 82.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 72.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 72.8%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 72.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 72.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 69.8%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 50.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 50.4%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 53.3%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 53.3%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 53.3%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+206}:\\ \;\;\;\;\frac{9 \cdot \frac{x}{\frac{z}{y}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{+175}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+87}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 12000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-12} \lor \neg \left(a \leq 1950000000\right) \land a \leq 5.1 \cdot 10^{+185}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= a -1.5e-119)
   (* -4.0 (/ a (/ c t)))
   (if (or (<= a 2.5e-12) (and (not (<= a 1950000000.0)) (<= a 5.1e+185)))
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (* -4.0 (* t (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.5e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if ((a <= 2.5e-12) || (!(a <= 1950000000.0) && (a <= 5.1e+185))) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= (-1.5d-119)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if ((a <= 2.5d-12) .or. (.not. (a <= 1950000000.0d0)) .and. (a <= 5.1d+185)) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.5e-119) {
		tmp = -4.0 * (a / (c / t));
	} else if ((a <= 2.5e-12) || (!(a <= 1950000000.0) && (a <= 5.1e+185))) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.5e-119:
		tmp = -4.0 * (a / (c / t))
	elif (a <= 2.5e-12) or (not (a <= 1950000000.0) and (a <= 5.1e+185)):
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.5e-119)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif ((a <= 2.5e-12) || (!(a <= 1950000000.0) && (a <= 5.1e+185)))
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(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])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.5e-119)
		tmp = -4.0 * (a / (c / t));
	elseif ((a <= 2.5e-12) || (~((a <= 1950000000.0)) && (a <= 5.1e+185)))
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[a, -1.5e-119], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.5e-12], And[N[Not[LessEqual[a, 1950000000.0]], $MachinePrecision], LessEqual[a, 5.1e+185]]], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5000000000000001e-119

   1. Initial program 78.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 78.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 78.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 77.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 54.7%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -1.5000000000000001e-119 < a < 2.49999999999999985e-12 or 1.95e9 < a < 5.09999999999999996e185

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 84.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 84.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 84.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 84.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 86.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.7%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 2.49999999999999985e-12 < a < 1.95e9 or 5.09999999999999996e185 < a

   1. Initial program 71.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 65.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 72.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 72.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 68.4%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 68.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 68.4%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 68.4%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 68.4%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 68.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 68.4%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 56.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 56.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 56.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 56.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 56.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 56.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 56.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 56.1%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 71.4%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 71.4%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 71.4%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-12} \lor \neg \left(a \leq 1950000000\right) \land a \leq 5.1 \cdot 10^{+185}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+220}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.9 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 29000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* y x))) (* z c))))
   (if (<= t -1.6e+220)
     (* -4.0 (/ a (/ c t)))
     (if (<= t -1.35e+178)
       t_1
       (if (<= t -7.9e-118)
         (/ (- (/ b z) (* 4.0 (* a t))) c)
         (if (<= t 29000000000.0) t_1 (* -4.0 (* t (/ a c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (y * x))) / (z * c);
	double tmp;
	if (t <= -1.6e+220) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -1.35e+178) {
		tmp = t_1;
	} else if (t <= -7.9e-118) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 29000000000.0) {
		tmp = t_1;
	} 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (y * x))) / (z * c)
    if (t <= (-1.6d+220)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-1.35d+178)) then
        tmp = t_1
    else if (t <= (-7.9d-118)) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else if (t <= 29000000000.0d0) then
        tmp = t_1
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (y * x))) / (z * c);
	double tmp;
	if (t <= -1.6e+220) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -1.35e+178) {
		tmp = t_1;
	} else if (t <= -7.9e-118) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 29000000000.0) {
		tmp = t_1;
	} 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])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (y * x))) / (z * c)
	tmp = 0
	if t <= -1.6e+220:
		tmp = -4.0 * (a / (c / t))
	elif t <= -1.35e+178:
		tmp = t_1
	elif t <= -7.9e-118:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	elif t <= 29000000000.0:
		tmp = t_1
	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])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c))
	tmp = 0.0
	if (t <= -1.6e+220)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -1.35e+178)
		tmp = t_1;
	elseif (t <= -7.9e-118)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	elseif (t <= 29000000000.0)
		tmp = t_1;
	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])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (y * x))) / (z * c);
	tmp = 0.0;
	if (t <= -1.6e+220)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -1.35e+178)
		tmp = t_1;
	elseif (t <= -7.9e-118)
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	elseif (t <= 29000000000.0)
		tmp = t_1;
	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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+220], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e+178], t$95$1, If[LessEqual[t, -7.9e-118], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 29000000000.0], t$95$1, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.59999999999999994e220

   1. Initial program 52.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 52.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 52.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 57.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 57.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 57.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 57.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 52.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 52.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 52.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 57.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 76.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 81.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 81.2%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -1.59999999999999994e220 < t < -1.35000000000000009e178 or -7.9000000000000004e-118 < t < 2.9e10

   1. Initial program 86.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 86.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 86.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      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* 86.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 86.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.9%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if -1.35000000000000009e178 < t < -7.9000000000000004e-118

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 75.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 73.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 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. Step-by-step derivation

      1. associate-+l- 75.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 74.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 74.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 74.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 68.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 86.6%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 77.8%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if 2.9e10 < t

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+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* 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 83.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      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* 77.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 82.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 72.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 72.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 72.8%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 72.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 72.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 72.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 69.8%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 69.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 50.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 50.4%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 53.3%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 53.3%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 53.3%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+220}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+178}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;t \leq -7.9 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 29000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+220}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+178}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -2.8e+220)
   (* -4.0 (/ a (/ c t)))
   (if (<= t -1.45e+178)
     (/ (/ (+ b (* y (* 9.0 x))) z) c)
     (if (<= t -3.4e-119)
       (/ (- (/ b z) (* 4.0 (* a t))) c)
       (if (<= t 4.2e+22)
         (/ (+ b (* 9.0 (* y x))) (* z c))
         (* -4.0 (* t (/ a c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
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 <= -2.8e+220) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -1.45e+178) {
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	} else if (t <= -3.4e-119) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 4.2e+22) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-2.8d+220)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-1.45d+178)) then
        tmp = ((b + (y * (9.0d0 * x))) / z) / c
    else if (t <= (-3.4d-119)) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else if (t <= 4.2d+22) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -2.8e+220) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -1.45e+178) {
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	} else if (t <= -3.4e-119) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else if (t <= 4.2e+22) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -2.8e+220:
		tmp = -4.0 * (a / (c / t))
	elif t <= -1.45e+178:
		tmp = ((b + (y * (9.0 * x))) / z) / c
	elif t <= -3.4e-119:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	elif t <= 4.2e+22:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -2.8e+220)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -1.45e+178)
		tmp = Float64(Float64(Float64(b + Float64(y * Float64(9.0 * x))) / z) / c);
	elseif (t <= -3.4e-119)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	elseif (t <= 4.2e+22)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(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])){:}
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 <= -2.8e+220)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -1.45e+178)
		tmp = ((b + (y * (9.0 * x))) / z) / c;
	elseif (t <= -3.4e-119)
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	elseif (t <= 4.2e+22)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -2.8e+220], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.45e+178], N[(N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, -3.4e-119], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t, 4.2e+22], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.8000000000000001e220

   1. Initial program 52.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 52.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 52.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 57.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 57.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 57.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 57.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 52.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 52.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 52.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 57.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 76.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 81.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 81.2%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -2.8000000000000001e220 < t < -1.45e178

   1. Initial program 71.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 85.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 85.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 85.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 71.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 71.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 71.2%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 71.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 71.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 71.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 85.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 85.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 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 z around 0 71.9%

       \[\leadsto \frac{\color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}}{c} \]
   11. Step-by-step derivation

       1. associate-*r* 71.9%

          \[\leadsto \frac{\frac{b + \color{blue}{\left(9 \cdot x\right) \cdot y}}{z}}{c} \]

   12. Simplified 71.9%

       \[\leadsto \frac{\color{blue}{\frac{b + \left(9 \cdot x\right) \cdot y}{z}}}{c} \]

   if -1.45e178 < t < -3.40000000000000024e-119

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 75.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 73.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 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. Step-by-step derivation

      1. associate-+l- 75.3%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 74.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 74.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 74.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 68.7%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 68.7%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 86.6%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 77.8%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if -3.40000000000000024e-119 < t < 4.1999999999999996e22

   1. Initial program 88.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 88.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 88.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 88.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 88.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.8%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 4.1999999999999996e22 < t

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 76.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 81.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 81.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 71.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 71.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 71.9%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 71.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 71.9%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 71.9%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 70.4%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 70.4%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 70.4%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 51.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 51.9%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 54.9%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 54.9%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 54.9%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+220}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+178}:\\ \;\;\;\;\frac{\frac{b + y \cdot \left(9 \cdot x\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+69} \lor \neg \left(z \leq 1.85 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -5.7e+69) (not (<= z 1.85e-149)))
   (/ (+ (* a (* t -4.0)) (/ (- b (* x (* y -9.0))) z)) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
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 <= -5.7e+69) || !(z <= 1.85e-149)) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-5.7d+69)) .or. (.not. (z <= 1.85d-149))) 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))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.7e+69) || !(z <= 1.85e-149)) {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -5.7e+69) or not (z <= 1.85e-149):
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -5.7e+69) || !(z <= 1.85e-149))
		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(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5.7e+69) || ~((z <= 1.85e-149)))
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -5.7e+69], N[Not[LessEqual[z, 1.85e-149]], $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[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7e69 or 1.84999999999999995e-149 < z

   1. Initial program 66.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 67.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 66.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 66.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 70.3%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 70.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 70.3%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 70.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 70.3%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 70.3%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 70.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 70.9%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 70.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 70.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 70.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 70.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 70.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 70.9%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 70.9%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 91.2%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in z around -inf 91.2%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 91.2%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 91.2%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 91.2%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 91.2%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. neg-mul-1 91.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       6. unsub-neg 91.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       7. *-commutative 91.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       8. associate-*l* 91.2%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 91.2%

       \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right) - \frac{x \cdot \left(y \cdot -9\right) - b}{z}}}{c} \]

   if -5.7e69 < z < 1.84999999999999995e-149

   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. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+69} \lor \neg \left(z \leq 1.85 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{if}\;9 \cdot x \leq -1 \cdot 10^{+85}:\\ \;\;\;\;t\_1 - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;9 \cdot x \leq 5000000000000:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 y) z) (/ x c))))
   (if (<= (* 9.0 x) -1e+85)
     (- t_1 (* 4.0 (* a (/ t c))))
     (if (<= (* 9.0 x) 5000000000000.0)
       (/ (- (/ b z) (* 4.0 (* a t))) c)
       (+ t_1 (/ (/ b c) z))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((9.0 * y) / z) * (x / c);
	double tmp;
	if ((9.0 * x) <= -1e+85) {
		tmp = t_1 - (4.0 * (a * (t / c)));
	} else if ((9.0 * x) <= 5000000000000.0) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = t_1 + ((b / c) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 * y) / z) * (x / c)
    if ((9.0d0 * x) <= (-1d+85)) then
        tmp = t_1 - (4.0d0 * (a * (t / c)))
    else if ((9.0d0 * x) <= 5000000000000.0d0) then
        tmp = ((b / z) - (4.0d0 * (a * t))) / c
    else
        tmp = t_1 + ((b / c) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((9.0 * y) / z) * (x / c);
	double tmp;
	if ((9.0 * x) <= -1e+85) {
		tmp = t_1 - (4.0 * (a * (t / c)));
	} else if ((9.0 * x) <= 5000000000000.0) {
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	} else {
		tmp = t_1 + ((b / c) / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((9.0 * y) / z) * (x / c)
	tmp = 0
	if (9.0 * x) <= -1e+85:
		tmp = t_1 - (4.0 * (a * (t / c)))
	elif (9.0 * x) <= 5000000000000.0:
		tmp = ((b / z) - (4.0 * (a * t))) / c
	else:
		tmp = t_1 + ((b / c) / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c))
	tmp = 0.0
	if (Float64(9.0 * x) <= -1e+85)
		tmp = Float64(t_1 - Float64(4.0 * Float64(a * Float64(t / c))));
	elseif (Float64(9.0 * x) <= 5000000000000.0)
		tmp = Float64(Float64(Float64(b / z) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(t_1 + Float64(Float64(b / c) / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 * y) / z) * (x / c);
	tmp = 0.0;
	if ((9.0 * x) <= -1e+85)
		tmp = t_1 - (4.0 * (a * (t / c)));
	elseif ((9.0 * x) <= 5000000000000.0)
		tmp = ((b / z) - (4.0 * (a * t))) / c;
	else
		tmp = t_1 + ((b / c) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(9.0 * x), $MachinePrecision], -1e+85], N[(t$95$1 - N[(4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(9.0 * x), $MachinePrecision], 5000000000000.0], N[(N[(N[(b / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(t$95$1 + N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 9) < -1e85

   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* 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 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* 70.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 76.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 62.9%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 62.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 62.8%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 62.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 62.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 62.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 62.9%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 65.8%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 65.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 65.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 65.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 65.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 65.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 65.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 65.8%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 71.5%

      \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 57.6%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)\right)} \]

       2. expm1-udef 52.3%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)} - 1\right)} \]

       3. associate-/l* 52.3%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{c}{t}}}\right)} - 1\right) \]

   11. Applied egg-rr 52.3%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 55.1%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)\right)} \]

       2. expm1-log1p 74.1%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

       3. associate-/l* 71.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

       4. *-rgt-identity 71.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \frac{\color{blue}{\left(a \cdot t\right) \cdot 1}}{c} \]

       5. associate-*r/ 71.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)} \]

       6. associate-*l* 74.1%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(a \cdot \left(t \cdot \frac{1}{c}\right)\right)} \]

       7. associate-*r/ 74.1%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \color{blue}{\frac{t \cdot 1}{c}}\right) \]

       8. *-rgt-identity 74.1%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \frac{\color{blue}{t}}{c}\right) \]

   13. Simplified 74.1%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

   if -1e85 < (*.f64 x 9) < 5e12

   1. Initial program 81.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 83.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 83.2%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 78.0%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 78.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 78.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 78.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 78.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 78.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 78.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 76.0%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 76.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 76.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 76.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 76.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 76.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 76.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 76.0%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 88.1%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in x around 0 75.9%

       \[\leadsto \color{blue}{\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}} \]

   if 5e12 < (*.f64 x 9)

   1. Initial program 75.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 71.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 75.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 78.2%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 75.0%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 75.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 75.0%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 75.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 75.0%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 75.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 72.0%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 72.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 72.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 72.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 72.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 72.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 72.0%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around 0 57.9%

      \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 57.9%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 58.9%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac 58.9%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\frac{-\frac{b}{c}}{z}} \]

   11. Simplified 58.9%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{\frac{-\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;9 \cdot x \leq -1 \cdot 10^{+85}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;9 \cdot x \leq 5000000000000:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} + \frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+221}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.05e+221)
   (- (* (/ (* 9.0 y) z) (/ x c)) (* 4.0 (* a (/ t c))))
   (/ (+ (* a (* t -4.0)) (/ (- b (* x (* y -9.0))) z)) c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.05e+221) {
		tmp = (((9.0 * y) / z) * (x / c)) - (4.0 * (a * (t / c)));
	} else {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-3.05d+221)) then
        tmp = (((9.0d0 * y) / z) * (x / c)) - (4.0d0 * (a * (t / c)))
    else
        tmp = ((a * (t * (-4.0d0))) + ((b - (x * (y * (-9.0d0)))) / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.05e+221) {
		tmp = (((9.0 * y) / z) * (x / c)) - (4.0 * (a * (t / c)));
	} else {
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.05e+221:
		tmp = (((9.0 * y) / z) * (x / c)) - (4.0 * (a * (t / c)))
	else:
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.05e+221)
		tmp = Float64(Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c)) - Float64(4.0 * Float64(a * Float64(t / c))));
	else
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.05e+221)
		tmp = (((9.0 * y) / z) * (x / c)) - (4.0 * (a * (t / c)));
	else
		tmp = ((a * (t * -4.0)) + ((b - (x * (y * -9.0))) / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -3.05e+221], N[(N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0499999999999999e221

   1. Initial program 55.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 55.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 55.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 60.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 55.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 55.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 55.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 60.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 60.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 60.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 55.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 55.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 55.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 55.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 55.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 55.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 55.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 66.2%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 66.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 66.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 66.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 66.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 66.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 66.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 66.2%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 90.4%

      \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \color{blue}{4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 58.5%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)\right)} \]

       2. expm1-udef 49.2%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot t}{c}\right)} - 1\right)} \]

       3. associate-/l* 53.4%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{c}{t}}}\right)} - 1\right) \]

   11. Applied egg-rr 53.4%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 62.8%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{c}{t}}\right)\right)} \]

       2. expm1-log1p 95.0%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

       3. associate-/l* 90.4%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

       4. *-rgt-identity 90.4%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \frac{\color{blue}{\left(a \cdot t\right) \cdot 1}}{c} \]

       5. associate-*r/ 90.4%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)} \]

       6. associate-*l* 95.0%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(a \cdot \left(t \cdot \frac{1}{c}\right)\right)} \]

       7. associate-*r/ 95.0%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \color{blue}{\frac{t \cdot 1}{c}}\right) \]

       8. *-rgt-identity 95.0%

          \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \frac{\color{blue}{t}}{c}\right) \]

   13. Simplified 95.0%

       \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

   if -3.0499999999999999e221 < t

   1. Initial program 80.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 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 76.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 76.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 76.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 76.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 76.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 76.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 76.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 74.2%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 74.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 74.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 74.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 74.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 74.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 74.2%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 89.6%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in z around -inf 90.0%

       \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]
   11. Step-by-step derivation

       1. mul-1-neg 90.0%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}\right)}}{c} \]

       2. unsub-neg 90.0%

          \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}}{c} \]

       3. *-commutative 90.0%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       4. associate-*l* 90.0%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right)} - \frac{-9 \cdot \left(x \cdot y\right) + -1 \cdot b}{z}}{c} \]

       5. neg-mul-1 90.0%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{-9 \cdot \left(x \cdot y\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]

       6. unsub-neg 90.0%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right) - b}}{z}}{c} \]

       7. *-commutative 90.0%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{\left(x \cdot y\right) \cdot -9} - b}{z}}{c} \]

       8. associate-*l* 90.0%

          \[\leadsto \frac{a \cdot \left(t \cdot -4\right) - \frac{\color{blue}{x \cdot \left(y \cdot -9\right)} - b}{z}}{c} \]

   12. Simplified 90.0%

       \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot -4\right) - \frac{x \cdot \left(y \cdot -9\right) - b}{z}}}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+221}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c} - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-5} \lor \neg \left(t \leq 3.3\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.05e-5) (not (<= t 3.3)))
   (* -4.0 (* t (/ a c)))
   (* b (/ (/ 1.0 z) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.05e-5) || !(t <= 3.3)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-2.05d-5)) .or. (.not. (t <= 3.3d0))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b * ((1.0d0 / z) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.05e-5) || !(t <= 3.3)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.05e-5) or not (t <= 3.3):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b * ((1.0 / z) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.05e-5) || !(t <= 3.3))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.05e-5) || ~((t <= 3.3)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b * ((1.0 / z) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[t, -2.05e-5], N[Not[LessEqual[t, 3.3]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05000000000000002e-5 or 3.2999999999999998 < t

   1. Initial program 72.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 77.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 70.8%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 70.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 70.8%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 70.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 70.8%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 70.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 70.8%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 66.5%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 66.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 66.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 66.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 66.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 66.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 66.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 66.5%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 55.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 55.0%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 57.2%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 57.2%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 57.2%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]

   if -2.05000000000000002e-5 < t < 3.2999999999999998

   1. Initial program 84.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   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 b around inf 45.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 45.2%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      2. *-commutative 45.2%

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

   9. Applied egg-rr 45.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 29.3%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 13.8%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 13.8%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 13.8%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 29.3%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 45.2%

          \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

       3. associate-/r* 45.8%

          \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

   13. Simplified 45.8%

       \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-5} \lor \neg \left(t \leq 3.3\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 0.72:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -1.8e-5)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 0.72) (* b (/ (/ 1.0 z) c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.8e-5) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 0.72) {
		tmp = b * ((1.0 / 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.
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 <= (-1.8d-5)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 0.72d0) then
        tmp = b * ((1.0d0 / 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;
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 <= -1.8e-5) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 0.72) {
		tmp = b * ((1.0 / 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])
[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 <= -1.8e-5:
		tmp = -4.0 * (a / (c / t))
	elif t <= 0.72:
		tmp = b * ((1.0 / 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])
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 <= -1.8e-5)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 0.72)
		tmp = Float64(b * Float64(Float64(1.0 / 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])){:}
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 <= -1.8e-5)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 0.72)
		tmp = b * ((1.0 / 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.
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, -1.8e-5], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.72], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.80000000000000005e-5

   1. Initial program 66.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 66.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 66.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 66.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 66.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 64.4%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -1.80000000000000005e-5 < t < 0.71999999999999997

   1. Initial program 84.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   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 b around inf 45.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 45.2%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

      2. *-commutative 45.2%

         \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

   9. Applied egg-rr 45.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 29.3%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

       2. expm1-udef 13.8%

          \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

       3. *-commutative 13.8%

          \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

   11. Applied egg-rr 13.8%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
   12. Step-by-step derivation

       1. expm1-def 29.3%

          \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

       2. expm1-log1p 45.2%

          \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

       3. associate-/r* 45.8%

          \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

   13. Simplified 45.8%

       \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

   if 0.71999999999999997 < t

   1. Initial program 77.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 83.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 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* 82.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-+l- 82.2%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 73.1%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 73.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 73.2%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 73.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 73.2%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 73.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 68.8%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 68.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 68.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 68.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 68.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 68.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 68.8%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in z around inf 49.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   10. Step-by-step derivation

       1. *-commutative 49.7%

          \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

       2. associate-*l/ 52.5%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

       3. *-commutative 52.5%

          \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   11. Simplified 52.5%

       \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 0.72:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.82 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 1.82e+31) (/ (/ b z) c) (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.82e+31) {
		tmp = (b / z) / c;
	} 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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= 1.82d+31) then
        tmp = (b / z) / c
    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;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.82e+31) {
		tmp = (b / z) / c;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 1.82e+31:
		tmp = (b / z) / c
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 1.82e+31)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 1.82e+31)
		tmp = (b / z) / c;
	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.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 1.82e+31], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.8200000000000001e31

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 78.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 78.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 78.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   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. Step-by-step derivation

      1. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z \cdot c} \]

      2. div-sub 73.7%

         \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c}} \]

      3. *-commutative 73.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      4. associate-*l* 73.7%

         \[\leadsto \frac{\color{blue}{9 \cdot \left(y \cdot x\right)}}{z \cdot c} - \frac{\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b}{z \cdot c} \]

      5. associate-*l* 73.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right)} - b}{z \cdot c} \]

      6. fma-neg 73.7%

         \[\leadsto \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\color{blue}{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}}{z \cdot c} \]

   6. Applied egg-rr 73.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c}} \]
   7. Step-by-step derivation

      1. associate-*r* 73.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      2. times-frac 72.5%

         \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c}} - \frac{\mathsf{fma}\left(z, 4 \cdot \left(t \cdot a\right), -b\right)}{z \cdot c} \]

      3. fma-udef 72.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) + \left(-b\right)}}{z \cdot c} \]

      4. unsub-neg 72.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{\color{blue}{z \cdot \left(4 \cdot \left(t \cdot a\right)\right) - b}}{z \cdot c} \]

      5. *-commutative 72.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(\left(t \cdot a\right) \cdot 4\right)} - b}{z \cdot c} \]

      6. *-commutative 72.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(\color{blue}{\left(a \cdot t\right)} \cdot 4\right) - b}{z \cdot c} \]

      7. associate-*l* 72.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \color{blue}{\left(a \cdot \left(t \cdot 4\right)\right)} - b}{z \cdot c} \]

      8. *-commutative 72.5%

         \[\leadsto \frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \color{blue}{\left(4 \cdot t\right)}\right) - b}{z \cdot c} \]

   8. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{9 \cdot y}{z} \cdot \frac{x}{c} - \frac{z \cdot \left(a \cdot \left(4 \cdot t\right)\right) - b}{z \cdot c}} \]

   9. Taylor expanded in c around 0 87.9%

      \[\leadsto \color{blue}{\frac{\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}} \]

   10. Taylor expanded in b around inf 35.9%

       \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]

   if 1.8200000000000001e31 < y

   1. Initial program 81.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 84.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 84.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 84.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 84.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 86.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 32.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 32.8%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 32.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.82 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ b \cdot \frac{1}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (* b (/ 1.0 (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * (1.0 / (z * c));
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b * (1.0d0 / (z * c))
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * (1.0 / (z * c));
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b * (1.0 / (z * c))

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b * Float64(1.0 / Float64(z * c)))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b * (1.0 / (z * c));
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 79.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 78.6%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 81.0%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 34.1%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Step-by-step derivation

   1. div-inv 35.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   2. *-commutative 35.2%

      \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

9. Applied egg-rr 35.2%

   \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]

10. Final simplification 35.2%

    \[\leadsto b \cdot \frac{1}{z \cdot c} \]
11. Add Preprocessing

Alternative 22: 35.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ b \cdot \frac{\frac{1}{c}}{z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (* b (/ (/ 1.0 c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * ((1.0 / c) / z);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b * ((1.0d0 / c) / z)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * ((1.0 / c) / z);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b * ((1.0 / c) / z)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b * Float64(Float64(1.0 / c) / z))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b * ((1.0 / c) / z);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 79.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 78.6%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 81.0%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 34.1%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Step-by-step derivation

   1. div-inv 35.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   2. *-commutative 35.2%

      \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

9. Applied egg-rr 35.2%

   \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
10. Step-by-step derivation

    1. expm1-log1p-u 23.9%

       \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

    2. expm1-udef 12.8%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

    3. *-commutative 12.8%

       \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

11. Applied egg-rr 12.8%

    \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
12. Step-by-step derivation

    1. expm1-def 23.9%

       \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

    2. expm1-log1p 35.2%

       \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

    3. *-commutative 35.2%

       \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

    4. associate-/r* 35.5%

       \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]

13. Simplified 35.5%

    \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]

14. Final simplification 35.5%

    \[\leadsto b \cdot \frac{\frac{1}{c}}{z} \]
15. Add Preprocessing

Alternative 23: 35.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ b \cdot \frac{\frac{1}{z}}{c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (* b (/ (/ 1.0 z) c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * ((1.0 / z) / c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b * ((1.0d0 / z) / c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b * ((1.0 / z) / c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b * ((1.0 / z) / c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b * Float64(Float64(1.0 / z) / c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b * ((1.0 / z) / c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 79.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 78.6%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 81.0%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 34.1%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Step-by-step derivation

   1. div-inv 35.2%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   2. *-commutative 35.2%

      \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

9. Applied egg-rr 35.2%

   \[\leadsto \color{blue}{b \cdot \frac{1}{c \cdot z}} \]
10. Step-by-step derivation

    1. expm1-log1p-u 23.9%

       \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)\right)} \]

    2. expm1-udef 12.8%

       \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{c \cdot z}\right)} - 1\right)} \]

    3. *-commutative 12.8%

       \[\leadsto b \cdot \left(e^{\mathsf{log1p}\left(\frac{1}{\color{blue}{z \cdot c}}\right)} - 1\right) \]

11. Applied egg-rr 12.8%

    \[\leadsto b \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)} - 1\right)} \]
12. Step-by-step derivation

    1. expm1-def 23.9%

       \[\leadsto b \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{z \cdot c}\right)\right)} \]

    2. expm1-log1p 35.2%

       \[\leadsto b \cdot \color{blue}{\frac{1}{z \cdot c}} \]

    3. associate-/r* 35.5%

       \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

13. Simplified 35.5%

    \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{z}}{c}} \]

14. Final simplification 35.5%

    \[\leadsto b \cdot \frac{\frac{1}{z}}{c} \]
15. Add Preprocessing

Alternative 24: 35.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.6%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.6%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 79.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.6%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 78.6%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 81.0%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 81.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 34.1%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 34.1%

   \[\leadsto \frac{b}{z \cdot c} \]
9. Add Preprocessing

Developer target: 80.8% 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 2024039 
(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)))