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

Percentage Accurate: 80.3% → 84.1%

Time: 23.3s

Alternatives: 22

Speedup: 0.7×

• 38.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot t\right)\\ t_2 := \frac{y \cdot \left(a \cdot \frac{\mathsf{fma}\left(-4, t, \frac{\frac{b}{z}}{a}\right)}{y} - \frac{x \cdot -9}{z}\right)}{c}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{y \cdot x}{t\_1} + \frac{b}{t\_1}\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+237}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* c (* z t)))
        (t_2
         (/
          (* y (- (* a (/ (fma -4.0 t (/ (/ b z) a)) y)) (/ (* x -9.0) z)))
          c)))
   (if (<= z -6.4e+52)
     t_2
     (if (<= z 2.5e-25)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* y x) c)) (/ b c))) z)
       (if (<= z 1.9e+107)
         (* t (+ (* -4.0 (/ a c)) (+ (* 9.0 (/ (* y x) t_1)) (/ b t_1))))
         (if (<= z 1.7e+237) t_2 (/ (* a (+ (* -4.0 t) (/ b (* z 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 = c * (z * t);
	double t_2 = (y * ((a * (fma(-4.0, t, ((b / z) / a)) / y)) - ((x * -9.0) / z))) / c;
	double tmp;
	if (z <= -6.4e+52) {
		tmp = t_2;
	} else if (z <= 2.5e-25) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((y * x) / c)) + (b / c))) / z;
	} else if (z <= 1.9e+107) {
		tmp = t * ((-4.0 * (a / c)) + ((9.0 * ((y * x) / t_1)) + (b / t_1)));
	} else if (z <= 1.7e+237) {
		tmp = t_2;
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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(c * Float64(z * t))
	t_2 = Float64(Float64(y * Float64(Float64(a * Float64(fma(-4.0, t, Float64(Float64(b / z) / a)) / y)) - Float64(Float64(x * -9.0) / z))) / c)
	tmp = 0.0
	if (z <= -6.4e+52)
		tmp = t_2;
	elseif (z <= 2.5e-25)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(y * x) / c)) + Float64(b / c))) / z);
	elseif (z <= 1.9e+107)
		tmp = Float64(t * Float64(Float64(-4.0 * Float64(a / c)) + Float64(Float64(9.0 * Float64(Float64(y * x) / t_1)) + Float64(b / t_1))));
	elseif (z <= 1.7e+237)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(z * a)))) / c);
	end
	return 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[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(a * N[(N[(-4.0 * t + N[(N[(b / z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * -9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -6.4e+52], t$95$2, If[LessEqual[z, 2.5e-25], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.9e+107], N[(t * N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+237], t$95$2, N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4e52 or 1.8999999999999999e107 < z < 1.7000000000000002e237

   1. Initial program 52.0%

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

      1. +-commutative 52.0%

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

      2. associate-+r- 52.0%

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

      3. *-commutative 52.0%

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

      4. associate-*r* 54.9%

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

      5. *-commutative 54.9%

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

      6. associate-+r- 54.9%

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

      7. +-commutative 54.9%

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

      8. associate-*l* 54.9%

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

      9. associate-*l* 59.4%

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

      10. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in a around inf 65.4%

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

   6. Taylor expanded in c around 0 72.6%

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

   7. Taylor expanded in y around -inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-in 78.1%

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

      3. mul-1-neg 78.1%

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

      4. unsub-neg 78.1%

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

      5. associate-*r/ 78.2%

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

      6. *-commutative 78.2%

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

      7. associate-/l* 69.8%

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

      8. fma-define 69.8%

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

      9. *-commutative 69.8%

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

      10. associate-/r* 72.8%

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

   9. Simplified 72.8%

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

   if -6.4e52 < z < 2.49999999999999981e-25

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. associate-+r- 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-*r* 94.8%

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

      5. *-commutative 94.8%

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

      6. associate-+r- 94.8%

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

      7. +-commutative 94.8%

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

      8. associate-*l* 94.8%

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

      9. associate-*l* 88.2%

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

      10. *-commutative 88.2%

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

   3. Simplified 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 z around 0 95.7%

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

   if 2.49999999999999981e-25 < z < 1.8999999999999999e107

   1. Initial program 83.0%

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

      1. +-commutative 83.0%

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

      2. associate-+r- 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-*r* 78.8%

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

      5. *-commutative 78.8%

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

      6. associate-+r- 78.8%

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

      7. +-commutative 78.8%

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

      8. associate-*l* 78.8%

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

      9. associate-*l* 82.9%

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

      10. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in t around inf 83.3%

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

   if 1.7000000000000002e237 < z

   1. Initial program 37.7%

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

      1. +-commutative 37.7%

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

      2. associate-+r- 37.7%

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

      3. *-commutative 37.7%

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

      4. associate-*r* 29.4%

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

      5. *-commutative 29.4%

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

      6. associate-+r- 29.4%

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

      7. +-commutative 29.4%

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

      8. associate-*l* 29.4%

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

      9. associate-*l* 45.5%

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

      10. *-commutative 45.5%

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

   3. Simplified 45.5%

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

   5. Taylor expanded in a around inf 76.5%

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

   6. Taylor expanded in c around 0 88.0%

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

   7. Taylor expanded in x around 0 92.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+52}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{\mathsf{fma}\left(-4, t, \frac{\frac{b}{z}}{a}\right)}{y} - \frac{x \cdot -9}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{y \cdot x}{c \cdot \left(z \cdot t\right)} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+237}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{\mathsf{fma}\left(-4, t, \frac{\frac{b}{z}}{a}\right)}{y} - \frac{x \cdot -9}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-50}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -1e-50)
     (/ (+ b (fma x (* y 9.0) (* t (* a (* z -4.0))))) (* z c))
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* y x) c)) (/ b c))) z)
       (if (<= t_1 1e+305)
         t_1
         (/
          (* a (+ (* -4.0 t) (+ (/ b (* z a)) (* 9.0 (/ (* y x) (* z 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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-50) {
		tmp = (b + fma(x, (y * 9.0), (t * (a * (z * -4.0))))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((y * x) / c)) + (b / c))) / z;
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-50)
		tmp = Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(y * x) / c)) + Float64(b / c))) / z);
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(Float64(b / Float64(z * a)) + Float64(9.0 * Float64(Float64(y * x) / Float64(z * a)))))) / c);
	end
	return 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[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-50], N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], t$95$1, N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.00000000000000001e-50

   1. Initial program 86.6%

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

   3. Simplified 83.3%

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

   if -1.00000000000000001e-50 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 59.0%

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

      1. +-commutative 59.0%

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

      2. associate-+r- 59.0%

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

      3. *-commutative 59.0%

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

      4. associate-*r* 53.0%

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

      5. *-commutative 53.0%

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

      6. associate-+r- 53.0%

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

      7. +-commutative 53.0%

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

      8. associate-*l* 52.9%

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

      9. associate-*l* 58.9%

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

      10. *-commutative 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in z around 0 97.2%

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

   if -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.9999999999999994e304

   1. Initial program 99.2%

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

   if 9.9999999999999994e304 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 49.9%

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

      1. +-commutative 49.9%

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

      2. associate-+r- 49.9%

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

      3. *-commutative 49.9%

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

      4. associate-*r* 58.0%

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

      5. *-commutative 58.0%

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

      6. associate-+r- 58.0%

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

      7. +-commutative 58.0%

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

      8. associate-*l* 58.0%

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

      9. associate-*l* 59.2%

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

      10. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in a around inf 70.5%

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

   6. Taylor expanded in c around 0 77.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -1 \cdot 10^{-50}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 10^{+305}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -1e-235)
     t_1
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (/ b c)) z)
       (if (<= t_1 1e+305)
         t_1
         (/
          (* a (+ (* -4.0 t) (+ (/ b (* z a)) (* 9.0 (/ (* y x) (* z 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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-235) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z;
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    if (t_1 <= (-1d-235)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (((-4.0d0) * ((a * (z * t)) / c)) + (b / c)) / z
    else if (t_1 <= 1d+305) then
        tmp = t_1
    else
        tmp = (a * (((-4.0d0) * t) + ((b / (z * a)) + (9.0d0 * ((y * x) / (z * 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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-235) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z;
	} else if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -1e-235:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z
	elif t_1 <= 1e+305:
		tmp = t_1
	else:
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-235)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(b / c)) / z);
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(Float64(b / Float64(z * a)) + Float64(9.0 * Float64(Float64(y * x) / Float64(z * 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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -1e-235)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z;
	elseif (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-235], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], t$95$1, N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -9.9999999999999996e-236 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.9999999999999994e304

   1. Initial program 91.1%

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

   if -9.9999999999999996e-236 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 43.9%

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

      1. +-commutative 43.9%

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

      2. associate-+r- 43.9%

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

      3. *-commutative 43.9%

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

      4. associate-*r* 39.3%

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

      5. *-commutative 39.3%

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

      6. associate-+r- 39.3%

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

      7. +-commutative 39.3%

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

      8. associate-*l* 39.3%

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

      9. associate-*l* 43.9%

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

      10. *-commutative 43.9%

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

   3. Simplified 43.9%

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

   5. Taylor expanded in z around 0 96.2%

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

      1. fma-define 96.2%

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

      2. associate-/l* 96.2%

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

      3. associate-/l* 92.5%

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

      4. fma-define 92.5%

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

      5. associate-/l* 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in x around 0 89.4%

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

   if 9.9999999999999994e304 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 49.9%

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

      1. +-commutative 49.9%

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

      2. associate-+r- 49.9%

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

      3. *-commutative 49.9%

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

      4. associate-*r* 58.0%

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

      5. *-commutative 58.0%

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

      6. associate-+r- 58.0%

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

      7. +-commutative 58.0%

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

      8. associate-*l* 58.0%

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

      9. associate-*l* 59.2%

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

      10. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in a around inf 70.5%

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

   6. Taylor expanded in c around 0 77.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -1 \cdot 10^{-235}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 10^{+305}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_2 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{-119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-185}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (* (/ y z) (/ x c)))) (t_2 (* t (* a (/ -4.0 c)))))
   (if (<= a -4e-119)
     t_2
     (if (<= a -4e-278)
       t_1
       (if (<= a 2.1e-185)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 5.1e+159)
           t_1
           (if (<= a 1.8e+261)
             t_2
             (if (<= a 2.8e+287)
               (* 9.0 (* x (/ y (* z c))))
               (* (/ a c) (* -4.0 t))))))))))

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 t_2 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -4e-119) {
		tmp = t_2;
	} else if (a <= -4e-278) {
		tmp = t_1;
	} else if (a <= 2.1e-185) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 5.1e+159) {
		tmp = t_1;
	} else if (a <= 1.8e+261) {
		tmp = t_2;
	} else if (a <= 2.8e+287) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / z) * (x / c))
    t_2 = t * (a * ((-4.0d0) / c))
    if (a <= (-4d-119)) then
        tmp = t_2
    else if (a <= (-4d-278)) then
        tmp = t_1
    else if (a <= 2.1d-185) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 5.1d+159) then
        tmp = t_1
    else if (a <= 1.8d+261) then
        tmp = t_2
    else if (a <= 2.8d+287) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else
        tmp = (a / c) * ((-4.0d0) * t)
    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 t_2 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -4e-119) {
		tmp = t_2;
	} else if (a <= -4e-278) {
		tmp = t_1;
	} else if (a <= 2.1e-185) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 5.1e+159) {
		tmp = t_1;
	} else if (a <= 1.8e+261) {
		tmp = t_2;
	} else if (a <= 2.8e+287) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	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))
	t_2 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -4e-119:
		tmp = t_2
	elif a <= -4e-278:
		tmp = t_1
	elif a <= 2.1e-185:
		tmp = (b / z) * (1.0 / c)
	elif a <= 5.1e+159:
		tmp = t_1
	elif a <= 1.8e+261:
		tmp = t_2
	elif a <= 2.8e+287:
		tmp = 9.0 * (x * (y / (z * c)))
	else:
		tmp = (a / c) * (-4.0 * t)
	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(y / z) * Float64(x / c)))
	t_2 = Float64(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -4e-119)
		tmp = t_2;
	elseif (a <= -4e-278)
		tmp = t_1;
	elseif (a <= 2.1e-185)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 5.1e+159)
		tmp = t_1;
	elseif (a <= 1.8e+261)
		tmp = t_2;
	elseif (a <= 2.8e+287)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	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));
	t_2 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -4e-119)
		tmp = t_2;
	elseif (a <= -4e-278)
		tmp = t_1;
	elseif (a <= 2.1e-185)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 5.1e+159)
		tmp = t_1;
	elseif (a <= 1.8e+261)
		tmp = t_2;
	elseif (a <= 2.8e+287)
		tmp = 9.0 * (x * (y / (z * c)));
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e-119], t$95$2, If[LessEqual[a, -4e-278], t$95$1, If[LessEqual[a, 2.1e-185], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e+159], t$95$1, If[LessEqual[a, 1.8e+261], t$95$2, If[LessEqual[a, 2.8e+287], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.00000000000000005e-119 or 5.09999999999999967e159 < a < 1.80000000000000009e261

   1. Initial program 67.3%

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

      1. +-commutative 67.3%

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

      2. associate-+r- 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*r* 63.2%

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

      5. *-commutative 63.2%

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

      6. associate-+r- 63.2%

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

      7. +-commutative 63.2%

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

      8. associate-*l* 63.2%

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

      9. associate-*l* 66.5%

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

      10. *-commutative 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in t around inf 71.2%

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

   6. Taylor expanded in x around 0 68.7%

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

   7. Taylor expanded in a around inf 58.9%

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

      1. associate-*r/ 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-/l* 58.9%

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

   9. Simplified 58.9%

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

   if -4.00000000000000005e-119 < a < -3.99999999999999975e-278 or 2.1e-185 < a < 5.09999999999999967e159

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-+r- 81.2%

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

      3. *-commutative 81.2%

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

      4. associate-*r* 84.7%

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

      5. *-commutative 84.7%

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

      6. associate-+r- 84.7%

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

      7. +-commutative 84.7%

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

      8. associate-*l* 84.7%

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

      9. associate-*l* 83.6%

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

      10. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around inf 49.3%

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

      1. times-frac 51.5%

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

   7. Applied egg-rr 51.5%

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

   if -3.99999999999999975e-278 < a < 2.1e-185

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-+r- 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*r* 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-+r- 82.0%

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

      7. +-commutative 82.0%

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

      8. associate-*l* 82.0%

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

      9. associate-*l* 82.0%

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

      10. *-commutative 82.0%

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

   3. Simplified 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. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

      1. *-un-lft-identity 51.2%

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

      2. associate-/r* 59.5%

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

   9. Applied egg-rr 59.5%

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

       1. div-inv 59.6%

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

   11. Applied egg-rr 59.6%

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

   if 1.80000000000000009e261 < a < 2.80000000000000001e287

   1. Initial program 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-+r- 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-+r- 82.7%

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

      7. +-commutative 82.7%

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

      8. associate-*l* 82.9%

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

      9. associate-*l* 34.9%

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

      10. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in z around 0 83.5%

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

      1. fma-define 83.5%

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

      2. associate-/l* 99.7%

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

      3. associate-/l* 83.9%

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

      4. fma-define 83.9%

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

      5. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   8. Taylor expanded in x around inf 51.8%

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

      1. associate-/l* 51.6%

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

      2. *-commutative 51.6%

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

   10. Simplified 51.6%

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

   if 2.80000000000000001e287 < a

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-+r- 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 45.1%

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

      5. *-commutative 45.1%

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

      6. associate-+r- 45.1%

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

      7. +-commutative 45.1%

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

      8. associate-*l* 45.1%

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

      9. associate-*l* 58.8%

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

      10. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. fma-define 58.8%

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

      2. associate-/l* 58.6%

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

      3. fma-define 58.6%

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

      4. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-278}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-185}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+159}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{y \cdot x}{z \cdot c}\\ t_2 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-277}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-185}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (/ (* y x) (* z c)))) (t_2 (* t (* a (/ -4.0 c)))))
   (if (<= a -3.6e-119)
     t_2
     (if (<= a -8e-277)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= a 2.1e-185)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 1.8e+107)
           t_1
           (if (<= a 1.8e+261)
             t_2
             (if (<= a 2.8e+287) t_1 (* (/ a c) (* -4.0 t))))))))))

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 * x) / (z * c));
	double t_2 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -3.6e-119) {
		tmp = t_2;
	} else if (a <= -8e-277) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (a <= 2.1e-185) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.8e+107) {
		tmp = t_1;
	} else if (a <= 1.8e+261) {
		tmp = t_2;
	} else if (a <= 2.8e+287) {
		tmp = t_1;
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y * x) / (z * c))
    t_2 = t * (a * ((-4.0d0) / c))
    if (a <= (-3.6d-119)) then
        tmp = t_2
    else if (a <= (-8d-277)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (a <= 2.1d-185) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 1.8d+107) then
        tmp = t_1
    else if (a <= 1.8d+261) then
        tmp = t_2
    else if (a <= 2.8d+287) then
        tmp = t_1
    else
        tmp = (a / c) * ((-4.0d0) * t)
    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 * x) / (z * c));
	double t_2 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -3.6e-119) {
		tmp = t_2;
	} else if (a <= -8e-277) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (a <= 2.1e-185) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.8e+107) {
		tmp = t_1;
	} else if (a <= 1.8e+261) {
		tmp = t_2;
	} else if (a <= 2.8e+287) {
		tmp = t_1;
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	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 * x) / (z * c))
	t_2 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -3.6e-119:
		tmp = t_2
	elif a <= -8e-277:
		tmp = 9.0 * ((y / z) * (x / c))
	elif a <= 2.1e-185:
		tmp = (b / z) * (1.0 / c)
	elif a <= 1.8e+107:
		tmp = t_1
	elif a <= 1.8e+261:
		tmp = t_2
	elif a <= 2.8e+287:
		tmp = t_1
	else:
		tmp = (a / c) * (-4.0 * t)
	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(y * x) / Float64(z * c)))
	t_2 = Float64(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -3.6e-119)
		tmp = t_2;
	elseif (a <= -8e-277)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (a <= 2.1e-185)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 1.8e+107)
		tmp = t_1;
	elseif (a <= 1.8e+261)
		tmp = t_2;
	elseif (a <= 2.8e+287)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	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 * x) / (z * c));
	t_2 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -3.6e-119)
		tmp = t_2;
	elseif (a <= -8e-277)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (a <= 2.1e-185)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 1.8e+107)
		tmp = t_1;
	elseif (a <= 1.8e+261)
		tmp = t_2;
	elseif (a <= 2.8e+287)
		tmp = t_1;
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e-119], t$95$2, If[LessEqual[a, -8e-277], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-185], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+107], t$95$1, If[LessEqual[a, 1.8e+261], t$95$2, If[LessEqual[a, 2.8e+287], t$95$1, N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.6e-119 or 1.7999999999999999e107 < a < 1.80000000000000009e261

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-+r- 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-*r* 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-+r- 63.4%

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

      7. +-commutative 63.4%

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

      8. associate-*l* 63.4%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in t around inf 71.0%

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

   6. Taylor expanded in x around 0 68.6%

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

   7. Taylor expanded in a around inf 60.0%

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

      1. associate-*r/ 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 60.0%

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

   9. Simplified 60.0%

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

   if -3.6e-119 < a < -7.99999999999999975e-277

   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. +-commutative 83.3%

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

      2. associate-+r- 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*r* 88.9%

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

      5. *-commutative 88.9%

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

      6. associate-+r- 88.9%

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

      7. +-commutative 88.9%

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

      8. associate-*l* 89.0%

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

      9. associate-*l* 89.0%

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

      10. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf 54.3%

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

      1. times-frac 54.2%

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

   7. Applied egg-rr 54.2%

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

   if -7.99999999999999975e-277 < a < 2.1e-185

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-+r- 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*r* 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-+r- 82.0%

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

      7. +-commutative 82.0%

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

      8. associate-*l* 82.0%

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

      9. associate-*l* 82.0%

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

      10. *-commutative 82.0%

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

   3. Simplified 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. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

      1. *-un-lft-identity 51.2%

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

      2. associate-/r* 59.5%

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

   9. Applied egg-rr 59.5%

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

       1. div-inv 59.6%

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

   11. Applied egg-rr 59.6%

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

   if 2.1e-185 < a < 1.7999999999999999e107 or 1.80000000000000009e261 < a < 2.80000000000000001e287

   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. +-commutative 81.6%

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

      2. associate-+r- 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*r* 83.6%

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

      5. *-commutative 83.6%

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

      6. associate-+r- 83.6%

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

      7. +-commutative 83.6%

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

      8. associate-*l* 83.5%

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

      9. associate-*l* 75.7%

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

      10. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in x around inf 47.7%

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

   if 2.80000000000000001e287 < a

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-+r- 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 45.1%

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

      5. *-commutative 45.1%

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

      6. associate-+r- 45.1%

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

      7. +-commutative 45.1%

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

      8. associate-*l* 45.1%

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

      9. associate-*l* 58.8%

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

      10. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. fma-define 58.8%

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

      2. associate-/l* 58.6%

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

      3. fma-define 58.6%

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

      4. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-277}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-185}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-182}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))))
   (if (<= a -4.2e-119)
     t_1
     (if (<= a -9.5e-280)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= a 1.3e-182)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 5.5e+107)
           (* 9.0 (/ (* y x) (* z c)))
           (if (<= a 1.8e+261)
             t_1
             (if (<= a 2.8e+287)
               (* (* x 9.0) (/ y (* z c)))
               (* (/ a c) (* -4.0 t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -4.2e-119) {
		tmp = t_1;
	} else if (a <= -9.5e-280) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (a <= 1.3e-182) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 5.5e+107) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 1.8e+261) {
		tmp = t_1;
	} else if (a <= 2.8e+287) {
		tmp = (x * 9.0) * (y / (z * c));
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    if (a <= (-4.2d-119)) then
        tmp = t_1
    else if (a <= (-9.5d-280)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (a <= 1.3d-182) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 5.5d+107) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= 1.8d+261) then
        tmp = t_1
    else if (a <= 2.8d+287) then
        tmp = (x * 9.0d0) * (y / (z * c))
    else
        tmp = (a / c) * ((-4.0d0) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -4.2e-119) {
		tmp = t_1;
	} else if (a <= -9.5e-280) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (a <= 1.3e-182) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 5.5e+107) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 1.8e+261) {
		tmp = t_1;
	} else if (a <= 2.8e+287) {
		tmp = (x * 9.0) * (y / (z * c));
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -4.2e-119:
		tmp = t_1
	elif a <= -9.5e-280:
		tmp = 9.0 * ((y / z) * (x / c))
	elif a <= 1.3e-182:
		tmp = (b / z) * (1.0 / c)
	elif a <= 5.5e+107:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= 1.8e+261:
		tmp = t_1
	elif a <= 2.8e+287:
		tmp = (x * 9.0) * (y / (z * c))
	else:
		tmp = (a / c) * (-4.0 * t)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -4.2e-119)
		tmp = t_1;
	elseif (a <= -9.5e-280)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (a <= 1.3e-182)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 5.5e+107)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= 1.8e+261)
		tmp = t_1;
	elseif (a <= 2.8e+287)
		tmp = Float64(Float64(x * 9.0) * Float64(y / Float64(z * c)));
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -4.2e-119)
		tmp = t_1;
	elseif (a <= -9.5e-280)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (a <= 1.3e-182)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 5.5e+107)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= 1.8e+261)
		tmp = t_1;
	elseif (a <= 2.8e+287)
		tmp = (x * 9.0) * (y / (z * c));
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-119], t$95$1, If[LessEqual[a, -9.5e-280], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-182], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e+107], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+261], t$95$1, If[LessEqual[a, 2.8e+287], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.2e-119 or 5.5000000000000003e107 < a < 1.80000000000000009e261

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-+r- 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-*r* 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-+r- 63.4%

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

      7. +-commutative 63.4%

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

      8. associate-*l* 63.4%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in t around inf 71.0%

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

   6. Taylor expanded in x around 0 68.6%

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

   7. Taylor expanded in a around inf 60.0%

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

      1. associate-*r/ 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 60.0%

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

   9. Simplified 60.0%

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

   if -4.2e-119 < a < -9.50000000000000082e-280

   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. +-commutative 83.3%

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

      2. associate-+r- 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*r* 88.9%

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

      5. *-commutative 88.9%

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

      6. associate-+r- 88.9%

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

      7. +-commutative 88.9%

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

      8. associate-*l* 89.0%

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

      9. associate-*l* 89.0%

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

      10. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf 54.3%

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

      1. times-frac 54.2%

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

   7. Applied egg-rr 54.2%

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

   if -9.50000000000000082e-280 < a < 1.30000000000000003e-182

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-+r- 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*r* 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-+r- 82.0%

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

      7. +-commutative 82.0%

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

      8. associate-*l* 82.0%

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

      9. associate-*l* 82.0%

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

      10. *-commutative 82.0%

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

   3. Simplified 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. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

      1. *-un-lft-identity 51.2%

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

      2. associate-/r* 59.5%

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

   9. Applied egg-rr 59.5%

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

       1. div-inv 59.6%

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

   11. Applied egg-rr 59.6%

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

   if 1.30000000000000003e-182 < a < 5.5000000000000003e107

   1. Initial program 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-+r- 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 83.7%

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

      5. *-commutative 83.7%

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

      6. associate-+r- 83.7%

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

      7. +-commutative 83.7%

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

      8. associate-*l* 83.6%

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

      9. associate-*l* 81.5%

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

      10. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in x around inf 47.2%

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

   if 1.80000000000000009e261 < a < 2.80000000000000001e287

   1. Initial program 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-+r- 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-+r- 82.7%

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

      7. +-commutative 82.7%

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

      8. associate-*l* 82.9%

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

      9. associate-*l* 34.9%

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

      10. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in z around 0 83.5%

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

      1. fma-define 83.5%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

      4. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 51.8%

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

      1. associate-/l* 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

   10. Simplified 51.6%

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

   if 2.80000000000000001e287 < a

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-+r- 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 45.1%

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

      5. *-commutative 45.1%

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

      6. associate-+r- 45.1%

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

      7. +-commutative 45.1%

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

      8. associate-*l* 45.1%

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

      9. associate-*l* 58.8%

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

      10. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. fma-define 58.8%

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

      2. associate-/l* 58.6%

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

      3. fma-define 58.6%

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

      4. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-280}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-182}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-274}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-182}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+108}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))))
   (if (<= a -3.2e-119)
     t_1
     (if (<= a -1.5e-274)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= a 2.7e-182)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 1.05e+108)
           (* 9.0 (/ (* y x) (* z c)))
           (if (<= a 1.8e+261)
             t_1
             (if (<= a 2.8e+287)
               (/ (* 9.0 (* y x)) (* z c))
               (* (/ a c) (* -4.0 t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -3.2e-119) {
		tmp = t_1;
	} else if (a <= -1.5e-274) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (a <= 2.7e-182) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.05e+108) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 1.8e+261) {
		tmp = t_1;
	} else if (a <= 2.8e+287) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    if (a <= (-3.2d-119)) then
        tmp = t_1
    else if (a <= (-1.5d-274)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (a <= 2.7d-182) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 1.05d+108) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= 1.8d+261) then
        tmp = t_1
    else if (a <= 2.8d+287) then
        tmp = (9.0d0 * (y * x)) / (z * c)
    else
        tmp = (a / c) * ((-4.0d0) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -3.2e-119) {
		tmp = t_1;
	} else if (a <= -1.5e-274) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (a <= 2.7e-182) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.05e+108) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 1.8e+261) {
		tmp = t_1;
	} else if (a <= 2.8e+287) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -3.2e-119:
		tmp = t_1
	elif a <= -1.5e-274:
		tmp = 9.0 * ((y / z) * (x / c))
	elif a <= 2.7e-182:
		tmp = (b / z) * (1.0 / c)
	elif a <= 1.05e+108:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= 1.8e+261:
		tmp = t_1
	elif a <= 2.8e+287:
		tmp = (9.0 * (y * x)) / (z * c)
	else:
		tmp = (a / c) * (-4.0 * t)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -3.2e-119)
		tmp = t_1;
	elseif (a <= -1.5e-274)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (a <= 2.7e-182)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 1.05e+108)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= 1.8e+261)
		tmp = t_1;
	elseif (a <= 2.8e+287)
		tmp = Float64(Float64(9.0 * Float64(y * x)) / Float64(z * c));
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -3.2e-119)
		tmp = t_1;
	elseif (a <= -1.5e-274)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (a <= 2.7e-182)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 1.05e+108)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= 1.8e+261)
		tmp = t_1;
	elseif (a <= 2.8e+287)
		tmp = (9.0 * (y * x)) / (z * c);
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e-119], t$95$1, If[LessEqual[a, -1.5e-274], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-182], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+108], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+261], t$95$1, If[LessEqual[a, 2.8e+287], N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.19999999999999993e-119 or 1.05000000000000005e108 < a < 1.80000000000000009e261

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-+r- 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-*r* 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-+r- 63.4%

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

      7. +-commutative 63.4%

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

      8. associate-*l* 63.4%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in t around inf 71.0%

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

   6. Taylor expanded in x around 0 68.6%

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

   7. Taylor expanded in a around inf 60.0%

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

      1. associate-*r/ 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 60.0%

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

   9. Simplified 60.0%

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

   if -3.19999999999999993e-119 < a < -1.49999999999999989e-274

   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. +-commutative 83.3%

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

      2. associate-+r- 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*r* 88.9%

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

      5. *-commutative 88.9%

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

      6. associate-+r- 88.9%

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

      7. +-commutative 88.9%

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

      8. associate-*l* 89.0%

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

      9. associate-*l* 89.0%

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

      10. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf 54.3%

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

      1. times-frac 54.2%

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

   7. Applied egg-rr 54.2%

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

   if -1.49999999999999989e-274 < a < 2.69999999999999999e-182

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-+r- 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*r* 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-+r- 82.0%

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

      7. +-commutative 82.0%

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

      8. associate-*l* 82.0%

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

      9. associate-*l* 82.0%

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

      10. *-commutative 82.0%

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

   3. Simplified 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. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

      1. *-un-lft-identity 51.2%

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

      2. associate-/r* 59.5%

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

   9. Applied egg-rr 59.5%

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

       1. div-inv 59.6%

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

   11. Applied egg-rr 59.6%

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

   if 2.69999999999999999e-182 < a < 1.05000000000000005e108

   1. Initial program 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-+r- 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 83.7%

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

      5. *-commutative 83.7%

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

      6. associate-+r- 83.7%

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

      7. +-commutative 83.7%

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

      8. associate-*l* 83.6%

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

      9. associate-*l* 81.5%

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

      10. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in x around inf 47.2%

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

   if 1.80000000000000009e261 < a < 2.80000000000000001e287

   1. Initial program 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-+r- 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-+r- 82.7%

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

      7. +-commutative 82.7%

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

      8. associate-*l* 82.9%

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

      9. associate-*l* 34.9%

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

      10. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in x around inf 51.8%

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

      1. associate-*r/ 51.8%

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

      2. *-commutative 51.8%

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

   7. Applied egg-rr 51.8%

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

   if 2.80000000000000001e287 < a

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-+r- 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 45.1%

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

      5. *-commutative 45.1%

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

      6. associate-+r- 45.1%

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

      7. +-commutative 45.1%

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

      8. associate-*l* 45.1%

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

      9. associate-*l* 58.8%

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

      10. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. fma-define 58.8%

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

      2. associate-/l* 58.6%

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

      3. fma-define 58.6%

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

      4. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-274}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-182}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+108}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-278}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (* t (* a (/ -4.0 c)))))
   (if (<= a -3.9e-119)
     t_1
     (if (<= a -4e-278)
       (/ (* 9.0 (* x (/ y z))) c)
       (if (<= a 2.4e-184)
         (* (/ b z) (/ 1.0 c))
         (if (<= a 1.8e+107)
           (* 9.0 (/ (* y x) (* z c)))
           (if (<= a 1.8e+261)
             t_1
             (if (<= a 2.8e+287)
               (/ (* 9.0 (* y x)) (* z c))
               (* (/ a c) (* -4.0 t))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -3.9e-119) {
		tmp = t_1;
	} else if (a <= -4e-278) {
		tmp = (9.0 * (x * (y / z))) / c;
	} else if (a <= 2.4e-184) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.8e+107) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 1.8e+261) {
		tmp = t_1;
	} else if (a <= 2.8e+287) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * ((-4.0d0) / c))
    if (a <= (-3.9d-119)) then
        tmp = t_1
    else if (a <= (-4d-278)) then
        tmp = (9.0d0 * (x * (y / z))) / c
    else if (a <= 2.4d-184) then
        tmp = (b / z) * (1.0d0 / c)
    else if (a <= 1.8d+107) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (a <= 1.8d+261) then
        tmp = t_1
    else if (a <= 2.8d+287) then
        tmp = (9.0d0 * (y * x)) / (z * c)
    else
        tmp = (a / c) * ((-4.0d0) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -3.9e-119) {
		tmp = t_1;
	} else if (a <= -4e-278) {
		tmp = (9.0 * (x * (y / z))) / c;
	} else if (a <= 2.4e-184) {
		tmp = (b / z) * (1.0 / c);
	} else if (a <= 1.8e+107) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (a <= 1.8e+261) {
		tmp = t_1;
	} else if (a <= 2.8e+287) {
		tmp = (9.0 * (y * x)) / (z * c);
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -3.9e-119:
		tmp = t_1
	elif a <= -4e-278:
		tmp = (9.0 * (x * (y / z))) / c
	elif a <= 2.4e-184:
		tmp = (b / z) * (1.0 / c)
	elif a <= 1.8e+107:
		tmp = 9.0 * ((y * x) / (z * c))
	elif a <= 1.8e+261:
		tmp = t_1
	elif a <= 2.8e+287:
		tmp = (9.0 * (y * x)) / (z * c)
	else:
		tmp = (a / c) * (-4.0 * t)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -3.9e-119)
		tmp = t_1;
	elseif (a <= -4e-278)
		tmp = Float64(Float64(9.0 * Float64(x * Float64(y / z))) / c);
	elseif (a <= 2.4e-184)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	elseif (a <= 1.8e+107)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (a <= 1.8e+261)
		tmp = t_1;
	elseif (a <= 2.8e+287)
		tmp = Float64(Float64(9.0 * Float64(y * x)) / Float64(z * c));
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -3.9e-119)
		tmp = t_1;
	elseif (a <= -4e-278)
		tmp = (9.0 * (x * (y / z))) / c;
	elseif (a <= 2.4e-184)
		tmp = (b / z) * (1.0 / c);
	elseif (a <= 1.8e+107)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (a <= 1.8e+261)
		tmp = t_1;
	elseif (a <= 2.8e+287)
		tmp = (9.0 * (y * x)) / (z * c);
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e-119], t$95$1, If[LessEqual[a, -4e-278], N[(N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 2.4e-184], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+107], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+261], t$95$1, If[LessEqual[a, 2.8e+287], N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.8999999999999999e-119 or 1.7999999999999999e107 < a < 1.80000000000000009e261

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. associate-+r- 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-*r* 63.4%

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

      5. *-commutative 63.4%

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

      6. associate-+r- 63.4%

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

      7. +-commutative 63.4%

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

      8. associate-*l* 63.4%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in t around inf 71.0%

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

   6. Taylor expanded in x around 0 68.6%

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

   7. Taylor expanded in a around inf 60.0%

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

      1. associate-*r/ 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-/l* 60.0%

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

   9. Simplified 60.0%

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

   if -3.8999999999999999e-119 < a < -3.99999999999999975e-278

   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. +-commutative 83.3%

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

      2. associate-+r- 83.3%

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

      3. *-commutative 83.3%

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

      4. associate-*r* 88.9%

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

      5. *-commutative 88.9%

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

      6. associate-+r- 88.9%

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

      7. +-commutative 88.9%

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

      8. associate-*l* 89.0%

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

      9. associate-*l* 89.0%

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

      10. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in a around inf 50.1%

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

   6. Taylor expanded in c around 0 60.9%

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

   7. Taylor expanded in x around inf 51.8%

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

      1. associate-/l* 54.4%

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

   9. Simplified 54.4%

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

   if -3.99999999999999975e-278 < a < 2.40000000000000024e-184

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-+r- 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*r* 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-+r- 82.0%

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

      7. +-commutative 82.0%

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

      8. associate-*l* 82.0%

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

      9. associate-*l* 82.0%

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

      10. *-commutative 82.0%

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

   3. Simplified 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. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   7. Simplified 51.2%

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

      1. *-un-lft-identity 51.2%

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

      2. associate-/r* 59.5%

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

   9. Applied egg-rr 59.5%

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

       1. div-inv 59.6%

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

   11. Applied egg-rr 59.6%

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

   if 2.40000000000000024e-184 < a < 1.7999999999999999e107

   1. Initial program 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-+r- 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 83.7%

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

      5. *-commutative 83.7%

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

      6. associate-+r- 83.7%

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

      7. +-commutative 83.7%

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

      8. associate-*l* 83.6%

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

      9. associate-*l* 81.5%

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

      10. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in x around inf 47.2%

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

   if 1.80000000000000009e261 < a < 2.80000000000000001e287

   1. Initial program 82.7%

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

      1. +-commutative 82.7%

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

      2. associate-+r- 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-+r- 82.7%

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

      7. +-commutative 82.7%

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

      8. associate-*l* 82.9%

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

      9. associate-*l* 34.9%

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

      10. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   5. Taylor expanded in x around inf 51.8%

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

      1. associate-*r/ 51.8%

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

      2. *-commutative 51.8%

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

   7. Applied egg-rr 51.8%

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

   if 2.80000000000000001e287 < a

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-+r- 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 45.1%

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

      5. *-commutative 45.1%

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

      6. associate-+r- 45.1%

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

      7. +-commutative 45.1%

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

      8. associate-*l* 45.1%

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

      9. associate-*l* 58.8%

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

      10. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. fma-define 58.8%

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

      2. associate-/l* 58.6%

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

      3. fma-define 58.6%

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

      4. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-278}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+261}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4 + \left(9 \cdot \frac{y \cdot x}{z \cdot t} + \frac{b}{z \cdot t}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.6e+61)
   (/ (* t (+ (* a -4.0) (+ (* 9.0 (/ (* y x) (* z t))) (/ b (* z t))))) c)
   (if (<= z 2.6e+67)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (/
      (* a (+ (* -4.0 t) (+ (/ b (* z a)) (* 9.0 (/ (* y x) (* z 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 (z <= -1.6e+61) {
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c;
	} else if (z <= 2.6e+67) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 (z <= (-1.6d+61)) then
        tmp = (t * ((a * (-4.0d0)) + ((9.0d0 * ((y * x) / (z * t))) + (b / (z * t))))) / c
    else if (z <= 2.6d+67) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (a * (((-4.0d0) * t) + ((b / (z * a)) + (9.0d0 * ((y * x) / (z * 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 (z <= -1.6e+61) {
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c;
	} else if (z <= 2.6e+67) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 z <= -1.6e+61:
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c
	elif z <= 2.6e+67:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 (z <= -1.6e+61)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(Float64(9.0 * Float64(Float64(y * x) / Float64(z * t))) + Float64(b / Float64(z * t))))) / c);
	elseif (z <= 2.6e+67)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(Float64(b / Float64(z * a)) + Float64(9.0 * Float64(Float64(y * x) / Float64(z * 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 (z <= -1.6e+61)
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c;
	elseif (z <= 2.6e+67)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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[z, -1.6e+61], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.6e+67], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e61

   1. Initial program 51.6%

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

      1. +-commutative 51.6%

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

      2. associate-+r- 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*r* 59.0%

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

      5. *-commutative 59.0%

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

      6. associate-+r- 59.0%

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

      7. +-commutative 59.0%

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

      8. associate-*l* 59.0%

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

      9. associate-*l* 62.8%

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

      10. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in t around inf 67.4%

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

   6. Taylor expanded in c around 0 75.5%

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

   if -1.5999999999999999e61 < z < 2.6e67

   1. Initial program 94.1%

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

   if 2.6e67 < z

   1. Initial program 46.6%

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

      1. +-commutative 46.6%

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

      2. associate-+r- 46.6%

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

      3. *-commutative 46.6%

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

      4. associate-*r* 38.9%

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

      5. *-commutative 38.9%

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

      6. associate-+r- 38.9%

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

      7. +-commutative 38.9%

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

      8. associate-*l* 38.9%

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

      9. associate-*l* 49.9%

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

      10. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in a around inf 70.2%

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

   6. Taylor expanded in c around 0 79.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4 + \left(9 \cdot \frac{y \cdot x}{z \cdot t} + \frac{b}{z \cdot t}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+38}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4 + \left(9 \cdot \frac{y \cdot x}{z \cdot t} + \frac{b}{z \cdot t}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7e+38)
   (/ (* t (+ (* a -4.0) (+ (* 9.0 (/ (* y x) (* z t))) (/ b (* z t))))) c)
   (if (<= z 2e-59)
     (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* y x) c)) (/ b c))) z)
     (/
      (* a (+ (* -4.0 t) (+ (/ b (* z a)) (* 9.0 (/ (* y x) (* z 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 (z <= -7e+38) {
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c;
	} else if (z <= 2e-59) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((y * x) / c)) + (b / c))) / z;
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 (z <= (-7d+38)) then
        tmp = (t * ((a * (-4.0d0)) + ((9.0d0 * ((y * x) / (z * t))) + (b / (z * t))))) / c
    else if (z <= 2d-59) then
        tmp = (((-4.0d0) * ((a * (z * t)) / c)) + ((9.0d0 * ((y * x) / c)) + (b / c))) / z
    else
        tmp = (a * (((-4.0d0) * t) + ((b / (z * a)) + (9.0d0 * ((y * x) / (z * 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 (z <= -7e+38) {
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c;
	} else if (z <= 2e-59) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((y * x) / c)) + (b / c))) / z;
	} else {
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 z <= -7e+38:
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c
	elif z <= 2e-59:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((y * x) / c)) + (b / c))) / z
	else:
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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 (z <= -7e+38)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) + Float64(Float64(9.0 * Float64(Float64(y * x) / Float64(z * t))) + Float64(b / Float64(z * t))))) / c);
	elseif (z <= 2e-59)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(y * x) / c)) + Float64(b / c))) / z);
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(Float64(b / Float64(z * a)) + Float64(9.0 * Float64(Float64(y * x) / Float64(z * 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 (z <= -7e+38)
		tmp = (t * ((a * -4.0) + ((9.0 * ((y * x) / (z * t))) + (b / (z * t))))) / c;
	elseif (z <= 2e-59)
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((y * x) / c)) + (b / c))) / z;
	else
		tmp = (a * ((-4.0 * t) + ((b / (z * a)) + (9.0 * ((y * x) / (z * 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[z, -7e+38], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2e-59], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000003e38

   1. Initial program 55.3%

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

      1. +-commutative 55.3%

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

      2. associate-+r- 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*r* 62.1%

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

      5. *-commutative 62.1%

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

      6. associate-+r- 62.1%

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

      7. +-commutative 62.1%

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

      8. associate-*l* 62.1%

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

      9. associate-*l* 65.7%

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

      10. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in t around inf 68.3%

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

   6. Taylor expanded in c around 0 77.3%

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

   if -7.00000000000000003e38 < z < 2.0000000000000001e-59

   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. Step-by-step derivation

      1. +-commutative 94.6%

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

      2. associate-+r- 94.6%

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

      3. *-commutative 94.6%

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

      4. associate-*r* 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-+r- 94.6%

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

      7. +-commutative 94.6%

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

      8. associate-*l* 94.6%

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

      9. associate-*l* 87.5%

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

      10. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around 0 95.5%

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

   if 2.0000000000000001e-59 < z

   1. Initial program 57.2%

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

      1. +-commutative 57.2%

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

      2. associate-+r- 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-*r* 51.4%

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

      5. *-commutative 51.4%

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

      6. associate-+r- 51.4%

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

      7. +-commutative 51.4%

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

      8. associate-*l* 51.3%

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

      9. associate-*l* 59.6%

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

      10. *-commutative 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in a around inf 73.7%

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

   6. Taylor expanded in c around 0 82.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+38}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4 + \left(9 \cdot \frac{y \cdot x}{z \cdot t} + \frac{b}{z \cdot t}\right)\right)}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \left(\frac{b}{z \cdot a} + 9 \cdot \frac{y \cdot x}{z \cdot a}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ t_2 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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))) (t_2 (* t (* a (/ -4.0 c)))))
   (if (<= a -4.2e-119)
     t_2
     (if (<= a 5.1e+159)
       t_1
       (if (<= a 4.6e+245)
         t_2
         (if (<= a 2.8e+287) t_1 (* (/ a c) (* -4.0 t))))))))

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 t_2 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -4.2e-119) {
		tmp = t_2;
	} else if (a <= 5.1e+159) {
		tmp = t_1;
	} else if (a <= 4.6e+245) {
		tmp = t_2;
	} else if (a <= 2.8e+287) {
		tmp = t_1;
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (y * x))) / (z * c)
    t_2 = t * (a * ((-4.0d0) / c))
    if (a <= (-4.2d-119)) then
        tmp = t_2
    else if (a <= 5.1d+159) then
        tmp = t_1
    else if (a <= 4.6d+245) then
        tmp = t_2
    else if (a <= 2.8d+287) then
        tmp = t_1
    else
        tmp = (a / c) * ((-4.0d0) * t)
    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 t_2 = t * (a * (-4.0 / c));
	double tmp;
	if (a <= -4.2e-119) {
		tmp = t_2;
	} else if (a <= 5.1e+159) {
		tmp = t_1;
	} else if (a <= 4.6e+245) {
		tmp = t_2;
	} else if (a <= 2.8e+287) {
		tmp = t_1;
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	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)
	t_2 = t * (a * (-4.0 / c))
	tmp = 0
	if a <= -4.2e-119:
		tmp = t_2
	elif a <= 5.1e+159:
		tmp = t_1
	elif a <= 4.6e+245:
		tmp = t_2
	elif a <= 2.8e+287:
		tmp = t_1
	else:
		tmp = (a / c) * (-4.0 * t)
	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))
	t_2 = Float64(t * Float64(a * Float64(-4.0 / c)))
	tmp = 0.0
	if (a <= -4.2e-119)
		tmp = t_2;
	elseif (a <= 5.1e+159)
		tmp = t_1;
	elseif (a <= 4.6e+245)
		tmp = t_2;
	elseif (a <= 2.8e+287)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	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);
	t_2 = t * (a * (-4.0 / c));
	tmp = 0.0;
	if (a <= -4.2e-119)
		tmp = t_2;
	elseif (a <= 5.1e+159)
		tmp = t_1;
	elseif (a <= 4.6e+245)
		tmp = t_2;
	elseif (a <= 2.8e+287)
		tmp = t_1;
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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]}, Block[{t$95$2 = N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-119], t$95$2, If[LessEqual[a, 5.1e+159], t$95$1, If[LessEqual[a, 4.6e+245], t$95$2, If[LessEqual[a, 2.8e+287], t$95$1, N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2e-119 or 5.09999999999999967e159 < a < 4.5999999999999999e245

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-+r- 67.9%

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

      3. *-commutative 67.9%

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

      4. associate-*r* 64.3%

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

      5. *-commutative 64.3%

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

      6. associate-+r- 64.3%

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

      7. +-commutative 64.3%

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

      8. associate-*l* 64.4%

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

      9. associate-*l* 67.0%

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

      10. *-commutative 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in t around inf 71.9%

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

   6. Taylor expanded in x around 0 69.3%

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

   7. Taylor expanded in a around inf 59.2%

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

      1. associate-*r/ 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-/l* 59.2%

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

   9. Simplified 59.2%

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

   if -4.2e-119 < a < 5.09999999999999967e159 or 4.5999999999999999e245 < a < 2.80000000000000001e287

   1. Initial program 78.1%

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

      1. +-commutative 78.1%

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

      2. associate-+r- 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*r* 82.1%

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

      5. *-commutative 82.1%

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

      6. associate-+r- 82.1%

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

      7. +-commutative 82.1%

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

      8. associate-*l* 82.1%

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

      9. associate-*l* 79.8%

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

      10. *-commutative 79.8%

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

   3. Simplified 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. Taylor expanded in x around inf 72.2%

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

   if 2.80000000000000001e287 < a

   1. Initial program 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-+r- 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 45.1%

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

      5. *-commutative 45.1%

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

      6. associate-+r- 45.1%

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

      7. +-commutative 45.1%

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

      8. associate-*l* 45.1%

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

      9. associate-*l* 58.8%

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

      10. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. fma-define 58.8%

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

      2. associate-/l* 58.6%

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

      3. fma-define 58.6%

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

      4. associate-/l* 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in a around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+159}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+245}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+287}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+141}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-25}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \end{array} \]

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 (<= z -5e+164)
   (* (* a t) (/ -4.0 c))
   (if (<= z -2.75e+141)
     (* (/ b c) (/ 1.0 z))
     (if (<= z -1.65e-50)
       (* (/ a c) (* -4.0 t))
       (if (<= z 1.65e-25)
         (* 9.0 (* x (/ y (* z c))))
         (* a (/ (* -4.0 t) 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 <= -5e+164) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= -2.75e+141) {
		tmp = (b / c) * (1.0 / z);
	} else if (z <= -1.65e-50) {
		tmp = (a / c) * (-4.0 * t);
	} else if (z <= 1.65e-25) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = a * ((-4.0 * t) / 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 <= (-5d+164)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (z <= (-2.75d+141)) then
        tmp = (b / c) * (1.0d0 / z)
    else if (z <= (-1.65d-50)) then
        tmp = (a / c) * ((-4.0d0) * t)
    else if (z <= 1.65d-25) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else
        tmp = a * (((-4.0d0) * t) / 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 <= -5e+164) {
		tmp = (a * t) * (-4.0 / c);
	} else if (z <= -2.75e+141) {
		tmp = (b / c) * (1.0 / z);
	} else if (z <= -1.65e-50) {
		tmp = (a / c) * (-4.0 * t);
	} else if (z <= 1.65e-25) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = a * ((-4.0 * t) / 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 <= -5e+164:
		tmp = (a * t) * (-4.0 / c)
	elif z <= -2.75e+141:
		tmp = (b / c) * (1.0 / z)
	elif z <= -1.65e-50:
		tmp = (a / c) * (-4.0 * t)
	elif z <= 1.65e-25:
		tmp = 9.0 * (x * (y / (z * c)))
	else:
		tmp = a * ((-4.0 * t) / 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 <= -5e+164)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (z <= -2.75e+141)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	elseif (z <= -1.65e-50)
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	elseif (z <= 1.65e-25)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	else
		tmp = Float64(a * Float64(Float64(-4.0 * t) / 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 <= -5e+164)
		tmp = (a * t) * (-4.0 / c);
	elseif (z <= -2.75e+141)
		tmp = (b / c) * (1.0 / z);
	elseif (z <= -1.65e-50)
		tmp = (a / c) * (-4.0 * t);
	elseif (z <= 1.65e-25)
		tmp = 9.0 * (x * (y / (z * c)));
	else
		tmp = a * ((-4.0 * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -5e+164], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.75e+141], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-50], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-25], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.9999999999999995e164

   1. Initial program 54.5%

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

      1. +-commutative 54.5%

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

      2. associate-+r- 54.5%

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

      3. *-commutative 54.5%

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

      4. associate-*r* 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-+r- 62.3%

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

      7. +-commutative 62.3%

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

      8. associate-*l* 62.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 65.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 65.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 65.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 62.8%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in c around 0 71.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \left(9 \cdot \frac{x \cdot y}{a \cdot z} + \frac{b}{a \cdot z}\right)\right)}{c}} \]

   7. Taylor expanded in a around inf 57.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*r/ 57.4%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. *-commutative 57.4%

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4}}{c} \]

      3. associate-/l* 57.4%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} \]

   9. Simplified 57.4%

      \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} \]

   if -4.9999999999999995e164 < z < -2.74999999999999984e141

   1. Initial program 59.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 59.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 59.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 59.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 58.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 58.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 58.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 58.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 58.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 60.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 60.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 60.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 72.2%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 72.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. div-inv 72.7%

         \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   9. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{\frac{b}{c} \cdot \frac{1}{z}} \]

   if -2.74999999999999984e141 < z < -1.6499999999999999e-50

   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. +-commutative 71.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 71.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 71.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 75.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 75.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 75.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 75.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 75.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 71.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 71.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 73.6%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. fma-define 73.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot \left(t \cdot z\right)}{c}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}}{z} \]

      2. associate-/l* 79.9%

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t \cdot z}{c}}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. fma-define 79.9%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \frac{t \cdot z}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c}, \frac{b}{c}\right)}\right)}{z} \]

      4. associate-/l* 79.9%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \frac{t \cdot z}{c}, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{c}}, \frac{b}{c}\right)\right)}{z} \]

   7. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4, a \cdot \frac{t \cdot z}{c}, \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}} \]

   8. Taylor expanded in a around inf 49.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 58.8%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

      3. associate-*l* 58.8%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \frac{a}{c}} \]

      4. *-commutative 58.8%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(-4 \cdot t\right)} \]

      5. *-commutative 58.8%

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\left(t \cdot -4\right)} \]

   10. Simplified 58.8%

       \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(t \cdot -4\right)} \]

   if -1.6499999999999999e-50 < z < 1.6499999999999999e-25

   1. Initial program 95.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 95.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 95.7%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 95.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 95.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 95.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 95.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 95.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 95.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 90.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 90.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 95.6%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. fma-define 95.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot \left(t \cdot z\right)}{c}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}}{z} \]

      2. associate-/l* 94.5%

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t \cdot z}{c}}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. associate-/l* 92.4%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \color{blue}{\left(t \cdot \frac{z}{c}\right)}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. fma-define 92.4%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c}, \frac{b}{c}\right)}\right)}{z} \]

      5. associate-/l* 90.3%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{c}}, \frac{b}{c}\right)\right)}{z} \]

   7. Simplified 90.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}} \]

   8. Taylor expanded in x around inf 59.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/l* 58.5%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

      2. *-commutative 58.5%

         \[\leadsto 9 \cdot \left(x \cdot \frac{y}{\color{blue}{z \cdot c}}\right) \]

   10. Simplified 58.5%

       \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]

   if 1.6499999999999999e-25 < z

   1. Initial program 56.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 56.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 56.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 56.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 50.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 50.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 50.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 50.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 50.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 58.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 58.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 60.3%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 60.3%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. associate-*l/ 60.4%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+141}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-25}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+85}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5.5e+65)
   (* t (/ (- (/ (/ b z) t) (* a 4.0)) c))
   (if (<= z 8.4e+85)
     (/ (+ b (- (* x (* y 9.0)) (* (* z 4.0) (* a t)))) (* z c))
     (/ (* a (+ (* -4.0 t) (/ b (* z 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 (z <= -5.5e+65) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (z <= 8.4e+85) {
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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 (z <= (-5.5d+65)) then
        tmp = t * ((((b / z) / t) - (a * 4.0d0)) / c)
    else if (z <= 8.4d+85) then
        tmp = (b + ((x * (y * 9.0d0)) - ((z * 4.0d0) * (a * t)))) / (z * c)
    else
        tmp = (a * (((-4.0d0) * t) + (b / (z * 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 (z <= -5.5e+65) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (z <= 8.4e+85) {
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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 z <= -5.5e+65:
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c)
	elif z <= 8.4e+85:
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (z * c)
	else:
		tmp = (a * ((-4.0 * t) + (b / (z * 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 (z <= -5.5e+65)
		tmp = Float64(t * Float64(Float64(Float64(Float64(b / z) / t) - Float64(a * 4.0)) / c));
	elseif (z <= 8.4e+85)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(z * 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 (z <= -5.5e+65)
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	elseif (z <= 8.4e+85)
		tmp = (b + ((x * (y * 9.0)) - ((z * 4.0) * (a * t)))) / (z * c);
	else
		tmp = (a * ((-4.0 * t) + (b / (z * 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[z, -5.5e+65], N[(t * N[(N[(N[(N[(b / z), $MachinePrecision] / t), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+85], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999996e65

   1. Initial program 51.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 51.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 51.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 51.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 59.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 59.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 59.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 59.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 59.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 62.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 62.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 62.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in x around 0 66.2%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]

   7. Taylor expanded in c around -inf 70.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)}{c}} \]
   8. Step-by-step derivation

      1. mul-1-neg 70.9%

         \[\leadsto \color{blue}{-\frac{t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)}{c}} \]

      2. associate-/l* 69.4%

         \[\leadsto -\color{blue}{t \cdot \frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{c}} \]

      3. distribute-rgt-neg-in 69.4%

         \[\leadsto \color{blue}{t \cdot \left(-\frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{c}\right)} \]

      4. distribute-neg-frac2 69.4%

         \[\leadsto t \cdot \color{blue}{\frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{-c}} \]

      5. +-commutative 69.4%

         \[\leadsto t \cdot \frac{\color{blue}{4 \cdot a + -1 \cdot \frac{b}{t \cdot z}}}{-c} \]

      6. mul-1-neg 69.4%

         \[\leadsto t \cdot \frac{4 \cdot a + \color{blue}{\left(-\frac{b}{t \cdot z}\right)}}{-c} \]

      7. unsub-neg 69.4%

         \[\leadsto t \cdot \frac{\color{blue}{4 \cdot a - \frac{b}{t \cdot z}}}{-c} \]

      8. *-commutative 69.4%

         \[\leadsto t \cdot \frac{\color{blue}{a \cdot 4} - \frac{b}{t \cdot z}}{-c} \]

      9. *-commutative 69.4%

         \[\leadsto t \cdot \frac{a \cdot 4 - \frac{b}{\color{blue}{z \cdot t}}}{-c} \]

      10. associate-/r* 72.5%

          \[\leadsto t \cdot \frac{a \cdot 4 - \color{blue}{\frac{\frac{b}{z}}{t}}}{-c} \]

   9. Simplified 72.5%

      \[\leadsto \color{blue}{t \cdot \frac{a \cdot 4 - \frac{\frac{b}{z}}{t}}{-c}} \]

   if -5.4999999999999996e65 < z < 8.4000000000000004e85

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 94.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 94.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 94.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 94.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 94.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 88.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 88.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   if 8.4000000000000004e85 < z

   1. Initial program 46.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 46.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 46.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 46.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 38.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 38.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 38.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 38.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 38.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 49.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 49.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in c around 0 79.5%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \left(9 \cdot \frac{x \cdot y}{a \cdot z} + \frac{b}{a \cdot z}\right)\right)}{c}} \]

   7. Taylor expanded in x around 0 76.6%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+85}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8.6e+61)
   (* t (/ (- (/ (/ b z) t) (* a 4.0)) c))
   (if (<= z 8.5e+74)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (/ (* a (+ (* -4.0 t) (/ b (* z 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 (z <= -8.6e+61) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (z <= 8.5e+74) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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 (z <= (-8.6d+61)) then
        tmp = t * ((((b / z) / t) - (a * 4.0d0)) / c)
    else if (z <= 8.5d+74) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (a * (((-4.0d0) * t) + (b / (z * 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 (z <= -8.6e+61) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (z <= 8.5e+74) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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 z <= -8.6e+61:
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c)
	elif z <= 8.5e+74:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (a * ((-4.0 * t) + (b / (z * 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 (z <= -8.6e+61)
		tmp = Float64(t * Float64(Float64(Float64(Float64(b / z) / t) - Float64(a * 4.0)) / c));
	elseif (z <= 8.5e+74)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(z * 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 (z <= -8.6e+61)
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	elseif (z <= 8.5e+74)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (a * ((-4.0 * t) + (b / (z * 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[z, -8.6e+61], N[(t * N[(N[(N[(N[(b / z), $MachinePrecision] / t), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+74], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000003e61

   1. Initial program 51.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 51.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 51.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 51.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 59.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 59.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 59.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 59.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 59.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 62.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 62.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 62.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in x around 0 66.2%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]

   7. Taylor expanded in c around -inf 70.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)}{c}} \]
   8. Step-by-step derivation

      1. mul-1-neg 70.9%

         \[\leadsto \color{blue}{-\frac{t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)}{c}} \]

      2. associate-/l* 69.4%

         \[\leadsto -\color{blue}{t \cdot \frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{c}} \]

      3. distribute-rgt-neg-in 69.4%

         \[\leadsto \color{blue}{t \cdot \left(-\frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{c}\right)} \]

      4. distribute-neg-frac2 69.4%

         \[\leadsto t \cdot \color{blue}{\frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{-c}} \]

      5. +-commutative 69.4%

         \[\leadsto t \cdot \frac{\color{blue}{4 \cdot a + -1 \cdot \frac{b}{t \cdot z}}}{-c} \]

      6. mul-1-neg 69.4%

         \[\leadsto t \cdot \frac{4 \cdot a + \color{blue}{\left(-\frac{b}{t \cdot z}\right)}}{-c} \]

      7. unsub-neg 69.4%

         \[\leadsto t \cdot \frac{\color{blue}{4 \cdot a - \frac{b}{t \cdot z}}}{-c} \]

      8. *-commutative 69.4%

         \[\leadsto t \cdot \frac{\color{blue}{a \cdot 4} - \frac{b}{t \cdot z}}{-c} \]

      9. *-commutative 69.4%

         \[\leadsto t \cdot \frac{a \cdot 4 - \frac{b}{\color{blue}{z \cdot t}}}{-c} \]

      10. associate-/r* 72.5%

          \[\leadsto t \cdot \frac{a \cdot 4 - \color{blue}{\frac{\frac{b}{z}}{t}}}{-c} \]

   9. Simplified 72.5%

      \[\leadsto \color{blue}{t \cdot \frac{a \cdot 4 - \frac{\frac{b}{z}}{t}}{-c}} \]

   if -8.6000000000000003e61 < z < 8.50000000000000028e74

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   if 8.50000000000000028e74 < z

   1. Initial program 46.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 46.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 46.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 46.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 38.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 38.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 38.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 38.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 38.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 49.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 49.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in c around 0 79.5%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \left(9 \cdot \frac{x \cdot y}{a \cdot z} + \frac{b}{a \cdot z}\right)\right)}{c}} \]

   7. Taylor expanded in x around 0 76.6%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+16} \lor \neg \left(z \leq 3.5 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.5e+16) (not (<= z 3.5e+22)))
   (/ (* a (+ (* -4.0 t) (/ b (* z a)))) c)
   (/ (+ b (* 9.0 (* y x))) (* 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 <= -2.5e+16) || !(z <= 3.5e+22)) {
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c;
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2.5d+16)) .or. (.not. (z <= 3.5d+22))) then
        tmp = (a * (((-4.0d0) * t) + (b / (z * a)))) / c
    else
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.5e+16) || !(z <= 3.5e+22)) {
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c;
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.5e+16) or not (z <= 3.5e+22):
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c
	else:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.5e+16) || !(z <= 3.5e+22))
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(z * a)))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.5e+16) || ~((z <= 3.5e+22)))
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c;
	else
		tmp = (b + (9.0 * (y * x))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.5e+16], N[Not[LessEqual[z, 3.5e+22]], $MachinePrecision]], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e16 or 3.5e22 < z

   1. Initial program 54.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 54.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 54.9%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 54.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 54.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 54.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 54.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 54.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 54.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 61.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 61.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.7%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in c around 0 77.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \left(9 \cdot \frac{x \cdot y}{a \cdot z} + \frac{b}{a \cdot z}\right)\right)}{c}} \]

   7. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}} \]

   if -2.5e16 < z < 3.5e22

   1. Initial program 94.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 94.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 94.8%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 94.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 94.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 94.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 94.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 94.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 94.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 88.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 88.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 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 82.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+16} \lor \neg \left(z \leq 3.5 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+29} \lor \neg \left(z \leq 3.4 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}}{z}\\ \end{array} \end{array} \]

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
 (if (or (<= z -8.2e+29) (not (<= z 3.4e+21)))
   (/ (* a (+ (* -4.0 t) (/ b (* z a)))) c)
   (/ (+ (* 9.0 (/ (* y x) c)) (/ 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 tmp;
	if ((z <= -8.2e+29) || !(z <= 3.4e+21)) {
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c;
	} else {
		tmp = ((9.0 * ((y * x) / c)) + (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) :: tmp
    if ((z <= (-8.2d+29)) .or. (.not. (z <= 3.4d+21))) then
        tmp = (a * (((-4.0d0) * t) + (b / (z * a)))) / c
    else
        tmp = ((9.0d0 * ((y * x) / c)) + (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 tmp;
	if ((z <= -8.2e+29) || !(z <= 3.4e+21)) {
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c;
	} else {
		tmp = ((9.0 * ((y * x) / c)) + (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):
	tmp = 0
	if (z <= -8.2e+29) or not (z <= 3.4e+21):
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c
	else:
		tmp = ((9.0 * ((y * x) / c)) + (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)
	tmp = 0.0
	if ((z <= -8.2e+29) || !(z <= 3.4e+21))
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(z * a)))) / c);
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / c)) + 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)
	tmp = 0.0;
	if ((z <= -8.2e+29) || ~((z <= 3.4e+21)))
		tmp = (a * ((-4.0 * t) + (b / (z * a)))) / c;
	else
		tmp = ((9.0 * ((y * x) / c)) + (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_] := If[Or[LessEqual[z, -8.2e+29], N[Not[LessEqual[z, 3.4e+21]], $MachinePrecision]], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000007e29 or 3.4e21 < z

   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. +-commutative 54.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 54.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 54.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 54.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 54.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 54.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 54.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 54.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 60.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 60.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.8%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in c around 0 78.8%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \left(9 \cdot \frac{x \cdot y}{a \cdot z} + \frac{b}{a \cdot z}\right)\right)}{c}} \]

   7. Taylor expanded in x around 0 74.9%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}} \]

   if -8.2000000000000007e29 < z < 3.4e21

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 94.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 94.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 94.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 94.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 94.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 87.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 87.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. fma-define 94.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot \left(t \cdot z\right)}{c}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}}{z} \]

      2. associate-/l* 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t \cdot z}{c}}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. associate-/l* 92.3%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \color{blue}{\left(t \cdot \frac{z}{c}\right)}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. fma-define 92.3%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c}, \frac{b}{c}\right)}\right)}{z} \]

      5. associate-/l* 89.6%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{c}}, \frac{b}{c}\right)\right)}{z} \]

   7. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}} \]

   8. Taylor expanded in a around 0 81.6%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+29} \lor \neg \left(z \leq 3.4 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.2e+29)
   (* t (/ (- (/ (/ b z) t) (* a 4.0)) c))
   (if (<= z 1.2e+23)
     (/ (+ (* 9.0 (/ (* y x) c)) (/ b c)) z)
     (/ (* a (+ (* -4.0 t) (/ b (* z 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 (z <= -1.2e+29) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (z <= 1.2e+23) {
		tmp = ((9.0 * ((y * x) / c)) + (b / c)) / z;
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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 (z <= (-1.2d+29)) then
        tmp = t * ((((b / z) / t) - (a * 4.0d0)) / c)
    else if (z <= 1.2d+23) then
        tmp = ((9.0d0 * ((y * x) / c)) + (b / c)) / z
    else
        tmp = (a * (((-4.0d0) * t) + (b / (z * 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 (z <= -1.2e+29) {
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	} else if (z <= 1.2e+23) {
		tmp = ((9.0 * ((y * x) / c)) + (b / c)) / z;
	} else {
		tmp = (a * ((-4.0 * t) + (b / (z * 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 z <= -1.2e+29:
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c)
	elif z <= 1.2e+23:
		tmp = ((9.0 * ((y * x) / c)) + (b / c)) / z
	else:
		tmp = (a * ((-4.0 * t) + (b / (z * 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 (z <= -1.2e+29)
		tmp = Float64(t * Float64(Float64(Float64(Float64(b / z) / t) - Float64(a * 4.0)) / c));
	elseif (z <= 1.2e+23)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y * x) / c)) + Float64(b / c)) / z);
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) + Float64(b / Float64(z * 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 (z <= -1.2e+29)
		tmp = t * ((((b / z) / t) - (a * 4.0)) / c);
	elseif (z <= 1.2e+23)
		tmp = ((9.0 * ((y * x) / c)) + (b / c)) / z;
	else
		tmp = (a * ((-4.0 * t) + (b / (z * 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[z, -1.2e+29], N[(t * N[(N[(N[(N[(b / z), $MachinePrecision] / t), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+23], N[(N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] + N[(b / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e29

   1. Initial program 57.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 57.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 57.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 63.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 63.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 63.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 63.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 63.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 67.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 67.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 67.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]

   7. Taylor expanded in c around -inf 74.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)}{c}} \]
   8. Step-by-step derivation

      1. mul-1-neg 74.3%

         \[\leadsto \color{blue}{-\frac{t \cdot \left(-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a\right)}{c}} \]

      2. associate-/l* 72.9%

         \[\leadsto -\color{blue}{t \cdot \frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{c}} \]

      3. distribute-rgt-neg-in 72.9%

         \[\leadsto \color{blue}{t \cdot \left(-\frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{c}\right)} \]

      4. distribute-neg-frac2 72.9%

         \[\leadsto t \cdot \color{blue}{\frac{-1 \cdot \frac{b}{t \cdot z} + 4 \cdot a}{-c}} \]

      5. +-commutative 72.9%

         \[\leadsto t \cdot \frac{\color{blue}{4 \cdot a + -1 \cdot \frac{b}{t \cdot z}}}{-c} \]

      6. mul-1-neg 72.9%

         \[\leadsto t \cdot \frac{4 \cdot a + \color{blue}{\left(-\frac{b}{t \cdot z}\right)}}{-c} \]

      7. unsub-neg 72.9%

         \[\leadsto t \cdot \frac{\color{blue}{4 \cdot a - \frac{b}{t \cdot z}}}{-c} \]

      8. *-commutative 72.9%

         \[\leadsto t \cdot \frac{\color{blue}{a \cdot 4} - \frac{b}{t \cdot z}}{-c} \]

      9. *-commutative 72.9%

         \[\leadsto t \cdot \frac{a \cdot 4 - \frac{b}{\color{blue}{z \cdot t}}}{-c} \]

      10. associate-/r* 75.7%

          \[\leadsto t \cdot \frac{a \cdot 4 - \color{blue}{\frac{\frac{b}{z}}{t}}}{-c} \]

   9. Simplified 75.7%

      \[\leadsto \color{blue}{t \cdot \frac{a \cdot 4 - \frac{\frac{b}{z}}{t}}{-c}} \]

   if -1.2e29 < z < 1.2e23

   1. Initial program 94.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 94.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 94.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 94.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 94.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 94.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 94.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 87.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 87.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 94.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. fma-define 94.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot \left(t \cdot z\right)}{c}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}}{z} \]

      2. associate-/l* 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t \cdot z}{c}}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. associate-/l* 92.3%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \color{blue}{\left(t \cdot \frac{z}{c}\right)}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      4. fma-define 92.3%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c}, \frac{b}{c}\right)}\right)}{z} \]

      5. associate-/l* 89.6%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{c}}, \frac{b}{c}\right)\right)}{z} \]

   7. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}} \]

   8. Taylor expanded in a around 0 81.6%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]

   if 1.2e23 < z

   1. Initial program 52.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 52.0%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 52.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 45.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 45.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 45.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 45.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 45.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 54.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 54.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 54.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 71.2%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c} + \left(9 \cdot \frac{x \cdot y}{a \cdot \left(c \cdot z\right)} + \frac{b}{a \cdot \left(c \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in c around 0 80.8%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \left(9 \cdot \frac{x \cdot y}{a \cdot z} + \frac{b}{a \cdot z}\right)\right)}{c}} \]

   7. Taylor expanded in x around 0 76.8%

      \[\leadsto \color{blue}{\frac{a \cdot \left(-4 \cdot t + \frac{b}{a \cdot z}\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{\frac{\frac{b}{z}}{t} - a \cdot 4}{c}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{9 \cdot \frac{y \cdot x}{c} + \frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t + \frac{b}{z \cdot a}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+80} \lor \neg \left(b \leq 3.6 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \end{array} \]

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 (<= b -5e+80) (not (<= b 3.6e+89)))
   (/ (/ b c) z)
   (* a (/ (* -4.0 t) 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 ((b <= -5e+80) || !(b <= 3.6e+89)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * ((-4.0 * t) / 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 ((b <= (-5d+80)) .or. (.not. (b <= 3.6d+89))) then
        tmp = (b / c) / z
    else
        tmp = a * (((-4.0d0) * t) / 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 ((b <= -5e+80) || !(b <= 3.6e+89)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * ((-4.0 * t) / 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 (b <= -5e+80) or not (b <= 3.6e+89):
		tmp = (b / c) / z
	else:
		tmp = a * ((-4.0 * t) / 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 ((b <= -5e+80) || !(b <= 3.6e+89))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(a * Float64(Float64(-4.0 * t) / 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 ((b <= -5e+80) || ~((b <= 3.6e+89)))
		tmp = (b / c) / z;
	else
		tmp = a * ((-4.0 * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -5e+80], N[Not[LessEqual[b, 3.6e+89]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999961e80 or 3.6e89 < b

   1. Initial program 72.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 72.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 72.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 71.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 71.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 71.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 71.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 71.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 75.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.2%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 63.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -4.99999999999999961e80 < b < 3.6e89

   1. Initial program 72.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 72.7%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 72.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 73.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 73.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 73.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 50.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 49.7%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*r* 49.7%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

      4. associate-*l/ 49.8%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} \]

   7. Simplified 49.8%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+80} \lor \neg \left(b \leq 3.6 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+82} \lor \neg \left(b \leq 9.5 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \end{array} \end{array} \]

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 (or (<= b -2.55e+82) (not (<= b 9.5e+89)))
   (/ (/ b c) z)
   (* t (* a (/ -4.0 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 ((b <= -2.55e+82) || !(b <= 9.5e+89)) {
		tmp = (b / c) / z;
	} else {
		tmp = t * (a * (-4.0 / 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 ((b <= (-2.55d+82)) .or. (.not. (b <= 9.5d+89))) then
        tmp = (b / c) / z
    else
        tmp = t * (a * ((-4.0d0) / 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 ((b <= -2.55e+82) || !(b <= 9.5e+89)) {
		tmp = (b / c) / z;
	} else {
		tmp = t * (a * (-4.0 / 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 (b <= -2.55e+82) or not (b <= 9.5e+89):
		tmp = (b / c) / z
	else:
		tmp = t * (a * (-4.0 / 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 ((b <= -2.55e+82) || !(b <= 9.5e+89))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(t * Float64(a * Float64(-4.0 / 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 ((b <= -2.55e+82) || ~((b <= 9.5e+89)))
		tmp = (b / c) / z;
	else
		tmp = t * (a * (-4.0 / 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[b, -2.55e+82], N[Not[LessEqual[b, 9.5e+89]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5500000000000001e82 or 9.5000000000000003e89 < b

   1. Initial program 72.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 72.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 72.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 71.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 71.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 71.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 71.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 71.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 75.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.2%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 63.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -2.5500000000000001e82 < b < 9.5000000000000003e89

   1. Initial program 72.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 72.7%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 72.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 73.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 73.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 73.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.8%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \left(9 \cdot \frac{x \cdot y}{c \cdot \left(t \cdot z\right)} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)\right)} \]

   6. Taylor expanded in x around 0 56.6%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]

   7. Taylor expanded in a around inf 53.5%

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \]
   8. Step-by-step derivation

      1. associate-*r/ 53.5%

         \[\leadsto t \cdot \color{blue}{\frac{-4 \cdot a}{c}} \]

      2. *-commutative 53.5%

         \[\leadsto t \cdot \frac{\color{blue}{a \cdot -4}}{c} \]

      3. associate-/l* 53.4%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \frac{-4}{c}\right)} \]

   9. Simplified 53.4%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \frac{-4}{c}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+82} \lor \neg \left(b \leq 9.5 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+79} \lor \neg \left(b \leq 7.8 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (or (<= b -2.9e+79) (not (<= b 7.8e+89)))
   (/ (/ b c) z)
   (* (/ a c) (* -4.0 t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2.9e+79) || !(b <= 7.8e+89)) {
		tmp = (b / c) / z;
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-2.9d+79)) .or. (.not. (b <= 7.8d+89))) then
        tmp = (b / c) / z
    else
        tmp = (a / c) * ((-4.0d0) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2.9e+79) || !(b <= 7.8e+89)) {
		tmp = (b / c) / z;
	} else {
		tmp = (a / c) * (-4.0 * t);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -2.9e+79) or not (b <= 7.8e+89):
		tmp = (b / c) / z
	else:
		tmp = (a / c) * (-4.0 * t)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -2.9e+79) || !(b <= 7.8e+89))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -2.9e+79) || ~((b <= 7.8e+89)))
		tmp = (b / c) / z;
	else
		tmp = (a / c) * (-4.0 * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -2.9e+79], N[Not[LessEqual[b, 7.8e+89]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.89999999999999992e79 or 7.80000000000000021e89 < b

   1. Initial program 72.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 72.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 72.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 71.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 71.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 71.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 71.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 71.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 75.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 75.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 50.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.2%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   7. Simplified 63.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -2.89999999999999992e79 < b < 7.80000000000000021e89

   1. Initial program 72.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 72.7%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 72.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 73.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 73.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 73.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 71.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 76.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. fma-define 76.4%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot \left(t \cdot z\right)}{c}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}}{z} \]

      2. associate-/l* 80.6%

         \[\leadsto \frac{\mathsf{fma}\left(-4, \color{blue}{a \cdot \frac{t \cdot z}{c}}, 9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]

      3. fma-define 80.6%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \frac{t \cdot z}{c}, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{c}, \frac{b}{c}\right)}\right)}{z} \]

      4. associate-/l* 79.8%

         \[\leadsto \frac{\mathsf{fma}\left(-4, a \cdot \frac{t \cdot z}{c}, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{c}}, \frac{b}{c}\right)\right)}{z} \]

   7. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-4, a \cdot \frac{t \cdot z}{c}, \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}} \]

   8. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 53.5%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

      3. associate-*l* 53.5%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \frac{a}{c}} \]

      4. *-commutative 53.5%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(-4 \cdot t\right)} \]

      5. *-commutative 53.5%

         \[\leadsto \frac{a}{c} \cdot \color{blue}{\left(t \cdot -4\right)} \]

   10. Simplified 53.5%

       \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(t \cdot -4\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+79} \lor \neg \left(b \leq 7.8 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

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 72.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. +-commutative 72.6%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

   2. associate-+r- 72.6%

      \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

   3. *-commutative 72.6%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

   4. associate-*r* 72.5%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

   5. *-commutative 72.5%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

   6. associate-+r- 72.5%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

   7. +-commutative 72.5%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   8. associate-*l* 72.5%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   9. associate-*l* 73.1%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   10. *-commutative 73.1%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 73.1%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 29.6%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 29.6%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 29.6%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 29.6%

   \[\leadsto \frac{b}{z \cdot c} \]
9. Add Preprocessing

Alternative 22: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{\frac{b}{c}}{z} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ (/ b c) z))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b / c) / z
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (b / c) / z;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = (b / c) / z;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. +-commutative 72.6%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

   2. associate-+r- 72.6%

      \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

   3. *-commutative 72.6%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

   4. associate-*r* 72.5%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

   5. *-commutative 72.5%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

   6. associate-+r- 72.5%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

   7. +-commutative 72.5%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   8. associate-*l* 72.5%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   9. associate-*l* 73.1%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   10. *-commutative 73.1%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 73.1%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 29.6%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. associate-/r* 34.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

7. Simplified 34.0%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

8. Final simplification 34.0%

   \[\leadsto \frac{\frac{b}{c}}{z} \]
9. Add Preprocessing

Developer target: 80.9% 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 2024055 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))