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

Percentage Accurate: 79.1% → 91.8%

Time: 25.7s

Alternatives: 18

Speedup: 0.7×

• 37.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c\_m}, \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c\_m}}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 2.5e+34)
    (/ (- (/ (+ b (* 9.0 (* x y))) z) (* 4.0 (* a t))) c_m)
    (fma -4.0 (* a (/ t c_m)) (/ (/ (fma x (* 9.0 y) b) c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 2.5e+34) {
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = fma(-4.0, (a * (t / c_m)), ((fma(x, (9.0 * y), b) / c_m) / z));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 2.5e+34)
		tmp = Float64(Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / z) - Float64(4.0 * Float64(a * t))) / c_m);
	else
		tmp = fma(-4.0, Float64(a * Float64(t / c_m)), Float64(Float64(fma(x, Float64(9.0 * y), b) / c_m) / z));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 2.5e+34], N[(N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 2.4999999999999999e34

   1. Initial program 83.3%

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

      1. associate-+l- 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*r* 82.7%

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

      4. *-commutative 82.7%

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

      5. associate-+l- 82.7%

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

      6. associate-*l* 82.2%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

      1. add-cube-cbrt 85.4%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 85.4%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 85.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 85.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 85.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 85.9%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 83.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 79.7%

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

   10. Taylor expanded in c around -inf 88.6%

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

   if 2.4999999999999999e34 < c

   1. Initial program 65.8%

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

      1. associate-+l- 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r* 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-+l- 68.0%

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

      6. associate-*l* 68.0%

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

      7. associate-*l* 66.2%

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

      8. *-commutative 66.2%

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

   3. Simplified 66.2%

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

      1. add-cube-cbrt 65.9%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 65.9%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 65.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 65.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 65.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 65.9%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 77.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 93.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ t_2 := a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ t_3 := \frac{b \cdot \frac{1}{z}}{c\_m}\\ t_4 := \frac{b}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;9 \cdot x \leq -5 \cdot 10^{+156}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{c\_m}\right)}{z}\\ \mathbf{elif}\;9 \cdot x \leq -1.3 \cdot 10^{+102}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;9 \cdot x \leq -3 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;9 \cdot x \leq -0.005:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;9 \cdot x \leq -2 \cdot 10^{-75}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;9 \cdot x \leq -1 \cdot 10^{-124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;9 \cdot x \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;9 \cdot x \leq -5 \cdot 10^{-305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;9 \cdot x \leq 10^{-289}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;9 \cdot x \leq 10000000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c_m) (/ y z))))
        (t_2 (* a (* -4.0 (/ t c_m))))
        (t_3 (/ (* b (/ 1.0 z)) c_m))
        (t_4 (/ b (* c_m z))))
   (*
    c_s
    (if (<= (* 9.0 x) -5e+156)
      (/ (* 9.0 (* x (/ y c_m))) z)
      (if (<= (* 9.0 x) -1.3e+102)
        t_4
        (if (<= (* 9.0 x) -3e+71)
          t_1
          (if (<= (* 9.0 x) -0.005)
            (* -4.0 (* t (/ a c_m)))
            (if (<= (* 9.0 x) -2e-75)
              t_4
              (if (<= (* 9.0 x) -1e-124)
                t_2
                (if (<= (* 9.0 x) -1e-273)
                  t_3
                  (if (<= (* 9.0 x) -5e-305)
                    t_2
                    (if (<= (* 9.0 x) 1e-289)
                      t_3
                      (if (<= (* 9.0 x) 10000000000000.0) t_2 t_1)))))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x / c_m) * (y / z));
	double t_2 = a * (-4.0 * (t / c_m));
	double t_3 = (b * (1.0 / z)) / c_m;
	double t_4 = b / (c_m * z);
	double tmp;
	if ((9.0 * x) <= -5e+156) {
		tmp = (9.0 * (x * (y / c_m))) / z;
	} else if ((9.0 * x) <= -1.3e+102) {
		tmp = t_4;
	} else if ((9.0 * x) <= -3e+71) {
		tmp = t_1;
	} else if ((9.0 * x) <= -0.005) {
		tmp = -4.0 * (t * (a / c_m));
	} else if ((9.0 * x) <= -2e-75) {
		tmp = t_4;
	} else if ((9.0 * x) <= -1e-124) {
		tmp = t_2;
	} else if ((9.0 * x) <= -1e-273) {
		tmp = t_3;
	} else if ((9.0 * x) <= -5e-305) {
		tmp = t_2;
	} else if ((9.0 * x) <= 1e-289) {
		tmp = t_3;
	} else if ((9.0 * x) <= 10000000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / c_m) * (y / z))
    t_2 = a * ((-4.0d0) * (t / c_m))
    t_3 = (b * (1.0d0 / z)) / c_m
    t_4 = b / (c_m * z)
    if ((9.0d0 * x) <= (-5d+156)) then
        tmp = (9.0d0 * (x * (y / c_m))) / z
    else if ((9.0d0 * x) <= (-1.3d+102)) then
        tmp = t_4
    else if ((9.0d0 * x) <= (-3d+71)) then
        tmp = t_1
    else if ((9.0d0 * x) <= (-0.005d0)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if ((9.0d0 * x) <= (-2d-75)) then
        tmp = t_4
    else if ((9.0d0 * x) <= (-1d-124)) then
        tmp = t_2
    else if ((9.0d0 * x) <= (-1d-273)) then
        tmp = t_3
    else if ((9.0d0 * x) <= (-5d-305)) then
        tmp = t_2
    else if ((9.0d0 * x) <= 1d-289) then
        tmp = t_3
    else if ((9.0d0 * x) <= 10000000000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x / c_m) * (y / z));
	double t_2 = a * (-4.0 * (t / c_m));
	double t_3 = (b * (1.0 / z)) / c_m;
	double t_4 = b / (c_m * z);
	double tmp;
	if ((9.0 * x) <= -5e+156) {
		tmp = (9.0 * (x * (y / c_m))) / z;
	} else if ((9.0 * x) <= -1.3e+102) {
		tmp = t_4;
	} else if ((9.0 * x) <= -3e+71) {
		tmp = t_1;
	} else if ((9.0 * x) <= -0.005) {
		tmp = -4.0 * (t * (a / c_m));
	} else if ((9.0 * x) <= -2e-75) {
		tmp = t_4;
	} else if ((9.0 * x) <= -1e-124) {
		tmp = t_2;
	} else if ((9.0 * x) <= -1e-273) {
		tmp = t_3;
	} else if ((9.0 * x) <= -5e-305) {
		tmp = t_2;
	} else if ((9.0 * x) <= 1e-289) {
		tmp = t_3;
	} else if ((9.0 * x) <= 10000000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((x / c_m) * (y / z))
	t_2 = a * (-4.0 * (t / c_m))
	t_3 = (b * (1.0 / z)) / c_m
	t_4 = b / (c_m * z)
	tmp = 0
	if (9.0 * x) <= -5e+156:
		tmp = (9.0 * (x * (y / c_m))) / z
	elif (9.0 * x) <= -1.3e+102:
		tmp = t_4
	elif (9.0 * x) <= -3e+71:
		tmp = t_1
	elif (9.0 * x) <= -0.005:
		tmp = -4.0 * (t * (a / c_m))
	elif (9.0 * x) <= -2e-75:
		tmp = t_4
	elif (9.0 * x) <= -1e-124:
		tmp = t_2
	elif (9.0 * x) <= -1e-273:
		tmp = t_3
	elif (9.0 * x) <= -5e-305:
		tmp = t_2
	elif (9.0 * x) <= 1e-289:
		tmp = t_3
	elif (9.0 * x) <= 10000000000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)))
	t_2 = Float64(a * Float64(-4.0 * Float64(t / c_m)))
	t_3 = Float64(Float64(b * Float64(1.0 / z)) / c_m)
	t_4 = Float64(b / Float64(c_m * z))
	tmp = 0.0
	if (Float64(9.0 * x) <= -5e+156)
		tmp = Float64(Float64(9.0 * Float64(x * Float64(y / c_m))) / z);
	elseif (Float64(9.0 * x) <= -1.3e+102)
		tmp = t_4;
	elseif (Float64(9.0 * x) <= -3e+71)
		tmp = t_1;
	elseif (Float64(9.0 * x) <= -0.005)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (Float64(9.0 * x) <= -2e-75)
		tmp = t_4;
	elseif (Float64(9.0 * x) <= -1e-124)
		tmp = t_2;
	elseif (Float64(9.0 * x) <= -1e-273)
		tmp = t_3;
	elseif (Float64(9.0 * x) <= -5e-305)
		tmp = t_2;
	elseif (Float64(9.0 * x) <= 1e-289)
		tmp = t_3;
	elseif (Float64(9.0 * x) <= 10000000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((x / c_m) * (y / z));
	t_2 = a * (-4.0 * (t / c_m));
	t_3 = (b * (1.0 / z)) / c_m;
	t_4 = b / (c_m * z);
	tmp = 0.0;
	if ((9.0 * x) <= -5e+156)
		tmp = (9.0 * (x * (y / c_m))) / z;
	elseif ((9.0 * x) <= -1.3e+102)
		tmp = t_4;
	elseif ((9.0 * x) <= -3e+71)
		tmp = t_1;
	elseif ((9.0 * x) <= -0.005)
		tmp = -4.0 * (t * (a / c_m));
	elseif ((9.0 * x) <= -2e-75)
		tmp = t_4;
	elseif ((9.0 * x) <= -1e-124)
		tmp = t_2;
	elseif ((9.0 * x) <= -1e-273)
		tmp = t_3;
	elseif ((9.0 * x) <= -5e-305)
		tmp = t_2;
	elseif ((9.0 * x) <= 1e-289)
		tmp = t_3;
	elseif ((9.0 * x) <= 10000000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$4 = N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[N[(9.0 * x), $MachinePrecision], -5e+156], N[(N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(9.0 * x), $MachinePrecision], -1.3e+102], t$95$4, If[LessEqual[N[(9.0 * x), $MachinePrecision], -3e+71], t$95$1, If[LessEqual[N[(9.0 * x), $MachinePrecision], -0.005], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(9.0 * x), $MachinePrecision], -2e-75], t$95$4, If[LessEqual[N[(9.0 * x), $MachinePrecision], -1e-124], t$95$2, If[LessEqual[N[(9.0 * x), $MachinePrecision], -1e-273], t$95$3, If[LessEqual[N[(9.0 * x), $MachinePrecision], -5e-305], t$95$2, If[LessEqual[N[(9.0 * x), $MachinePrecision], 1e-289], t$95$3, If[LessEqual[N[(9.0 * x), $MachinePrecision], 10000000000000.0], t$95$2, t$95$1]]]]]]]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x 9) < -4.99999999999999992e156

   1. Initial program 81.5%

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

      1. associate-+l- 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*r* 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-+l- 83.8%

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

      6. associate-*l* 83.8%

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

      7. associate-*l* 84.1%

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

      8. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in x around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/r* 70.2%

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

      3. associate-*l/ 70.2%

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

      4. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

   if -4.99999999999999992e156 < (*.f64 x 9) < -1.30000000000000003e102 or -0.0050000000000000001 < (*.f64 x 9) < -1.9999999999999999e-75

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-+l- 87.2%

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

      6. associate-*l* 87.1%

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

      7. associate-*l* 83.0%

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

      8. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   if -1.30000000000000003e102 < (*.f64 x 9) < -3.00000000000000013e71 or 1e13 < (*.f64 x 9)

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 78.5%

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

      4. *-commutative 78.5%

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

      5. associate-+l- 78.5%

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

      6. associate-*l* 78.5%

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

      7. associate-*l* 78.7%

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

      8. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x around inf 44.0%

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

      1. times-frac 54.5%

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

   7. Simplified 54.5%

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

   if -3.00000000000000013e71 < (*.f64 x 9) < -0.0050000000000000001

   1. Initial program 71.8%

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

      1. associate-+l- 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-*r* 44.6%

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

      4. *-commutative 44.6%

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

      5. associate-+l- 44.6%

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

      6. associate-*l* 44.8%

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

      7. associate-*l* 72.0%

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

      8. *-commutative 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-/l* 44.6%

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

   7. Simplified 44.6%

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

   if -1.9999999999999999e-75 < (*.f64 x 9) < -9.99999999999999933e-125 or -1e-273 < (*.f64 x 9) < -4.99999999999999985e-305 or 1e-289 < (*.f64 x 9) < 1e13

   1. Initial program 79.0%

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

      1. associate-+l- 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*r* 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-+l- 77.8%

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

      6. associate-*l* 76.6%

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

      7. associate-*l* 81.4%

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

      8. *-commutative 81.4%

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

   3. Simplified 81.4%

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

      1. add-cube-cbrt 81.2%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 81.2%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 82.4%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/l* 54.3%

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

      3. associate-*l* 54.3%

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

   9. Simplified 54.3%

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

   if -9.99999999999999933e-125 < (*.f64 x 9) < -1e-273 or -4.99999999999999985e-305 < (*.f64 x 9) < 1e-289

   1. Initial program 88.9%

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

      1. associate-+l- 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 88.9%

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

      8. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   6. Applied egg-rr 64.5%

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

   7. Taylor expanded in b around inf 60.2%

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

      1. associate-*r/ 67.6%

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

   9. Applied egg-rr 67.6%

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot b}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;9 \cdot x \leq -5 \cdot 10^{+156}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{elif}\;9 \cdot x \leq -1.3 \cdot 10^{+102}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;9 \cdot x \leq -3 \cdot 10^{+71}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;9 \cdot x \leq -0.005:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;9 \cdot x \leq -2 \cdot 10^{-75}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;9 \cdot x \leq -1 \cdot 10^{-124}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;9 \cdot x \leq -1 \cdot 10^{-273}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;9 \cdot x \leq -5 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;9 \cdot x \leq 10^{-289}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;9 \cdot x \leq 10000000000000:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ t_2 := \frac{1}{\frac{c\_m \cdot z}{b}}\\ t_3 := \frac{b \cdot \frac{1}{z}}{c\_m}\\ t_4 := a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-285}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4}{c\_m}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-134}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-91}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+168}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+175}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c_m) (/ x z))))
        (t_2 (/ 1.0 (/ (* c_m z) b)))
        (t_3 (/ (* b (/ 1.0 z)) c_m))
        (t_4 (* a (* -4.0 (/ t c_m)))))
   (*
    c_s
    (if (<= y -9.5e-60)
      (* 9.0 (* (/ x c_m) (/ y z)))
      (if (<= y -1.95e-285)
        (/ b (* c_m z))
        (if (<= y 6.5e-191)
          (/ (* (* a t) -4.0) c_m)
          (if (<= y 8.2e-134)
            t_3
            (if (<= y 2.5e-91)
              (* -4.0 (* t (/ a c_m)))
              (if (<= y 8.6e-47)
                t_2
                (if (<= y 5.2e+37)
                  t_4
                  (if (<= y 1.9e+99)
                    t_2
                    (if (<= y 5.2e+142)
                      t_1
                      (if (<= y 9.5e+168)
                        t_3
                        (if (<= y 3.2e+175) t_4 t_1))))))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((y / c_m) * (x / z));
	double t_2 = 1.0 / ((c_m * z) / b);
	double t_3 = (b * (1.0 / z)) / c_m;
	double t_4 = a * (-4.0 * (t / c_m));
	double tmp;
	if (y <= -9.5e-60) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if (y <= -1.95e-285) {
		tmp = b / (c_m * z);
	} else if (y <= 6.5e-191) {
		tmp = ((a * t) * -4.0) / c_m;
	} else if (y <= 8.2e-134) {
		tmp = t_3;
	} else if (y <= 2.5e-91) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (y <= 8.6e-47) {
		tmp = t_2;
	} else if (y <= 5.2e+37) {
		tmp = t_4;
	} else if (y <= 1.9e+99) {
		tmp = t_2;
	} else if (y <= 5.2e+142) {
		tmp = t_1;
	} else if (y <= 9.5e+168) {
		tmp = t_3;
	} else if (y <= 3.2e+175) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / c_m) * (x / z))
    t_2 = 1.0d0 / ((c_m * z) / b)
    t_3 = (b * (1.0d0 / z)) / c_m
    t_4 = a * ((-4.0d0) * (t / c_m))
    if (y <= (-9.5d-60)) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else if (y <= (-1.95d-285)) then
        tmp = b / (c_m * z)
    else if (y <= 6.5d-191) then
        tmp = ((a * t) * (-4.0d0)) / c_m
    else if (y <= 8.2d-134) then
        tmp = t_3
    else if (y <= 2.5d-91) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (y <= 8.6d-47) then
        tmp = t_2
    else if (y <= 5.2d+37) then
        tmp = t_4
    else if (y <= 1.9d+99) then
        tmp = t_2
    else if (y <= 5.2d+142) then
        tmp = t_1
    else if (y <= 9.5d+168) then
        tmp = t_3
    else if (y <= 3.2d+175) then
        tmp = t_4
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((y / c_m) * (x / z));
	double t_2 = 1.0 / ((c_m * z) / b);
	double t_3 = (b * (1.0 / z)) / c_m;
	double t_4 = a * (-4.0 * (t / c_m));
	double tmp;
	if (y <= -9.5e-60) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if (y <= -1.95e-285) {
		tmp = b / (c_m * z);
	} else if (y <= 6.5e-191) {
		tmp = ((a * t) * -4.0) / c_m;
	} else if (y <= 8.2e-134) {
		tmp = t_3;
	} else if (y <= 2.5e-91) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (y <= 8.6e-47) {
		tmp = t_2;
	} else if (y <= 5.2e+37) {
		tmp = t_4;
	} else if (y <= 1.9e+99) {
		tmp = t_2;
	} else if (y <= 5.2e+142) {
		tmp = t_1;
	} else if (y <= 9.5e+168) {
		tmp = t_3;
	} else if (y <= 3.2e+175) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((y / c_m) * (x / z))
	t_2 = 1.0 / ((c_m * z) / b)
	t_3 = (b * (1.0 / z)) / c_m
	t_4 = a * (-4.0 * (t / c_m))
	tmp = 0
	if y <= -9.5e-60:
		tmp = 9.0 * ((x / c_m) * (y / z))
	elif y <= -1.95e-285:
		tmp = b / (c_m * z)
	elif y <= 6.5e-191:
		tmp = ((a * t) * -4.0) / c_m
	elif y <= 8.2e-134:
		tmp = t_3
	elif y <= 2.5e-91:
		tmp = -4.0 * (t * (a / c_m))
	elif y <= 8.6e-47:
		tmp = t_2
	elif y <= 5.2e+37:
		tmp = t_4
	elif y <= 1.9e+99:
		tmp = t_2
	elif y <= 5.2e+142:
		tmp = t_1
	elif y <= 9.5e+168:
		tmp = t_3
	elif y <= 3.2e+175:
		tmp = t_4
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / z)))
	t_2 = Float64(1.0 / Float64(Float64(c_m * z) / b))
	t_3 = Float64(Float64(b * Float64(1.0 / z)) / c_m)
	t_4 = Float64(a * Float64(-4.0 * Float64(t / c_m)))
	tmp = 0.0
	if (y <= -9.5e-60)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	elseif (y <= -1.95e-285)
		tmp = Float64(b / Float64(c_m * z));
	elseif (y <= 6.5e-191)
		tmp = Float64(Float64(Float64(a * t) * -4.0) / c_m);
	elseif (y <= 8.2e-134)
		tmp = t_3;
	elseif (y <= 2.5e-91)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (y <= 8.6e-47)
		tmp = t_2;
	elseif (y <= 5.2e+37)
		tmp = t_4;
	elseif (y <= 1.9e+99)
		tmp = t_2;
	elseif (y <= 5.2e+142)
		tmp = t_1;
	elseif (y <= 9.5e+168)
		tmp = t_3;
	elseif (y <= 3.2e+175)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((y / c_m) * (x / z));
	t_2 = 1.0 / ((c_m * z) / b);
	t_3 = (b * (1.0 / z)) / c_m;
	t_4 = a * (-4.0 * (t / c_m));
	tmp = 0.0;
	if (y <= -9.5e-60)
		tmp = 9.0 * ((x / c_m) * (y / z));
	elseif (y <= -1.95e-285)
		tmp = b / (c_m * z);
	elseif (y <= 6.5e-191)
		tmp = ((a * t) * -4.0) / c_m;
	elseif (y <= 8.2e-134)
		tmp = t_3;
	elseif (y <= 2.5e-91)
		tmp = -4.0 * (t * (a / c_m));
	elseif (y <= 8.6e-47)
		tmp = t_2;
	elseif (y <= 5.2e+37)
		tmp = t_4;
	elseif (y <= 1.9e+99)
		tmp = t_2;
	elseif (y <= 5.2e+142)
		tmp = t_1;
	elseif (y <= 9.5e+168)
		tmp = t_3;
	elseif (y <= 3.2e+175)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(N[(c$95$m * z), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[y, -9.5e-60], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-285], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-191], N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[y, 8.2e-134], t$95$3, If[LessEqual[y, 2.5e-91], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-47], t$95$2, If[LessEqual[y, 5.2e+37], t$95$4, If[LessEqual[y, 1.9e+99], t$95$2, If[LessEqual[y, 5.2e+142], t$95$1, If[LessEqual[y, 9.5e+168], t$95$3, If[LessEqual[y, 3.2e+175], t$95$4, t$95$1]]]]]]]]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -9.49999999999999958e-60

   1. Initial program 79.1%

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

      1. associate-+l- 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*r* 81.6%

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

      4. *-commutative 81.6%

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

      5. associate-+l- 81.6%

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

      6. associate-*l* 81.6%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around inf 48.8%

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

      1. times-frac 49.0%

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

   7. Simplified 49.0%

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

   if -9.49999999999999958e-60 < y < -1.94999999999999993e-285

   1. Initial program 81.6%

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

      1. associate-+l- 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*r* 83.2%

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

      4. *-commutative 83.2%

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

      5. associate-+l- 83.2%

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

      6. associate-*l* 83.2%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

   if -1.94999999999999993e-285 < y < 6.4999999999999995e-191

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*r* 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-+l- 89.8%

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

      6. associate-*l* 89.8%

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

      7. associate-*l* 89.9%

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

      8. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around inf 45.3%

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

      1. associate-*r/ 45.3%

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

   7. Simplified 45.3%

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

   if 6.4999999999999995e-191 < y < 8.2000000000000004e-134 or 5.20000000000000043e142 < y < 9.49999999999999979e168

   1. Initial program 67.5%

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

      1. associate-+l- 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 67.9%

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

      8. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   6. Applied egg-rr 45.7%

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

   7. Taylor expanded in b around inf 36.0%

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

      1. associate-*r/ 41.1%

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

   9. Applied egg-rr 41.1%

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

   if 8.2000000000000004e-134 < y < 2.49999999999999999e-91

   1. Initial program 77.5%

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

      1. associate-+l- 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. associate-*l* 66.6%

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

      7. associate-*l* 77.5%

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

      8. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in z around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. *-commutative 45.6%

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

      3. associate-/l* 45.7%

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

   7. Simplified 45.7%

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

   if 2.49999999999999999e-91 < y < 8.5999999999999995e-47 or 5.1999999999999998e37 < y < 1.9e99

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-+l- 67.1%

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

      6. associate-*l* 67.2%

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

      7. associate-*l* 67.8%

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

      8. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   6. Applied egg-rr 54.5%

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

   7. Taylor expanded in b around inf 22.7%

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

      1. clear-num 22.7%

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

      2. frac-times 22.7%

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

      3. metadata-eval 22.7%

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

   9. Applied egg-rr 22.7%

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

       1. *-commutative 22.7%

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

       2. associate-*l/ 35.6%

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

       3. associate-/r/ 35.6%

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

   11. Simplified 35.6%

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

       1. associate-*l/ 35.6%

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

       2. *-un-lft-identity 35.6%

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

       3. clear-num 35.6%

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

       4. *-commutative 35.6%

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

   13. Applied egg-rr 35.6%

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

   if 8.5999999999999995e-47 < y < 5.1999999999999998e37 or 9.49999999999999979e168 < y < 3.20000000000000022e175

   1. Initial program 79.6%

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

      1. associate-+l- 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r* 79.6%

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

      4. *-commutative 79.6%

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

      5. associate-+l- 79.6%

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

      6. associate-*l* 79.6%

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

      7. associate-*l* 83.7%

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

      8. *-commutative 83.7%

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

   3. Simplified 83.7%

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

      1. add-cube-cbrt 83.5%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 83.6%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 83.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 83.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 83.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 83.4%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-/l* 55.3%

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

      3. associate-*l* 55.3%

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

   9. Simplified 55.3%

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

   if 1.9e99 < y < 5.20000000000000043e142 or 3.20000000000000022e175 < y

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-*r* 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-+l- 78.0%

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

      6. associate-*l* 75.4%

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

      7. associate-*l* 77.8%

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

      8. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. times-frac 72.8%

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

   7. Simplified 72.8%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-285}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4}{c}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-91}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{1}{\frac{c \cdot z}{b}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;\frac{1}{\frac{c \cdot z}{b}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+142}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{c\_m \cdot z}{b}}\\ t_2 := \frac{b \cdot \frac{1}{z}}{c\_m}\\ t_3 := a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-188}:\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4}{c\_m}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-92}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+142}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+176}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{9 \cdot x}{c\_m \cdot z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ (* c_m z) b)))
        (t_2 (/ (* b (/ 1.0 z)) c_m))
        (t_3 (* a (* -4.0 (/ t c_m)))))
   (*
    c_s
    (if (<= y -1.05e-60)
      (* 9.0 (* (/ x c_m) (/ y z)))
      (if (<= y -2.7e-285)
        (/ b (* c_m z))
        (if (<= y 1.28e-188)
          (/ (* (* a t) -4.0) c_m)
          (if (<= y 4.5e-133)
            t_2
            (if (<= y 1.15e-92)
              (* -4.0 (* t (/ a c_m)))
              (if (<= y 7.8e-47)
                t_1
                (if (<= y 9.8e+33)
                  t_3
                  (if (<= y 5.5e+99)
                    t_1
                    (if (<= y 5.2e+142)
                      (* 9.0 (* (/ y c_m) (/ x z)))
                      (if (<= y 3.1e+168)
                        t_2
                        (if (<= y 3e+176)
                          t_3
                          (* y (/ (* 9.0 x) (* c_m z)))))))))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 1.0 / ((c_m * z) / b);
	double t_2 = (b * (1.0 / z)) / c_m;
	double t_3 = a * (-4.0 * (t / c_m));
	double tmp;
	if (y <= -1.05e-60) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if (y <= -2.7e-285) {
		tmp = b / (c_m * z);
	} else if (y <= 1.28e-188) {
		tmp = ((a * t) * -4.0) / c_m;
	} else if (y <= 4.5e-133) {
		tmp = t_2;
	} else if (y <= 1.15e-92) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (y <= 7.8e-47) {
		tmp = t_1;
	} else if (y <= 9.8e+33) {
		tmp = t_3;
	} else if (y <= 5.5e+99) {
		tmp = t_1;
	} else if (y <= 5.2e+142) {
		tmp = 9.0 * ((y / c_m) * (x / z));
	} else if (y <= 3.1e+168) {
		tmp = t_2;
	} else if (y <= 3e+176) {
		tmp = t_3;
	} else {
		tmp = y * ((9.0 * x) / (c_m * z));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 1.0d0 / ((c_m * z) / b)
    t_2 = (b * (1.0d0 / z)) / c_m
    t_3 = a * ((-4.0d0) * (t / c_m))
    if (y <= (-1.05d-60)) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else if (y <= (-2.7d-285)) then
        tmp = b / (c_m * z)
    else if (y <= 1.28d-188) then
        tmp = ((a * t) * (-4.0d0)) / c_m
    else if (y <= 4.5d-133) then
        tmp = t_2
    else if (y <= 1.15d-92) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (y <= 7.8d-47) then
        tmp = t_1
    else if (y <= 9.8d+33) then
        tmp = t_3
    else if (y <= 5.5d+99) then
        tmp = t_1
    else if (y <= 5.2d+142) then
        tmp = 9.0d0 * ((y / c_m) * (x / z))
    else if (y <= 3.1d+168) then
        tmp = t_2
    else if (y <= 3d+176) then
        tmp = t_3
    else
        tmp = y * ((9.0d0 * x) / (c_m * z))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 1.0 / ((c_m * z) / b);
	double t_2 = (b * (1.0 / z)) / c_m;
	double t_3 = a * (-4.0 * (t / c_m));
	double tmp;
	if (y <= -1.05e-60) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if (y <= -2.7e-285) {
		tmp = b / (c_m * z);
	} else if (y <= 1.28e-188) {
		tmp = ((a * t) * -4.0) / c_m;
	} else if (y <= 4.5e-133) {
		tmp = t_2;
	} else if (y <= 1.15e-92) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (y <= 7.8e-47) {
		tmp = t_1;
	} else if (y <= 9.8e+33) {
		tmp = t_3;
	} else if (y <= 5.5e+99) {
		tmp = t_1;
	} else if (y <= 5.2e+142) {
		tmp = 9.0 * ((y / c_m) * (x / z));
	} else if (y <= 3.1e+168) {
		tmp = t_2;
	} else if (y <= 3e+176) {
		tmp = t_3;
	} else {
		tmp = y * ((9.0 * x) / (c_m * z));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 1.0 / ((c_m * z) / b)
	t_2 = (b * (1.0 / z)) / c_m
	t_3 = a * (-4.0 * (t / c_m))
	tmp = 0
	if y <= -1.05e-60:
		tmp = 9.0 * ((x / c_m) * (y / z))
	elif y <= -2.7e-285:
		tmp = b / (c_m * z)
	elif y <= 1.28e-188:
		tmp = ((a * t) * -4.0) / c_m
	elif y <= 4.5e-133:
		tmp = t_2
	elif y <= 1.15e-92:
		tmp = -4.0 * (t * (a / c_m))
	elif y <= 7.8e-47:
		tmp = t_1
	elif y <= 9.8e+33:
		tmp = t_3
	elif y <= 5.5e+99:
		tmp = t_1
	elif y <= 5.2e+142:
		tmp = 9.0 * ((y / c_m) * (x / z))
	elif y <= 3.1e+168:
		tmp = t_2
	elif y <= 3e+176:
		tmp = t_3
	else:
		tmp = y * ((9.0 * x) / (c_m * z))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(1.0 / Float64(Float64(c_m * z) / b))
	t_2 = Float64(Float64(b * Float64(1.0 / z)) / c_m)
	t_3 = Float64(a * Float64(-4.0 * Float64(t / c_m)))
	tmp = 0.0
	if (y <= -1.05e-60)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	elseif (y <= -2.7e-285)
		tmp = Float64(b / Float64(c_m * z));
	elseif (y <= 1.28e-188)
		tmp = Float64(Float64(Float64(a * t) * -4.0) / c_m);
	elseif (y <= 4.5e-133)
		tmp = t_2;
	elseif (y <= 1.15e-92)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (y <= 7.8e-47)
		tmp = t_1;
	elseif (y <= 9.8e+33)
		tmp = t_3;
	elseif (y <= 5.5e+99)
		tmp = t_1;
	elseif (y <= 5.2e+142)
		tmp = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / z)));
	elseif (y <= 3.1e+168)
		tmp = t_2;
	elseif (y <= 3e+176)
		tmp = t_3;
	else
		tmp = Float64(y * Float64(Float64(9.0 * x) / Float64(c_m * z)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 1.0 / ((c_m * z) / b);
	t_2 = (b * (1.0 / z)) / c_m;
	t_3 = a * (-4.0 * (t / c_m));
	tmp = 0.0;
	if (y <= -1.05e-60)
		tmp = 9.0 * ((x / c_m) * (y / z));
	elseif (y <= -2.7e-285)
		tmp = b / (c_m * z);
	elseif (y <= 1.28e-188)
		tmp = ((a * t) * -4.0) / c_m;
	elseif (y <= 4.5e-133)
		tmp = t_2;
	elseif (y <= 1.15e-92)
		tmp = -4.0 * (t * (a / c_m));
	elseif (y <= 7.8e-47)
		tmp = t_1;
	elseif (y <= 9.8e+33)
		tmp = t_3;
	elseif (y <= 5.5e+99)
		tmp = t_1;
	elseif (y <= 5.2e+142)
		tmp = 9.0 * ((y / c_m) * (x / z));
	elseif (y <= 3.1e+168)
		tmp = t_2;
	elseif (y <= 3e+176)
		tmp = t_3;
	else
		tmp = y * ((9.0 * x) / (c_m * z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(1.0 / N[(N[(c$95$m * z), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[y, -1.05e-60], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-285], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e-188], N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[y, 4.5e-133], t$95$2, If[LessEqual[y, 1.15e-92], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-47], t$95$1, If[LessEqual[y, 9.8e+33], t$95$3, If[LessEqual[y, 5.5e+99], t$95$1, If[LessEqual[y, 5.2e+142], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+168], t$95$2, If[LessEqual[y, 3e+176], t$95$3, N[(y * N[(N[(9.0 * x), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]), $MachinePrecision]]]]

Derivation

1. Split input into 9 regimes

2. if y < -1.04999999999999996e-60

   1. Initial program 79.1%

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

      1. associate-+l- 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*r* 81.6%

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

      4. *-commutative 81.6%

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

      5. associate-+l- 81.6%

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

      6. associate-*l* 81.6%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around inf 48.8%

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

      1. times-frac 49.0%

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

   7. Simplified 49.0%

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

   if -1.04999999999999996e-60 < y < -2.6999999999999998e-285

   1. Initial program 81.6%

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

      1. associate-+l- 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*r* 83.2%

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

      4. *-commutative 83.2%

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

      5. associate-+l- 83.2%

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

      6. associate-*l* 83.2%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in b around inf 51.6%

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

      1. *-commutative 51.6%

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

   7. Simplified 51.6%

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

   if -2.6999999999999998e-285 < y < 1.28e-188

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*r* 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-+l- 89.8%

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

      6. associate-*l* 89.8%

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

      7. associate-*l* 89.9%

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

      8. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around inf 45.3%

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

      1. associate-*r/ 45.3%

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

   7. Simplified 45.3%

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

   if 1.28e-188 < y < 4.50000000000000009e-133 or 5.20000000000000043e142 < y < 3.09999999999999996e168

   1. Initial program 67.5%

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

      1. associate-+l- 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 67.9%

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

      8. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   6. Applied egg-rr 45.7%

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

   7. Taylor expanded in b around inf 36.0%

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

      1. associate-*r/ 41.1%

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

   9. Applied egg-rr 41.1%

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

   if 4.50000000000000009e-133 < y < 1.15000000000000008e-92

   1. Initial program 77.5%

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

      1. associate-+l- 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. associate-*l* 66.6%

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

      7. associate-*l* 77.5%

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

      8. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in z around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. *-commutative 45.6%

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

      3. associate-/l* 45.7%

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

   7. Simplified 45.7%

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

   if 1.15000000000000008e-92 < y < 7.79999999999999956e-47 or 9.80000000000000027e33 < y < 5.5000000000000002e99

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 67.1%

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

      4. *-commutative 67.1%

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

      5. associate-+l- 67.1%

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

      6. associate-*l* 67.2%

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

      7. associate-*l* 67.8%

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

      8. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   6. Applied egg-rr 54.5%

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

   7. Taylor expanded in b around inf 22.7%

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

      1. clear-num 22.7%

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

      2. frac-times 22.7%

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

      3. metadata-eval 22.7%

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

   9. Applied egg-rr 22.7%

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

       1. *-commutative 22.7%

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

       2. associate-*l/ 35.6%

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

       3. associate-/r/ 35.6%

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

   11. Simplified 35.6%

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

       1. associate-*l/ 35.6%

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

       2. *-un-lft-identity 35.6%

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

       3. clear-num 35.6%

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

       4. *-commutative 35.6%

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

   13. Applied egg-rr 35.6%

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

   if 7.79999999999999956e-47 < y < 9.80000000000000027e33 or 3.09999999999999996e168 < y < 3e176

   1. Initial program 76.4%

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

      1. associate-+l- 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-*r* 76.5%

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

      4. *-commutative 76.5%

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

      5. associate-+l- 76.5%

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

      6. associate-*l* 76.5%

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

      7. associate-*l* 80.3%

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

      8. *-commutative 80.3%

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

   3. Simplified 80.3%

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

      1. add-cube-cbrt 80.2%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 80.2%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 80.2%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 80.2%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 80.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 80.0%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-/l* 53.1%

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

      3. associate-*l* 53.1%

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

   9. Simplified 53.1%

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

   if 5.5000000000000002e99 < y < 5.20000000000000043e142

   1. Initial program 80.0%

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

      1. associate-+l- 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. associate-*l* 80.0%

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

      7. associate-*l* 80.0%

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

      8. *-commutative 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. times-frac 80.4%

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

   7. Simplified 80.4%

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

   if 3e176 < y

   1. Initial program 85.7%

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

      1. associate-+l- 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*r* 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-+l- 80.0%

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

      6. associate-*l* 77.0%

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

      7. associate-*l* 79.7%

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

      8. *-commutative 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. times-frac 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in x around 0 68.3%

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

      1. associate-*r/ 68.4%

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

      2. associate-*r* 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

      5. associate-/l* 73.1%

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

      6. *-commutative 73.1%

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

   10. Simplified 73.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-188}:\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4}{c}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-92}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{1}{\frac{c \cdot z}{b}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{1}{\frac{c \cdot z}{b}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+142}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+168}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{9 \cdot x}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b \cdot \frac{1}{z}}{c\_m}\\ t_2 := \frac{b}{c\_m \cdot z}\\ t_3 := 9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ t_4 := a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -0.0005:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-125}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-306}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1080000000000:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (* b (/ 1.0 z)) c_m))
        (t_2 (/ b (* c_m z)))
        (t_3 (* 9.0 (* (/ x c_m) (/ y z))))
        (t_4 (* a (* -4.0 (/ t c_m)))))
   (*
    c_s
    (if (<= x -3.1e+155)
      t_3
      (if (<= x -1.45e+101)
        t_2
        (if (<= x -2.1e+54)
          t_3
          (if (<= x -0.0005)
            (* -4.0 (* t (/ a c_m)))
            (if (<= x -4.2e-78)
              t_2
              (if (<= x -1.1e-125)
                t_4
                (if (<= x -1.6e-274)
                  t_1
                  (if (<= x -5.3e-306)
                    t_4
                    (if (<= x 6.5e-286)
                      t_1
                      (if (<= x 1080000000000.0) t_4 t_3)))))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b * (1.0 / z)) / c_m;
	double t_2 = b / (c_m * z);
	double t_3 = 9.0 * ((x / c_m) * (y / z));
	double t_4 = a * (-4.0 * (t / c_m));
	double tmp;
	if (x <= -3.1e+155) {
		tmp = t_3;
	} else if (x <= -1.45e+101) {
		tmp = t_2;
	} else if (x <= -2.1e+54) {
		tmp = t_3;
	} else if (x <= -0.0005) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (x <= -4.2e-78) {
		tmp = t_2;
	} else if (x <= -1.1e-125) {
		tmp = t_4;
	} else if (x <= -1.6e-274) {
		tmp = t_1;
	} else if (x <= -5.3e-306) {
		tmp = t_4;
	} else if (x <= 6.5e-286) {
		tmp = t_1;
	} else if (x <= 1080000000000.0) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b * (1.0d0 / z)) / c_m
    t_2 = b / (c_m * z)
    t_3 = 9.0d0 * ((x / c_m) * (y / z))
    t_4 = a * ((-4.0d0) * (t / c_m))
    if (x <= (-3.1d+155)) then
        tmp = t_3
    else if (x <= (-1.45d+101)) then
        tmp = t_2
    else if (x <= (-2.1d+54)) then
        tmp = t_3
    else if (x <= (-0.0005d0)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (x <= (-4.2d-78)) then
        tmp = t_2
    else if (x <= (-1.1d-125)) then
        tmp = t_4
    else if (x <= (-1.6d-274)) then
        tmp = t_1
    else if (x <= (-5.3d-306)) then
        tmp = t_4
    else if (x <= 6.5d-286) then
        tmp = t_1
    else if (x <= 1080000000000.0d0) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b * (1.0 / z)) / c_m;
	double t_2 = b / (c_m * z);
	double t_3 = 9.0 * ((x / c_m) * (y / z));
	double t_4 = a * (-4.0 * (t / c_m));
	double tmp;
	if (x <= -3.1e+155) {
		tmp = t_3;
	} else if (x <= -1.45e+101) {
		tmp = t_2;
	} else if (x <= -2.1e+54) {
		tmp = t_3;
	} else if (x <= -0.0005) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (x <= -4.2e-78) {
		tmp = t_2;
	} else if (x <= -1.1e-125) {
		tmp = t_4;
	} else if (x <= -1.6e-274) {
		tmp = t_1;
	} else if (x <= -5.3e-306) {
		tmp = t_4;
	} else if (x <= 6.5e-286) {
		tmp = t_1;
	} else if (x <= 1080000000000.0) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b * (1.0 / z)) / c_m
	t_2 = b / (c_m * z)
	t_3 = 9.0 * ((x / c_m) * (y / z))
	t_4 = a * (-4.0 * (t / c_m))
	tmp = 0
	if x <= -3.1e+155:
		tmp = t_3
	elif x <= -1.45e+101:
		tmp = t_2
	elif x <= -2.1e+54:
		tmp = t_3
	elif x <= -0.0005:
		tmp = -4.0 * (t * (a / c_m))
	elif x <= -4.2e-78:
		tmp = t_2
	elif x <= -1.1e-125:
		tmp = t_4
	elif x <= -1.6e-274:
		tmp = t_1
	elif x <= -5.3e-306:
		tmp = t_4
	elif x <= 6.5e-286:
		tmp = t_1
	elif x <= 1080000000000.0:
		tmp = t_4
	else:
		tmp = t_3
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b * Float64(1.0 / z)) / c_m)
	t_2 = Float64(b / Float64(c_m * z))
	t_3 = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)))
	t_4 = Float64(a * Float64(-4.0 * Float64(t / c_m)))
	tmp = 0.0
	if (x <= -3.1e+155)
		tmp = t_3;
	elseif (x <= -1.45e+101)
		tmp = t_2;
	elseif (x <= -2.1e+54)
		tmp = t_3;
	elseif (x <= -0.0005)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (x <= -4.2e-78)
		tmp = t_2;
	elseif (x <= -1.1e-125)
		tmp = t_4;
	elseif (x <= -1.6e-274)
		tmp = t_1;
	elseif (x <= -5.3e-306)
		tmp = t_4;
	elseif (x <= 6.5e-286)
		tmp = t_1;
	elseif (x <= 1080000000000.0)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b * (1.0 / z)) / c_m;
	t_2 = b / (c_m * z);
	t_3 = 9.0 * ((x / c_m) * (y / z));
	t_4 = a * (-4.0 * (t / c_m));
	tmp = 0.0;
	if (x <= -3.1e+155)
		tmp = t_3;
	elseif (x <= -1.45e+101)
		tmp = t_2;
	elseif (x <= -2.1e+54)
		tmp = t_3;
	elseif (x <= -0.0005)
		tmp = -4.0 * (t * (a / c_m));
	elseif (x <= -4.2e-78)
		tmp = t_2;
	elseif (x <= -1.1e-125)
		tmp = t_4;
	elseif (x <= -1.6e-274)
		tmp = t_1;
	elseif (x <= -5.3e-306)
		tmp = t_4;
	elseif (x <= 6.5e-286)
		tmp = t_1;
	elseif (x <= 1080000000000.0)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -3.1e+155], t$95$3, If[LessEqual[x, -1.45e+101], t$95$2, If[LessEqual[x, -2.1e+54], t$95$3, If[LessEqual[x, -0.0005], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-78], t$95$2, If[LessEqual[x, -1.1e-125], t$95$4, If[LessEqual[x, -1.6e-274], t$95$1, If[LessEqual[x, -5.3e-306], t$95$4, If[LessEqual[x, 6.5e-286], t$95$1, If[LessEqual[x, 1080000000000.0], t$95$4, t$95$3]]]]]]]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.09999999999999989e155 or -1.44999999999999994e101 < x < -2.09999999999999986e54 or 1.08e12 < x

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-+l- 79.1%

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

      6. associate-*l* 79.2%

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

      7. associate-*l* 79.4%

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

      8. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around inf 53.4%

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

      1. times-frac 58.8%

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

   7. Simplified 58.8%

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

   if -3.09999999999999989e155 < x < -1.44999999999999994e101 or -5.0000000000000001e-4 < x < -4.2000000000000001e-78

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-+l- 87.2%

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

      6. associate-*l* 87.1%

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

      7. associate-*l* 83.0%

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

      8. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   if -2.09999999999999986e54 < x < -5.0000000000000001e-4

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 61.6%

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

      4. *-commutative 61.6%

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

      5. associate-+l- 61.6%

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

      6. associate-*l* 61.9%

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

      7. associate-*l* 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-/l* 42.1%

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

   7. Simplified 42.1%

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

   if -4.2000000000000001e-78 < x < -1.09999999999999997e-125 or -1.59999999999999989e-274 < x < -5.2999999999999998e-306 or 6.5000000000000004e-286 < x < 1.08e12

   1. Initial program 79.0%

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

      1. associate-+l- 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*r* 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-+l- 77.8%

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

      6. associate-*l* 76.6%

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

      7. associate-*l* 81.4%

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

      8. *-commutative 81.4%

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

   3. Simplified 81.4%

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

      1. add-cube-cbrt 81.2%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 81.2%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 82.4%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/l* 54.3%

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

      3. associate-*l* 54.3%

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

   9. Simplified 54.3%

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

   if -1.09999999999999997e-125 < x < -1.59999999999999989e-274 or -5.2999999999999998e-306 < x < 6.5000000000000004e-286

   1. Initial program 88.9%

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

      1. associate-+l- 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 88.9%

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

      8. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   6. Applied egg-rr 64.5%

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

   7. Taylor expanded in b around inf 60.2%

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

      1. associate-*r/ 67.6%

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

   9. Applied egg-rr 67.6%

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot b}{c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -0.0005:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-274}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-286}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 1080000000000:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ t_2 := \frac{b \cdot \frac{1}{z}}{c\_m}\\ t_3 := \frac{b}{c\_m \cdot z}\\ t_4 := 9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+155}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c\_m \cdot z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c_m))))
        (t_2 (/ (* b (/ 1.0 z)) c_m))
        (t_3 (/ b (* c_m z)))
        (t_4 (* 9.0 (* (/ x c_m) (/ y z)))))
   (*
    c_s
    (if (<= x -4e+155)
      (* 9.0 (/ (* x y) (* c_m z)))
      (if (<= x -1.45e+101)
        t_3
        (if (<= x -2.1e+54)
          t_4
          (if (<= x -6.5e-5)
            (* -4.0 (* t (/ a c_m)))
            (if (<= x -1.65e-78)
              t_3
              (if (<= x -4.1e-126)
                t_1
                (if (<= x -1.2e-274)
                  t_2
                  (if (<= x -5.2e-306)
                    t_1
                    (if (<= x 2.1e-276)
                      t_2
                      (if (<= x 3.6e+14) t_1 t_4)))))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = a * (-4.0 * (t / c_m));
	double t_2 = (b * (1.0 / z)) / c_m;
	double t_3 = b / (c_m * z);
	double t_4 = 9.0 * ((x / c_m) * (y / z));
	double tmp;
	if (x <= -4e+155) {
		tmp = 9.0 * ((x * y) / (c_m * z));
	} else if (x <= -1.45e+101) {
		tmp = t_3;
	} else if (x <= -2.1e+54) {
		tmp = t_4;
	} else if (x <= -6.5e-5) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (x <= -1.65e-78) {
		tmp = t_3;
	} else if (x <= -4.1e-126) {
		tmp = t_1;
	} else if (x <= -1.2e-274) {
		tmp = t_2;
	} else if (x <= -5.2e-306) {
		tmp = t_1;
	} else if (x <= 2.1e-276) {
		tmp = t_2;
	} else if (x <= 3.6e+14) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c_m))
    t_2 = (b * (1.0d0 / z)) / c_m
    t_3 = b / (c_m * z)
    t_4 = 9.0d0 * ((x / c_m) * (y / z))
    if (x <= (-4d+155)) then
        tmp = 9.0d0 * ((x * y) / (c_m * z))
    else if (x <= (-1.45d+101)) then
        tmp = t_3
    else if (x <= (-2.1d+54)) then
        tmp = t_4
    else if (x <= (-6.5d-5)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (x <= (-1.65d-78)) then
        tmp = t_3
    else if (x <= (-4.1d-126)) then
        tmp = t_1
    else if (x <= (-1.2d-274)) then
        tmp = t_2
    else if (x <= (-5.2d-306)) then
        tmp = t_1
    else if (x <= 2.1d-276) then
        tmp = t_2
    else if (x <= 3.6d+14) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = a * (-4.0 * (t / c_m));
	double t_2 = (b * (1.0 / z)) / c_m;
	double t_3 = b / (c_m * z);
	double t_4 = 9.0 * ((x / c_m) * (y / z));
	double tmp;
	if (x <= -4e+155) {
		tmp = 9.0 * ((x * y) / (c_m * z));
	} else if (x <= -1.45e+101) {
		tmp = t_3;
	} else if (x <= -2.1e+54) {
		tmp = t_4;
	} else if (x <= -6.5e-5) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (x <= -1.65e-78) {
		tmp = t_3;
	} else if (x <= -4.1e-126) {
		tmp = t_1;
	} else if (x <= -1.2e-274) {
		tmp = t_2;
	} else if (x <= -5.2e-306) {
		tmp = t_1;
	} else if (x <= 2.1e-276) {
		tmp = t_2;
	} else if (x <= 3.6e+14) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = a * (-4.0 * (t / c_m))
	t_2 = (b * (1.0 / z)) / c_m
	t_3 = b / (c_m * z)
	t_4 = 9.0 * ((x / c_m) * (y / z))
	tmp = 0
	if x <= -4e+155:
		tmp = 9.0 * ((x * y) / (c_m * z))
	elif x <= -1.45e+101:
		tmp = t_3
	elif x <= -2.1e+54:
		tmp = t_4
	elif x <= -6.5e-5:
		tmp = -4.0 * (t * (a / c_m))
	elif x <= -1.65e-78:
		tmp = t_3
	elif x <= -4.1e-126:
		tmp = t_1
	elif x <= -1.2e-274:
		tmp = t_2
	elif x <= -5.2e-306:
		tmp = t_1
	elif x <= 2.1e-276:
		tmp = t_2
	elif x <= 3.6e+14:
		tmp = t_1
	else:
		tmp = t_4
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c_m)))
	t_2 = Float64(Float64(b * Float64(1.0 / z)) / c_m)
	t_3 = Float64(b / Float64(c_m * z))
	t_4 = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)))
	tmp = 0.0
	if (x <= -4e+155)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z)));
	elseif (x <= -1.45e+101)
		tmp = t_3;
	elseif (x <= -2.1e+54)
		tmp = t_4;
	elseif (x <= -6.5e-5)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (x <= -1.65e-78)
		tmp = t_3;
	elseif (x <= -4.1e-126)
		tmp = t_1;
	elseif (x <= -1.2e-274)
		tmp = t_2;
	elseif (x <= -5.2e-306)
		tmp = t_1;
	elseif (x <= 2.1e-276)
		tmp = t_2;
	elseif (x <= 3.6e+14)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = a * (-4.0 * (t / c_m));
	t_2 = (b * (1.0 / z)) / c_m;
	t_3 = b / (c_m * z);
	t_4 = 9.0 * ((x / c_m) * (y / z));
	tmp = 0.0;
	if (x <= -4e+155)
		tmp = 9.0 * ((x * y) / (c_m * z));
	elseif (x <= -1.45e+101)
		tmp = t_3;
	elseif (x <= -2.1e+54)
		tmp = t_4;
	elseif (x <= -6.5e-5)
		tmp = -4.0 * (t * (a / c_m));
	elseif (x <= -1.65e-78)
		tmp = t_3;
	elseif (x <= -4.1e-126)
		tmp = t_1;
	elseif (x <= -1.2e-274)
		tmp = t_2;
	elseif (x <= -5.2e-306)
		tmp = t_1;
	elseif (x <= 2.1e-276)
		tmp = t_2;
	elseif (x <= 3.6e+14)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$3 = N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -4e+155], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e+101], t$95$3, If[LessEqual[x, -2.1e+54], t$95$4, If[LessEqual[x, -6.5e-5], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.65e-78], t$95$3, If[LessEqual[x, -4.1e-126], t$95$1, If[LessEqual[x, -1.2e-274], t$95$2, If[LessEqual[x, -5.2e-306], t$95$1, If[LessEqual[x, 2.1e-276], t$95$2, If[LessEqual[x, 3.6e+14], t$95$1, t$95$4]]]]]]]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.00000000000000003e155

   1. Initial program 81.5%

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

      1. associate-+l- 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*r* 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-+l- 83.8%

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

      6. associate-*l* 83.8%

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

      7. associate-*l* 84.1%

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

      8. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in x around inf 70.1%

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

   if -4.00000000000000003e155 < x < -1.44999999999999994e101 or -6.49999999999999943e-5 < x < -1.64999999999999991e-78

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-+l- 87.2%

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

      6. associate-*l* 87.1%

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

      7. associate-*l* 83.0%

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

      8. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   if -1.44999999999999994e101 < x < -2.09999999999999986e54 or 3.6e14 < x

   1. Initial program 74.8%

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

      1. associate-+l- 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-*r* 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-+l- 76.2%

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

      6. associate-*l* 76.2%

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

      7. associate-*l* 76.4%

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

      8. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in x around inf 42.8%

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

      1. times-frac 54.4%

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

   7. Simplified 54.4%

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

   if -2.09999999999999986e54 < x < -6.49999999999999943e-5

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 61.6%

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

      4. *-commutative 61.6%

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

      5. associate-+l- 61.6%

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

      6. associate-*l* 61.9%

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

      7. associate-*l* 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-/l* 42.1%

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

   7. Simplified 42.1%

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

   if -1.64999999999999991e-78 < x < -4.0999999999999997e-126 or -1.2e-274 < x < -5.2000000000000001e-306 or 2.1e-276 < x < 3.6e14

   1. Initial program 79.5%

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

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

      5. associate-+l- 77.0%

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

      6. associate-*l* 75.8%

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

      7. associate-*l* 80.7%

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

      8. *-commutative 80.7%

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

   3. Simplified 80.7%

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

      1. add-cube-cbrt 80.6%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 80.5%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 81.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 81.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 81.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 81.7%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-/l* 53.8%

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

      3. associate-*l* 53.8%

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

   9. Simplified 53.8%

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

   if -4.0999999999999997e-126 < x < -1.2e-274 or -5.2000000000000001e-306 < x < 2.1e-276

   1. Initial program 87.3%

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

      1. associate-+l- 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-*r* 87.1%

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

      4. *-commutative 87.1%

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

      5. associate-+l- 87.1%

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

      6. associate-*l* 87.1%

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

      7. associate-*l* 89.7%

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

      8. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   6. Applied egg-rr 59.8%

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

   7. Taylor expanded in b around inf 56.0%

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

      1. associate-*r/ 62.8%

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

   9. Applied egg-rr 62.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot b}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+155}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-78}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-274}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-276}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ t_2 := \frac{b \cdot \frac{1}{z}}{c\_m}\\ t_3 := \frac{b}{c\_m \cdot z}\\ t_4 := 9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c\_m}}{z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-280}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8200000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c_m))))
        (t_2 (/ (* b (/ 1.0 z)) c_m))
        (t_3 (/ b (* c_m z)))
        (t_4 (* 9.0 (* (/ x c_m) (/ y z)))))
   (*
    c_s
    (if (<= x -3.1e+155)
      (* 9.0 (/ (* y (/ x c_m)) z))
      (if (<= x -1.45e+101)
        t_3
        (if (<= x -9e+52)
          t_4
          (if (<= x -1.22e-5)
            (* -4.0 (* t (/ a c_m)))
            (if (<= x -5.8e-78)
              t_3
              (if (<= x -8.5e-126)
                t_1
                (if (<= x -1.95e-274)
                  t_2
                  (if (<= x -5.3e-306)
                    t_1
                    (if (<= x 4.2e-280)
                      t_2
                      (if (<= x 8200000000000.0) t_1 t_4)))))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = a * (-4.0 * (t / c_m));
	double t_2 = (b * (1.0 / z)) / c_m;
	double t_3 = b / (c_m * z);
	double t_4 = 9.0 * ((x / c_m) * (y / z));
	double tmp;
	if (x <= -3.1e+155) {
		tmp = 9.0 * ((y * (x / c_m)) / z);
	} else if (x <= -1.45e+101) {
		tmp = t_3;
	} else if (x <= -9e+52) {
		tmp = t_4;
	} else if (x <= -1.22e-5) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (x <= -5.8e-78) {
		tmp = t_3;
	} else if (x <= -8.5e-126) {
		tmp = t_1;
	} else if (x <= -1.95e-274) {
		tmp = t_2;
	} else if (x <= -5.3e-306) {
		tmp = t_1;
	} else if (x <= 4.2e-280) {
		tmp = t_2;
	} else if (x <= 8200000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c_m))
    t_2 = (b * (1.0d0 / z)) / c_m
    t_3 = b / (c_m * z)
    t_4 = 9.0d0 * ((x / c_m) * (y / z))
    if (x <= (-3.1d+155)) then
        tmp = 9.0d0 * ((y * (x / c_m)) / z)
    else if (x <= (-1.45d+101)) then
        tmp = t_3
    else if (x <= (-9d+52)) then
        tmp = t_4
    else if (x <= (-1.22d-5)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (x <= (-5.8d-78)) then
        tmp = t_3
    else if (x <= (-8.5d-126)) then
        tmp = t_1
    else if (x <= (-1.95d-274)) then
        tmp = t_2
    else if (x <= (-5.3d-306)) then
        tmp = t_1
    else if (x <= 4.2d-280) then
        tmp = t_2
    else if (x <= 8200000000000.0d0) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = a * (-4.0 * (t / c_m));
	double t_2 = (b * (1.0 / z)) / c_m;
	double t_3 = b / (c_m * z);
	double t_4 = 9.0 * ((x / c_m) * (y / z));
	double tmp;
	if (x <= -3.1e+155) {
		tmp = 9.0 * ((y * (x / c_m)) / z);
	} else if (x <= -1.45e+101) {
		tmp = t_3;
	} else if (x <= -9e+52) {
		tmp = t_4;
	} else if (x <= -1.22e-5) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (x <= -5.8e-78) {
		tmp = t_3;
	} else if (x <= -8.5e-126) {
		tmp = t_1;
	} else if (x <= -1.95e-274) {
		tmp = t_2;
	} else if (x <= -5.3e-306) {
		tmp = t_1;
	} else if (x <= 4.2e-280) {
		tmp = t_2;
	} else if (x <= 8200000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = a * (-4.0 * (t / c_m))
	t_2 = (b * (1.0 / z)) / c_m
	t_3 = b / (c_m * z)
	t_4 = 9.0 * ((x / c_m) * (y / z))
	tmp = 0
	if x <= -3.1e+155:
		tmp = 9.0 * ((y * (x / c_m)) / z)
	elif x <= -1.45e+101:
		tmp = t_3
	elif x <= -9e+52:
		tmp = t_4
	elif x <= -1.22e-5:
		tmp = -4.0 * (t * (a / c_m))
	elif x <= -5.8e-78:
		tmp = t_3
	elif x <= -8.5e-126:
		tmp = t_1
	elif x <= -1.95e-274:
		tmp = t_2
	elif x <= -5.3e-306:
		tmp = t_1
	elif x <= 4.2e-280:
		tmp = t_2
	elif x <= 8200000000000.0:
		tmp = t_1
	else:
		tmp = t_4
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c_m)))
	t_2 = Float64(Float64(b * Float64(1.0 / z)) / c_m)
	t_3 = Float64(b / Float64(c_m * z))
	t_4 = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)))
	tmp = 0.0
	if (x <= -3.1e+155)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / c_m)) / z));
	elseif (x <= -1.45e+101)
		tmp = t_3;
	elseif (x <= -9e+52)
		tmp = t_4;
	elseif (x <= -1.22e-5)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (x <= -5.8e-78)
		tmp = t_3;
	elseif (x <= -8.5e-126)
		tmp = t_1;
	elseif (x <= -1.95e-274)
		tmp = t_2;
	elseif (x <= -5.3e-306)
		tmp = t_1;
	elseif (x <= 4.2e-280)
		tmp = t_2;
	elseif (x <= 8200000000000.0)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = a * (-4.0 * (t / c_m));
	t_2 = (b * (1.0 / z)) / c_m;
	t_3 = b / (c_m * z);
	t_4 = 9.0 * ((x / c_m) * (y / z));
	tmp = 0.0;
	if (x <= -3.1e+155)
		tmp = 9.0 * ((y * (x / c_m)) / z);
	elseif (x <= -1.45e+101)
		tmp = t_3;
	elseif (x <= -9e+52)
		tmp = t_4;
	elseif (x <= -1.22e-5)
		tmp = -4.0 * (t * (a / c_m));
	elseif (x <= -5.8e-78)
		tmp = t_3;
	elseif (x <= -8.5e-126)
		tmp = t_1;
	elseif (x <= -1.95e-274)
		tmp = t_2;
	elseif (x <= -5.3e-306)
		tmp = t_1;
	elseif (x <= 4.2e-280)
		tmp = t_2;
	elseif (x <= 8200000000000.0)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$3 = N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[x, -3.1e+155], N[(9.0 * N[(N[(y * N[(x / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e+101], t$95$3, If[LessEqual[x, -9e+52], t$95$4, If[LessEqual[x, -1.22e-5], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-78], t$95$3, If[LessEqual[x, -8.5e-126], t$95$1, If[LessEqual[x, -1.95e-274], t$95$2, If[LessEqual[x, -5.3e-306], t$95$1, If[LessEqual[x, 4.2e-280], t$95$2, If[LessEqual[x, 8200000000000.0], t$95$1, t$95$4]]]]]]]]]]), $MachinePrecision]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.09999999999999989e155

   1. Initial program 81.5%

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

      1. associate-+l- 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*r* 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-+l- 83.8%

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

      6. associate-*l* 83.8%

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

      7. associate-*l* 84.1%

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

      8. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in x around inf 70.1%

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

      1. times-frac 65.7%

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

   7. Simplified 65.7%

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

      1. associate-*r/ 70.3%

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

   9. Applied egg-rr 70.3%

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

   if -3.09999999999999989e155 < x < -1.44999999999999994e101 or -1.22000000000000001e-5 < x < -5.8000000000000001e-78

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-+l- 87.2%

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

      6. associate-*l* 87.1%

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

      7. associate-*l* 83.0%

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

      8. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   if -1.44999999999999994e101 < x < -8.9999999999999999e52 or 8.2e12 < x

   1. Initial program 75.2%

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

      1. associate-+l- 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-*r* 76.5%

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

      4. *-commutative 76.5%

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

      5. associate-+l- 76.5%

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

      6. associate-*l* 76.6%

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

      7. associate-*l* 76.7%

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

      8. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around inf 43.6%

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

      1. times-frac 55.0%

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

   7. Simplified 55.0%

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

   if -8.9999999999999999e52 < x < -1.22000000000000001e-5

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 52.4%

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

      4. *-commutative 52.4%

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

      5. associate-+l- 52.4%

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

      6. associate-*l* 52.4%

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

      7. associate-*l* 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

      3. associate-/l* 51.9%

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

   7. Simplified 51.9%

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

   if -5.8000000000000001e-78 < x < -8.49999999999999938e-126 or -1.94999999999999993e-274 < x < -5.2999999999999998e-306 or 4.20000000000000002e-280 < x < 8.2e12

   1. Initial program 79.0%

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

      1. associate-+l- 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*r* 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-+l- 77.8%

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

      6. associate-*l* 76.6%

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

      7. associate-*l* 81.4%

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

      8. *-commutative 81.4%

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

   3. Simplified 81.4%

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

      1. add-cube-cbrt 81.2%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 81.2%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 82.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 82.4%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/l* 54.3%

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

      3. associate-*l* 54.3%

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

   9. Simplified 54.3%

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

   if -8.49999999999999938e-126 < x < -1.94999999999999993e-274 or -5.2999999999999998e-306 < x < 4.20000000000000002e-280

   1. Initial program 88.9%

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

      1. associate-+l- 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*r* 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-+l- 86.1%

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

      6. associate-*l* 86.1%

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

      7. associate-*l* 88.9%

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

      8. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   6. Applied egg-rr 64.5%

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

   7. Taylor expanded in b around inf 60.2%

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

      1. associate-*r/ 67.6%

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

   9. Applied egg-rr 67.6%

      \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot b}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-5}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-274}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-280}:\\ \;\;\;\;\frac{b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;x \leq 8200000000000:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -0.00034:\\ \;\;\;\;\frac{t\_1 - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+139}:\\ \;\;\;\;\frac{b + t\_1}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* x y))) (t_2 (/ (- (/ b z) (* a (* 4.0 t))) c_m)))
   (*
    c_s
    (if (<= z -2.85e+48)
      t_2
      (if (<= z -0.00034)
        (/ (- t_1 (* 4.0 (* a (* z t)))) (* c_m z))
        (if (<= z -1.7e-62)
          (+ (* -4.0 (/ (* a t) c_m)) (/ b (* c_m z)))
          (if (<= z 6.6e+139) (/ (+ b t_1) (* c_m z)) t_2)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * (x * y);
	double t_2 = ((b / z) - (a * (4.0 * t))) / c_m;
	double tmp;
	if (z <= -2.85e+48) {
		tmp = t_2;
	} else if (z <= -0.00034) {
		tmp = (t_1 - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= -1.7e-62) {
		tmp = (-4.0 * ((a * t) / c_m)) + (b / (c_m * z));
	} else if (z <= 6.6e+139) {
		tmp = (b + t_1) / (c_m * z);
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * (x * y)
    t_2 = ((b / z) - (a * (4.0d0 * t))) / c_m
    if (z <= (-2.85d+48)) then
        tmp = t_2
    else if (z <= (-0.00034d0)) then
        tmp = (t_1 - (4.0d0 * (a * (z * t)))) / (c_m * z)
    else if (z <= (-1.7d-62)) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + (b / (c_m * z))
    else if (z <= 6.6d+139) then
        tmp = (b + t_1) / (c_m * z)
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * (x * y);
	double t_2 = ((b / z) - (a * (4.0 * t))) / c_m;
	double tmp;
	if (z <= -2.85e+48) {
		tmp = t_2;
	} else if (z <= -0.00034) {
		tmp = (t_1 - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if (z <= -1.7e-62) {
		tmp = (-4.0 * ((a * t) / c_m)) + (b / (c_m * z));
	} else if (z <= 6.6e+139) {
		tmp = (b + t_1) / (c_m * z);
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * (x * y)
	t_2 = ((b / z) - (a * (4.0 * t))) / c_m
	tmp = 0
	if z <= -2.85e+48:
		tmp = t_2
	elif z <= -0.00034:
		tmp = (t_1 - (4.0 * (a * (z * t)))) / (c_m * z)
	elif z <= -1.7e-62:
		tmp = (-4.0 * ((a * t) / c_m)) + (b / (c_m * z))
	elif z <= 6.6e+139:
		tmp = (b + t_1) / (c_m * z)
	else:
		tmp = t_2
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(x * y))
	t_2 = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m)
	tmp = 0.0
	if (z <= -2.85e+48)
		tmp = t_2;
	elseif (z <= -0.00034)
		tmp = Float64(Float64(t_1 - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c_m * z));
	elseif (z <= -1.7e-62)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(b / Float64(c_m * z)));
	elseif (z <= 6.6e+139)
		tmp = Float64(Float64(b + t_1) / Float64(c_m * z));
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * (x * y);
	t_2 = ((b / z) - (a * (4.0 * t))) / c_m;
	tmp = 0.0;
	if (z <= -2.85e+48)
		tmp = t_2;
	elseif (z <= -0.00034)
		tmp = (t_1 - (4.0 * (a * (z * t)))) / (c_m * z);
	elseif (z <= -1.7e-62)
		tmp = (-4.0 * ((a * t) / c_m)) + (b / (c_m * z));
	elseif (z <= 6.6e+139)
		tmp = (b + t_1) / (c_m * z);
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -2.85e+48], t$95$2, If[LessEqual[z, -0.00034], N[(N[(t$95$1 - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-62], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+139], N[(N[(b + t$95$1), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.84999999999999984e48 or 6.6000000000000003e139 < z

   1. Initial program 56.2%

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

      1. associate-+l- 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-*r* 56.9%

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

      4. *-commutative 56.9%

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

      5. associate-+l- 56.9%

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

      6. associate-*l* 55.8%

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

      7. associate-*l* 63.3%

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

      8. *-commutative 63.3%

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

   3. Simplified 63.3%

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

      1. add-cube-cbrt 63.2%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 63.3%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 64.3%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 64.3%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 64.3%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 64.3%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 83.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 73.1%

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

   10. Taylor expanded in c around -inf 91.5%

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

   11. Taylor expanded in x around 0 81.1%

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

       1. +-commutative 81.1%

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

       2. mul-1-neg 81.1%

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

       3. unsub-neg 81.1%

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

       4. associate-*r* 81.1%

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

       5. *-commutative 81.1%

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

       6. associate-*l* 81.1%

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

   13. Simplified 81.1%

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

   if -2.84999999999999984e48 < z < -3.4e-4

   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. Step-by-step derivation

      1. associate-+l- 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*r* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-+l- 99.5%

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

      6. associate-*l* 100.0%

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

      7. associate-*l* 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around 0 90.9%

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

   if -3.4e-4 < z < -1.69999999999999994e-62

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-+l- 99.9%

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

      6. associate-*l* 99.9%

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

      7. associate-*l* 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.9%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 99.9%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 99.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 99.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 99.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 92.2%

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

   10. Taylor expanded in x around 0 99.9%

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

   if -1.69999999999999994e-62 < z < 6.6000000000000003e139

   1. Initial program 93.2%

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

      1. associate-+l- 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*r* 92.5%

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

      4. *-commutative 92.5%

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

      5. associate-+l- 92.5%

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

      6. associate-*l* 92.5%

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

      7. associate-*l* 91.9%

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

      8. *-commutative 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around 0 79.7%

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

      1. *-commutative 79.7%

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

   7. Simplified 79.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq -0.00034:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+139}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-37} \lor \neg \left(z \leq 1.12 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -2.9e-37) (not (<= z 1.12e-149)))
    (/ (+ (* (* a t) -4.0) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c_m)
    (/ (+ b (* 9.0 (* x y))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.9e-37) || !(z <= 1.12e-149)) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-2.9d-37)) .or. (.not. (z <= 1.12d-149))) then
        tmp = (((a * t) * (-4.0d0)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c_m
    else
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.9e-37) || !(z <= 1.12e-149)) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -2.9e-37) or not (z <= 1.12e-149):
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m
	else:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -2.9e-37) || !(z <= 1.12e-149))
		tmp = Float64(Float64(Float64(Float64(a * t) * -4.0) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -2.9e-37) || ~((z <= 1.12e-149)))
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	else
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -2.9e-37], N[Not[LessEqual[z, 1.12e-149]], $MachinePrecision]], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.90000000000000005e-37 or 1.11999999999999999e-149 < z

   1. Initial program 70.7%

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

      1. associate-+l- 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*r* 70.5%

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

      4. *-commutative 70.5%

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

      5. associate-+l- 70.5%

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

      6. associate-*l* 70.0%

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

      7. associate-*l* 75.5%

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

      8. *-commutative 75.5%

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

   3. Simplified 75.5%

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

      1. add-cube-cbrt 75.3%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 75.3%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 75.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 75.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 75.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 75.9%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 84.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 78.7%

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

   10. Taylor expanded in c around 0 91.6%

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

   if -2.90000000000000005e-37 < z < 1.11999999999999999e-149

   1. Initial program 96.7%

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

      1. associate-+l- 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*r* 96.7%

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

      4. *-commutative 96.7%

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

      5. associate-+l- 96.7%

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

      6. associate-*l* 96.7%

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

      7. associate-*l* 93.7%

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

      8. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in z around 0 87.4%

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

      1. *-commutative 87.4%

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

   7. Simplified 87.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-37} \lor \neg \left(z \leq 1.12 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -200000000000 \lor \neg \left(z \leq 2 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -200000000000.0) (not (<= z 2e+71)))
    (/ (+ (* (* a t) -4.0) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c_m)
    (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -200000000000.0) || !(z <= 2e+71)) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-200000000000.0d0)) .or. (.not. (z <= 2d+71))) then
        tmp = (((a * t) * (-4.0d0)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c_m
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((a * t) * (z * 4.0d0)))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -200000000000.0) || !(z <= 2e+71)) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -200000000000.0) or not (z <= 2e+71):
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m
	else:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -200000000000.0) || !(z <= 2e+71))
		tmp = Float64(Float64(Float64(Float64(a * t) * -4.0) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -200000000000.0) || ~((z <= 2e+71)))
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	else
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -200000000000.0], N[Not[LessEqual[z, 2e+71]], $MachinePrecision]], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2e11 or 2.0000000000000001e71 < z

   1. Initial program 60.0%

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

      1. associate-+l- 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*r* 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-+l- 59.7%

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

      6. associate-*l* 58.8%

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

      7. associate-*l* 67.2%

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

      8. *-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. Step-by-step derivation

      1. add-cube-cbrt 67.1%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 67.1%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 68.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 68.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 67.9%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 67.9%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 84.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 73.9%

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

   10. Taylor expanded in c around 0 92.6%

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

   if -2e11 < z < 2.0000000000000001e71

   1. Initial program 94.7%

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

      1. associate-+l- 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-*r* 94.7%

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

      4. *-commutative 94.7%

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

      5. associate-+l- 94.7%

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

      6. associate-*l* 94.7%

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

      7. associate-*l* 92.8%

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

      8. *-commutative 92.8%

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

   3. Simplified 92.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -200000000000 \lor \neg \left(z \leq 2 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+19} \lor \neg \left(z \leq 1.3 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -5e+19) (not (<= z 1.3e+71)))
    (/ (+ (* (* a t) -4.0) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c_m)
    (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -5e+19) || !(z <= 1.3e+71)) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-5d+19)) .or. (.not. (z <= 1.3d+71))) then
        tmp = (((a * t) * (-4.0d0)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c_m
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -5e+19) || !(z <= 1.3e+71)) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -5e+19) or not (z <= 1.3e+71):
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -5e+19) || !(z <= 1.3e+71))
		tmp = Float64(Float64(Float64(Float64(a * t) * -4.0) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -5e+19) || ~((z <= 1.3e+71)))
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -5e+19], N[Not[LessEqual[z, 1.3e+71]], $MachinePrecision]], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5e19 or 1.29999999999999996e71 < z

   1. Initial program 59.6%

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

      1. associate-+l- 59.6%

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

      2. *-commutative 59.6%

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

      3. associate-*r* 59.4%

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

      4. *-commutative 59.4%

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

      5. associate-+l- 59.4%

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

      6. associate-*l* 58.4%

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

      7. associate-*l* 66.9%

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

      8. *-commutative 66.9%

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

   3. Simplified 66.9%

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

      1. add-cube-cbrt 66.8%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 66.8%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 67.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 67.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 67.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 67.7%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 84.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 73.6%

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

   10. Taylor expanded in c around 0 92.5%

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

   if -5e19 < z < 1.29999999999999996e71

   1. Initial program 94.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+19} \lor \neg \left(z \leq 1.3 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c\_m}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+71}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -2e+26)
    (/ (+ (* (* a t) -4.0) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c_m)
    (if (<= z 1.3e+71)
      (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c_m z))
      (/ (- (/ (+ b (* 9.0 (* x y))) z) (* 4.0 (* a t))) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2e+26) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else if (z <= 1.3e+71) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (z <= (-2d+26)) then
        tmp = (((a * t) * (-4.0d0)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c_m
    else if (z <= 1.3d+71) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (c_m * z)
    else
        tmp = (((b + (9.0d0 * (x * y))) / z) - (4.0d0 * (a * t))) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2e+26) {
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	} else if (z <= 1.3e+71) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -2e+26:
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m
	elif z <= 1.3e+71:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z)
	else:
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -2e+26)
		tmp = Float64(Float64(Float64(Float64(a * t) * -4.0) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c_m);
	elseif (z <= 1.3e+71)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / z) - Float64(4.0 * Float64(a * t))) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -2e+26)
		tmp = (((a * t) * -4.0) + ((9.0 * ((x * y) / z)) + (b / z))) / c_m;
	elseif (z <= 1.3e+71)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c_m * z);
	else
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -2e+26], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[z, 1.3e+71], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e26

   1. Initial program 59.4%

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

      1. associate-+l- 59.4%

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

      2. *-commutative 59.4%

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

      3. associate-*r* 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-+l- 60.5%

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

      6. associate-*l* 59.0%

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

      7. associate-*l* 67.1%

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

      8. *-commutative 67.1%

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

   3. Simplified 67.1%

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

      1. add-cube-cbrt 67.0%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 67.0%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 68.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 68.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 68.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 68.5%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 81.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 73.7%

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

   10. Taylor expanded in c around 0 90.5%

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

   if -2.0000000000000001e26 < z < 1.29999999999999996e71

   1. Initial program 94.7%

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

   if 1.29999999999999996e71 < z

   1. Initial program 60.0%

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

      1. associate-+l- 60.0%

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

      2. *-commutative 60.0%

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

      3. associate-*r* 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-+l- 57.7%

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

      6. associate-*l* 57.7%

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

      7. associate-*l* 66.6%

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

      8. *-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. Step-by-step derivation

      1. add-cube-cbrt 66.5%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 66.5%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 66.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 66.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 66.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 66.5%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 73.6%

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

   10. Taylor expanded in c around -inf 95.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{z} + 4 \cdot \left(a \cdot t\right)}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\left(a \cdot t\right) \cdot -4 + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+71}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 2.15 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} - 4 \cdot \left(a \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}}{z} - 4 \cdot \frac{a \cdot t}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 2.15e+42)
    (/ (- (/ (+ b (* 9.0 (* x y))) z) (* 4.0 (* a t))) c_m)
    (- (/ (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)) z) (* 4.0 (/ (* a t) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 2.15e+42) {
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = (((9.0 * ((x * y) / c_m)) + (b / c_m)) / z) - (4.0 * ((a * t) / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (c_m <= 2.15d+42) then
        tmp = (((b + (9.0d0 * (x * y))) / z) - (4.0d0 * (a * t))) / c_m
    else
        tmp = (((9.0d0 * ((x * y) / c_m)) + (b / c_m)) / z) - (4.0d0 * ((a * t) / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 2.15e+42) {
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	} else {
		tmp = (((9.0 * ((x * y) / c_m)) + (b / c_m)) / z) - (4.0 * ((a * t) / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 2.15e+42:
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m
	else:
		tmp = (((9.0 * ((x * y) / c_m)) + (b / c_m)) / z) - (4.0 * ((a * t) / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 2.15e+42)
		tmp = Float64(Float64(Float64(Float64(b + Float64(9.0 * Float64(x * y))) / z) - Float64(4.0 * Float64(a * t))) / c_m);
	else
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m)) / z) - Float64(4.0 * Float64(Float64(a * t) / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 2.15e+42)
		tmp = (((b + (9.0 * (x * y))) / z) - (4.0 * (a * t))) / c_m;
	else
		tmp = (((9.0 * ((x * y) / c_m)) + (b / c_m)) / z) - (4.0 * ((a * t) / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 2.15e+42], N[(N[(N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 2.1499999999999999e42

   1. Initial program 83.5%

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

      1. associate-+l- 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*r* 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-+l- 82.9%

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

      6. associate-*l* 82.4%

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

      7. associate-*l* 85.3%

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

      8. *-commutative 85.3%

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

   3. Simplified 85.3%

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

      1. add-cube-cbrt 85.1%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 85.1%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 85.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 85.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 85.6%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 85.6%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 83.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 79.9%

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

   10. Taylor expanded in c around -inf 88.3%

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

   if 2.1499999999999999e42 < c

   1. Initial program 64.3%

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

      1. associate-+l- 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. associate-*l* 66.5%

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

      7. associate-*l* 66.7%

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

      8. *-commutative 66.7%

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

   3. Simplified 66.7%

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

      1. add-cube-cbrt 66.5%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 66.5%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 66.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 66.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 66.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 66.5%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 78.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 93.1%

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

   10. Taylor expanded in c around -inf 82.7%

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

   11. Taylor expanded in z around -inf 86.4%

       \[\leadsto -1 \cdot \color{blue}{\left(-1 \cdot \frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z} + 4 \cdot \frac{a \cdot t}{c}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.15 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z} - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z} - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+63} \lor \neg \left(z \leq 8.6 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -3e+63) (not (<= z 8.6e+139)))
    (/ (- (/ b z) (* a (* 4.0 t))) c_m)
    (/ (+ b (* 9.0 (* x y))) (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3e+63) || !(z <= 8.6e+139)) {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-3d+63)) .or. (.not. (z <= 8.6d+139))) then
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    else
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3e+63) || !(z <= 8.6e+139)) {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	} else {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -3e+63) or not (z <= 8.6e+139):
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	else:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -3e+63) || !(z <= 8.6e+139))
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -3e+63) || ~((z <= 8.6e+139)))
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	else
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -3e+63], N[Not[LessEqual[z, 8.6e+139]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999999e63 or 8.5999999999999996e139 < z

   1. Initial program 54.2%

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

      1. associate-+l- 54.2%

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

      2. *-commutative 54.2%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

      5. associate-+l- 54.9%

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

      6. associate-*l* 53.8%

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

      7. associate-*l* 61.7%

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

      8. *-commutative 61.7%

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

   3. Simplified 61.7%

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

      1. add-cube-cbrt 61.6%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 61.6%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 62.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 62.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 62.7%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 62.7%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around 0 82.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \left(9 \cdot \left({1}^{0.3333333333333333} \cdot \frac{x \cdot y}{c \cdot z}\right) + \frac{b}{c \cdot z}\right)} \]

   9. Simplified 74.0%

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

   10. Taylor expanded in c around -inf 91.1%

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

   11. Taylor expanded in x around 0 81.4%

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

       1. +-commutative 81.4%

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

       2. mul-1-neg 81.4%

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

       3. unsub-neg 81.4%

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

       4. associate-*r* 81.4%

          \[\leadsto -1 \cdot \frac{\color{blue}{\left(4 \cdot a\right) \cdot t} - \frac{b}{z}}{c} \]

       5. *-commutative 81.4%

          \[\leadsto -1 \cdot \frac{\color{blue}{\left(a \cdot 4\right)} \cdot t - \frac{b}{z}}{c} \]

       6. associate-*l* 81.4%

          \[\leadsto -1 \cdot \frac{\color{blue}{a \cdot \left(4 \cdot t\right)} - \frac{b}{z}}{c} \]

   13. Simplified 81.4%

       \[\leadsto -1 \cdot \color{blue}{\frac{a \cdot \left(4 \cdot t\right) - \frac{b}{z}}{c}} \]

   if -2.99999999999999999e63 < z < 8.5999999999999996e139

   1. Initial program 94.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 94.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 94.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 93.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 93.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 93.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 93.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 93.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.7%

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 78.7%

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+63} \lor \neg \left(z \leq 8.6 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+209}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -1.16e+166)
    (* a (* -4.0 (/ t c_m)))
    (if (<= z 1.8e+209)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (* -4.0 (* t (/ a c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.16e+166) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (z <= 1.8e+209) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (z <= (-1.16d+166)) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else if (z <= 1.8d+209) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.16e+166) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (z <= 1.8e+209) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -1.16e+166:
		tmp = a * (-4.0 * (t / c_m))
	elif z <= 1.8e+209:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	else:
		tmp = -4.0 * (t * (a / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -1.16e+166)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	elseif (z <= 1.8e+209)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -1.16e+166)
		tmp = a * (-4.0 * (t / c_m));
	elseif (z <= 1.8e+209)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	else
		tmp = -4.0 * (t * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -1.16e+166], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+209], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.16000000000000002e166

   1. Initial program 40.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 40.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 40.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 46.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 46.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 46.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 43.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 52.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 52.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 52.5%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 52.6%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 55.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 55.5%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 55.4%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 55.4%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 65.0%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*l* 65.0%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   if -1.16000000000000002e166 < z < 1.80000000000000006e209

   1. Initial program 90.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 90.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 90.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 90.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 90.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 90.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 90.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 90.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 90.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 75.2%

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 75.2%

         \[\leadsto \frac{b + 9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 75.2%

      \[\leadsto \color{blue}{\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}} \]

   if 1.80000000000000006e209 < z

   1. Initial program 49.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 49.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 49.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 45.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 45.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 45.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 45.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 53.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 53.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 53.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 72.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 72.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-/l* 65.4%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+209}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -6.3e+44)
    (/ (/ b c_m) z)
    (if (<= b 1.8e+42) (* a (* -4.0 (/ t c_m))) (/ b (* c_m z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -6.3e+44) {
		tmp = (b / c_m) / z;
	} else if (b <= 1.8e+42) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-6.3d+44)) then
        tmp = (b / c_m) / z
    else if (b <= 1.8d+42) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -6.3e+44) {
		tmp = (b / c_m) / z;
	} else if (b <= 1.8e+42) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -6.3e+44:
		tmp = (b / c_m) / z
	elif b <= 1.8e+42:
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -6.3e+44)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (b <= 1.8e+42)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -6.3e+44)
		tmp = (b / c_m) / z;
	elseif (b <= 1.8e+42)
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -6.3e+44], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 1.8e+42], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -6.3e44

   1. Initial program 76.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 76.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   6. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)\right) + b}{c}} \]

   7. Taylor expanded in b around inf 62.9%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{b}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 63.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{b}{c}}{z}} \]

      2. *-un-lft-identity 63.0%

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   9. Applied egg-rr 63.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -6.3e44 < b < 1.8e42

   1. Initial program 78.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 82.4%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 82.3%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 83.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 83.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 83.1%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 83.1%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 47.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 48.6%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*l* 48.6%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   9. Simplified 48.6%

      \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   if 1.8e42 < b

   1. Initial program 88.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 78.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 61.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 61.4%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c\_m \cdot z}{b}}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -7e+44)
    (/ (/ b c_m) z)
    (if (<= b 6e+42) (* a (* -4.0 (/ t c_m))) (/ 1.0 (/ (* c_m z) b))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -7e+44) {
		tmp = (b / c_m) / z;
	} else if (b <= 6e+42) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = 1.0 / ((c_m * z) / b);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-7d+44)) then
        tmp = (b / c_m) / z
    else if (b <= 6d+42) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else
        tmp = 1.0d0 / ((c_m * z) / b)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -7e+44) {
		tmp = (b / c_m) / z;
	} else if (b <= 6e+42) {
		tmp = a * (-4.0 * (t / c_m));
	} else {
		tmp = 1.0 / ((c_m * z) / b);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -7e+44:
		tmp = (b / c_m) / z
	elif b <= 6e+42:
		tmp = a * (-4.0 * (t / c_m))
	else:
		tmp = 1.0 / ((c_m * z) / b)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -7e+44)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (b <= 6e+42)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	else
		tmp = Float64(1.0 / Float64(Float64(c_m * z) / b));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -7e+44)
		tmp = (b / c_m) / z;
	elseif (b <= 6e+42)
		tmp = a * (-4.0 * (t / c_m));
	else
		tmp = 1.0 / ((c_m * z) / b);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -7e+44], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 6e+42], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(c$95$m * z), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -6.9999999999999998e44

   1. Initial program 76.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 76.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   6. Applied egg-rr 74.6%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)\right) + b}{c}} \]

   7. Taylor expanded in b around inf 62.9%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{b}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 63.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{b}{c}}{z}} \]

      2. *-un-lft-identity 63.0%

         \[\leadsto \frac{\color{blue}{\frac{b}{c}}}{z} \]

   9. Applied egg-rr 63.0%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if -6.9999999999999998e44 < b < 6.00000000000000058e42

   1. Initial program 78.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 81.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 82.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 82.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 82.4%

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(9 \cdot y\right)}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      2. pow3 82.3%

         \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{x \cdot \left(9 \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      3. associate-*r* 83.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(x \cdot 9\right) \cdot y}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      4. *-commutative 83.0%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{\left(9 \cdot x\right)} \cdot y}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

      5. associate-*l* 83.1%

         \[\leadsto \frac{\left({\left(\sqrt[3]{\color{blue}{9 \cdot \left(x \cdot y\right)}}\right)}^{3} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   6. Applied egg-rr 83.1%

      \[\leadsto \frac{\left(\color{blue}{{\left(\sqrt[3]{9 \cdot \left(x \cdot y\right)}\right)}^{3}} - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c} \]

   7. Taylor expanded in z around inf 47.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 48.6%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

      3. associate-*l* 48.6%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   9. Simplified 48.6%

      \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   if 6.00000000000000058e42 < b

   1. Initial program 88.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 78.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   6. Applied egg-rr 62.7%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, 4 \cdot \left(z \cdot \left(t \cdot a\right)\right)\right) + b}{c}} \]

   7. Taylor expanded in b around inf 55.0%

      \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{b}{c}} \]
   8. Step-by-step derivation

      1. clear-num 55.0%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{1}{\frac{c}{b}}} \]

      2. frac-times 53.3%

         \[\leadsto \color{blue}{\frac{1 \cdot 1}{z \cdot \frac{c}{b}}} \]

      3. metadata-eval 53.3%

         \[\leadsto \frac{\color{blue}{1}}{z \cdot \frac{c}{b}} \]

   9. Applied egg-rr 53.3%

      \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{c}{b}}} \]
   10. Step-by-step derivation

       1. *-commutative 53.3%

          \[\leadsto \frac{1}{\color{blue}{\frac{c}{b} \cdot z}} \]

       2. associate-*l/ 61.4%

          \[\leadsto \frac{1}{\color{blue}{\frac{c \cdot z}{b}}} \]

       3. associate-/r/ 61.3%

          \[\leadsto \color{blue}{\frac{1}{c \cdot z} \cdot b} \]

   11. Simplified 61.3%

       \[\leadsto \color{blue}{\frac{1}{c \cdot z} \cdot b} \]
   12. Step-by-step derivation

       1. associate-*l/ 61.4%

          \[\leadsto \color{blue}{\frac{1 \cdot b}{c \cdot z}} \]

       2. *-un-lft-identity 61.4%

          \[\leadsto \frac{\color{blue}{b}}{c \cdot z} \]

       3. clear-num 61.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b}}} \]

       4. *-commutative 61.4%

          \[\leadsto \frac{1}{\frac{\color{blue}{z \cdot c}}{b}} \]

   13. Applied egg-rr 61.4%

       \[\leadsto \color{blue}{\frac{1}{\frac{z \cdot c}{b}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c \cdot z}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 80.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 80.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 80.1%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 80.1%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 80.1%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 79.7%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 82.1%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 82.1%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 82.1%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 38.0%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 38.0%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 38.0%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 38.0%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer target: 80.3% 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 2024047 
(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)))