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

Percentage Accurate: 79.0% → 85.3%

Time: 18.7s

Alternatives: 20

Speedup: 0.2×

• 36.4% 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: 79.0% 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: 85.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 6 \cdot 10^{-41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{c\_m \cdot z}\\ \mathbf{elif}\;c\_m \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;\frac{t\_1 + -4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;c\_m \leq 5 \cdot 10^{+216} \lor \neg \left(c\_m \leq 2.85 \cdot 10^{+263}\right):\\ \;\;\;\;b \cdot \left(\frac{1}{c\_m \cdot z} + \frac{\mathsf{fma}\left(9, \frac{x \cdot \frac{y}{c\_m}}{z}, a \cdot \frac{t \cdot -4}{c\_m}\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(\left(t \cdot z\right) \cdot \frac{a}{c\_m}\right) + t\_1}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 c_m) (* 9.0 (/ (* x y) c_m)))))
   (*
    c_s
    (if (<= c_m 6e-41)
      (/ (+ (fma x (* 9.0 y) (* t (* a (* z -4.0)))) b) (* c_m z))
      (if (<= c_m 1.3e+150)
        (/ (+ t_1 (* -4.0 (* (/ z c_m) (* t a)))) z)
        (if (or (<= c_m 5e+216) (not (<= c_m 2.85e+263)))
          (*
           b
           (+
            (/ 1.0 (* c_m z))
            (/ (fma 9.0 (/ (* x (/ y c_m)) z) (* a (/ (* t -4.0) c_m))) b)))
          (/ (+ (* -4.0 (* (* t z) (/ a c_m))) t_1) 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 = (b / c_m) + (9.0 * ((x * y) / c_m));
	double tmp;
	if (c_m <= 6e-41) {
		tmp = (fma(x, (9.0 * y), (t * (a * (z * -4.0)))) + b) / (c_m * z);
	} else if (c_m <= 1.3e+150) {
		tmp = (t_1 + (-4.0 * ((z / c_m) * (t * a)))) / z;
	} else if ((c_m <= 5e+216) || !(c_m <= 2.85e+263)) {
		tmp = b * ((1.0 / (c_m * z)) + (fma(9.0, ((x * (y / c_m)) / z), (a * ((t * -4.0) / c_m))) / b));
	} else {
		tmp = ((-4.0 * ((t * z) * (a / c_m))) + t_1) / 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(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / c_m)))
	tmp = 0.0
	if (c_m <= 6e-41)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0)))) + b) / Float64(c_m * z));
	elseif (c_m <= 1.3e+150)
		tmp = Float64(Float64(t_1 + Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a)))) / z);
	elseif ((c_m <= 5e+216) || !(c_m <= 2.85e+263))
		tmp = Float64(b * Float64(Float64(1.0 / Float64(c_m * z)) + Float64(fma(9.0, Float64(Float64(x * Float64(y / c_m)) / z), Float64(a * Float64(Float64(t * -4.0) / c_m))) / b)));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(t * z) * Float64(a / c_m))) + t_1) / 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_] := Block[{t$95$1 = N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[c$95$m, 6e-41], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c$95$m, 1.3e+150], N[(N[(t$95$1 + N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[c$95$m, 5e+216], N[Not[LessEqual[c$95$m, 2.85e+263]], $MachinePrecision]], N[(b * N[(N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / z), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if c < 5.99999999999999978e-41

   1. Initial program 80.5%

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

   3. Simplified 82.9%

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

   if 5.99999999999999978e-41 < c < 1.30000000000000003e150

   1. Initial program 75.3%

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

      1. associate-+l- 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-+l- 82.6%

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

      6. associate-*l* 82.6%

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

      7. associate-*l* 85.2%

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

      8. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around 0 82.8%

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

      1. associate-/l* 82.8%

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

      2. associate-*r/ 87.6%

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

      3. associate-*r* 95.0%

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

   7. Applied egg-rr 95.0%

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

   if 1.30000000000000003e150 < c < 4.9999999999999998e216 or 2.85000000000000022e263 < c

   1. Initial program 74.3%

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

      1. associate-+l- 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*r* 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* 76.1%

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

      7. associate-*l* 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. Taylor expanded in b around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate--l+ 59.1%

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

      3. *-commutative 59.1%

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

      4. times-frac 67.2%

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

      5. associate-*l/ 71.7%

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

      6. associate-/l* 67.0%

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

      7. associate-/l* 67.1%

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

      8. associate-*r/ 67.1%

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

      9. associate-/l/ 67.5%

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

      10. associate-*r/ 67.5%

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

      11. div-sub 67.5%

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

   7. Simplified 93.7%

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

   if 4.9999999999999998e216 < c < 2.85000000000000022e263

   1. Initial program 28.2%

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

      1. associate-+l- 28.2%

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

      2. *-commutative 28.2%

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

      3. associate-*r* 20.1%

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

      4. *-commutative 20.1%

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

      5. associate-+l- 20.1%

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

      6. associate-*l* 20.0%

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

      7. associate-*l* 19.8%

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

      8. *-commutative 19.8%

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

   3. Simplified 19.8%

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

   5. Taylor expanded in z around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. *-un-lft-identity 72.8%

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

      3. times-frac 81.6%

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

   7. Applied egg-rr 81.6%

      \[\leadsto \frac{-4 \cdot \color{blue}{\left(\frac{t \cdot z}{1} \cdot \frac{a}{c}\right)} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 6 \cdot 10^{-41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{c \cdot z}\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+150}:\\ \;\;\;\;\frac{\left(\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}\right) + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+216} \lor \neg \left(c \leq 2.85 \cdot 10^{+263}\right):\\ \;\;\;\;b \cdot \left(\frac{1}{c \cdot z} + \frac{\mathsf{fma}\left(9, \frac{x \cdot \frac{y}{c}}{z}, a \cdot \frac{t \cdot -4}{c}\right)}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(\left(t \cdot z\right) \cdot \frac{a}{c}\right) + \left(\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{c\_m \cdot z}\\ \mathbf{elif}\;c\_m \leq 1.05 \cdot 10^{+216} \lor \neg \left(c\_m \leq 9.2 \cdot 10^{+259}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c\_m}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c\_m}, \frac{b}{c\_m}\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(\left(t \cdot z\right) \cdot \frac{a}{c\_m}\right) + \left(\frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}\right)}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 1.9e-41)
    (/ (+ (fma x (* 9.0 y) (* t (* a (* z -4.0)))) b) (* c_m z))
    (if (or (<= c_m 1.05e+216) (not (<= c_m 9.2e+259)))
      (/
       (fma -4.0 (* a (* t (/ z c_m))) (fma 9.0 (* x (/ y c_m)) (/ b c_m)))
       z)
      (/
       (+ (* -4.0 (* (* t z) (/ a c_m))) (+ (/ b c_m) (* 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 (c_m <= 1.9e-41) {
		tmp = (fma(x, (9.0 * y), (t * (a * (z * -4.0)))) + b) / (c_m * z);
	} else if ((c_m <= 1.05e+216) || !(c_m <= 9.2e+259)) {
		tmp = fma(-4.0, (a * (t * (z / c_m))), fma(9.0, (x * (y / c_m)), (b / c_m))) / z;
	} else {
		tmp = ((-4.0 * ((t * z) * (a / c_m))) + ((b / c_m) + (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 (c_m <= 1.9e-41)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0)))) + b) / Float64(c_m * z));
	elseif ((c_m <= 1.05e+216) || !(c_m <= 9.2e+259))
		tmp = Float64(fma(-4.0, Float64(a * Float64(t * Float64(z / c_m))), fma(9.0, Float64(x * Float64(y / c_m)), Float64(b / c_m))) / z);
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(t * z) * Float64(a / c_m))) + Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / 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, 1.9e-41], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c$95$m, 1.05e+216], N[Not[LessEqual[c$95$m, 9.2e+259]], $MachinePrecision]], N[(N[(-4.0 * N[(a * N[(t * N[(z / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if c < 1.8999999999999999e-41

   1. Initial program 80.5%

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

   3. Simplified 82.9%

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

   if 1.8999999999999999e-41 < c < 1.05000000000000001e216 or 9.2000000000000004e259 < c

   1. Initial program 73.4%

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

      1. associate-+l- 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-+l- 78.8%

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

      6. associate-*l* 78.8%

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

      7. associate-*l* 78.9%

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

      8. *-commutative 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in z around 0 79.7%

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

      1. fma-define 79.7%

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

      2. associate-/l* 79.6%

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

      3. associate-/l* 84.2%

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

      4. fma-define 84.2%

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

      5. associate-/l* 88.9%

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

   7. Simplified 88.9%

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

   if 1.05000000000000001e216 < c < 9.2000000000000004e259

   1. Initial program 36.8%

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

      1. associate-+l- 36.8%

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

      2. *-commutative 36.8%

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

      3. associate-*r* 28.7%

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

      4. *-commutative 28.7%

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

      5. associate-+l- 28.7%

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

      6. associate-*l* 28.6%

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

      7. associate-*l* 19.9%

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

      8. *-commutative 19.9%

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

   3. Simplified 19.9%

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

   5. Taylor expanded in z around 0 73.0%

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

      1. *-commutative 73.0%

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

      2. *-un-lft-identity 73.0%

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

      3. times-frac 81.7%

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

   7. Applied egg-rr 81.7%

      \[\leadsto \frac{-4 \cdot \color{blue}{\left(\frac{t \cdot z}{1} \cdot \frac{a}{c}\right)} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{c \cdot z}\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+216} \lor \neg \left(c \leq 9.2 \cdot 10^{+259}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(t \cdot \frac{z}{c}\right), \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(\left(t \cdot z\right) \cdot \frac{a}{c}\right) + \left(\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+229}:\\ \;\;\;\;\frac{\left(\frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c\_m}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -5e-263)
      (/ (+ b (- (* x (* 9.0 y)) (* (* t a) (* z 4.0)))) (* c_m z))
      (if (<= t_1 2e+229)
        (/
         (+
          (+ (/ b c_m) (* 9.0 (/ (* x y) c_m)))
          (* -4.0 (/ (* a (* t z)) c_m)))
         z)
        (if (<= t_1 INFINITY)
          (/ (+ (fma x (* 9.0 y) (* t (* a (* z -4.0)))) b) (* c_m z))
          (* a (/ (* t -4.0) 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 t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -5e-263) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 2e+229) {
		tmp = (((b / c_m) + (9.0 * ((x * y) / c_m))) + (-4.0 * ((a * (t * z)) / c_m))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma(x, (9.0 * y), (t * (a * (z * -4.0)))) + b) / (c_m * z);
	} else {
		tmp = a * ((t * -4.0) / 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)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -5e-263)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(t * a) * Float64(z * 4.0)))) / Float64(c_m * z));
	elseif (t_1 <= 2e+229)
		tmp = Float64(Float64(Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / c_m))) + Float64(-4.0 * Float64(Float64(a * Float64(t * z)) / c_m))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0)))) + b) / Float64(c_m * z));
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	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_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-263], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+229], N[(N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.00000000000000006e-263

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 85.0%

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

      4. *-commutative 85.0%

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

      5. associate-+l- 85.0%

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

      6. associate-*l* 85.0%

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

      7. associate-*l* 85.0%

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

      8. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   if -5.00000000000000006e-263 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 2e229

   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* 81.3%

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

      4. *-commutative 81.3%

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

      5. associate-+l- 81.3%

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

      6. associate-*l* 81.3%

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

      7. associate-*l* 78.6%

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

      8. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in z around 0 98.1%

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

   if 2e229 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 82.3%

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

   3. Simplified 88.8%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 15.5%

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

      4. *-commutative 15.5%

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

      5. associate-+l- 15.5%

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

      6. associate-*l* 15.5%

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

      7. associate-*l* 15.5%

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

      8. *-commutative 15.5%

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

   3. Simplified 15.5%

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

   5. Taylor expanded in z around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 81.3%

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

      3. associate-*r* 81.3%

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

      4. associate-*l/ 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 2 \cdot 10^{+229}:\\ \;\;\;\;\frac{\left(\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}\right) + -4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-222}:\\ \;\;\;\;\frac{\frac{b}{c\_m} + -4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -5e-263)
      (/ (+ b (- (* x (* 9.0 y)) (* (* t a) (* z 4.0)))) (* c_m z))
      (if (<= t_1 5e-222)
        (/ (+ (/ b c_m) (* -4.0 (* (/ z c_m) (* t a)))) z)
        (if (<= t_1 INFINITY) t_1 (* a (/ (* t -4.0) 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 t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -5e-263) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 5e-222) {
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -5e-263) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 5e-222) {
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / 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):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_1 <= -5e-263:
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z)
	elif t_1 <= 5e-222:
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / 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)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -5e-263)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(t * a) * Float64(z * 4.0)))) / Float64(c_m * z));
	elseif (t_1 <= 5e-222)
		tmp = Float64(Float64(Float64(b / c_m) + Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a)))) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / 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)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_1 <= -5e-263)
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	elseif (t_1 <= 5e-222)
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / 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_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-263], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-222], N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.00000000000000006e-263

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 85.0%

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

      4. *-commutative 85.0%

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

      5. associate-+l- 85.0%

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

      6. associate-*l* 85.0%

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

      7. associate-*l* 85.0%

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

      8. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   if -5.00000000000000006e-263 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 5.00000000000000008e-222

   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* 35.2%

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

      4. *-commutative 35.2%

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

      5. associate-+l- 35.2%

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

      6. associate-*l* 35.2%

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

      7. associate-*l* 40.9%

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

      8. *-commutative 40.9%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in z around 0 99.6%

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

      1. associate-/l* 94.4%

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

      2. associate-*r/ 94.5%

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

      3. associate-*r* 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in x around 0 88.9%

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

   if 5.00000000000000008e-222 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.4%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 15.5%

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

      4. *-commutative 15.5%

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

      5. associate-+l- 15.5%

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

      6. associate-*l* 15.5%

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

      7. associate-*l* 15.5%

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

      8. *-commutative 15.5%

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

   3. Simplified 15.5%

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

   5. Taylor expanded in z around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 81.3%

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

      3. associate-*r* 81.3%

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

      4. associate-*l/ 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 5 \cdot 10^{-222}:\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-222}:\\ \;\;\;\;\frac{\left(\frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}\right) + -4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -5e-263)
      (/ (+ b (- (* x (* 9.0 y)) (* (* t a) (* z 4.0)))) (* c_m z))
      (if (<= t_1 5e-222)
        (/
         (+
          (+ (/ b c_m) (* 9.0 (/ (* x y) c_m)))
          (* -4.0 (* (/ z c_m) (* t a))))
         z)
        (if (<= t_1 INFINITY) t_1 (* a (/ (* t -4.0) 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 t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -5e-263) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 5e-222) {
		tmp = (((b / c_m) + (9.0 * ((x * y) / c_m))) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c_m);
	}
	return c_s * tmp;
}

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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -5e-263) {
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 5e-222) {
		tmp = (((b / c_m) + (9.0 * ((x * y) / c_m))) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / 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):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_1 <= -5e-263:
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z)
	elif t_1 <= 5e-222:
		tmp = (((b / c_m) + (9.0 * ((x * y) / c_m))) + (-4.0 * ((z / c_m) * (t * a)))) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / 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)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -5e-263)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(t * a) * Float64(z * 4.0)))) / Float64(c_m * z));
	elseif (t_1 <= 5e-222)
		tmp = Float64(Float64(Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / c_m))) + Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a)))) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / 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)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_1 <= -5e-263)
		tmp = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	elseif (t_1 <= 5e-222)
		tmp = (((b / c_m) + (9.0 * ((x * y) / c_m))) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / 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_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-263], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-222], N[(N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.00000000000000006e-263

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 85.0%

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

      4. *-commutative 85.0%

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

      5. associate-+l- 85.0%

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

      6. associate-*l* 85.0%

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

      7. associate-*l* 85.0%

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

      8. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   if -5.00000000000000006e-263 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 5.00000000000000008e-222

   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* 35.2%

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

      4. *-commutative 35.2%

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

      5. associate-+l- 35.2%

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

      6. associate-*l* 35.2%

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

      7. associate-*l* 40.9%

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

      8. *-commutative 40.9%

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

   3. Simplified 40.9%

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

   5. Taylor expanded in z around 0 99.6%

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

      1. associate-/l* 94.4%

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

      2. associate-*r/ 94.5%

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

      3. associate-*r* 99.7%

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

   7. Applied egg-rr 99.7%

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

   if 5.00000000000000008e-222 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.4%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 15.5%

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

      4. *-commutative 15.5%

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

      5. associate-+l- 15.5%

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

      6. associate-*l* 15.5%

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

      7. associate-*l* 15.5%

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

      8. *-commutative 15.5%

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

   3. Simplified 15.5%

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

   5. Taylor expanded in z around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 81.3%

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

      3. associate-*r* 81.3%

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

      4. associate-*l/ 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -5 \cdot 10^{-263}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 5 \cdot 10^{-222}:\\ \;\;\;\;\frac{\left(\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}\right) + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c\_m \cdot z}\\ t_2 := -4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right)\\ t_3 := \frac{t\_2 + x \cdot \left(9 \cdot \frac{y}{c\_m}\right)}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{b}{c\_m} + t\_2}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (* 4.0 (* a (* t z)))) (* c_m z)))
        (t_2 (* -4.0 (* (/ z c_m) (* t a))))
        (t_3 (/ (+ t_2 (* x (* 9.0 (/ y c_m)))) z)))
   (*
    c_s
    (if (<= b -2.7e+52)
      t_1
      (if (<= b 2.3e-96)
        t_3
        (if (<= b 7.9e-59)
          t_1
          (if (<= b 3.8e-25)
            t_3
            (if (<= b 5.5e+75)
              (/ (+ b (* x (* 9.0 y))) (* c_m z))
              (if (<= b 6.7e+168)
                (/ (+ (/ b c_m) t_2) z)
                (/ (+ 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 t_1 = (b - (4.0 * (a * (t * z)))) / (c_m * z);
	double t_2 = -4.0 * ((z / c_m) * (t * a));
	double t_3 = (t_2 + (x * (9.0 * (y / c_m)))) / z;
	double tmp;
	if (b <= -2.7e+52) {
		tmp = t_1;
	} else if (b <= 2.3e-96) {
		tmp = t_3;
	} else if (b <= 7.9e-59) {
		tmp = t_1;
	} else if (b <= 3.8e-25) {
		tmp = t_3;
	} else if (b <= 5.5e+75) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if (b <= 6.7e+168) {
		tmp = ((b / c_m) + t_2) / z;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b - (4.0d0 * (a * (t * z)))) / (c_m * z)
    t_2 = (-4.0d0) * ((z / c_m) * (t * a))
    t_3 = (t_2 + (x * (9.0d0 * (y / c_m)))) / z
    if (b <= (-2.7d+52)) then
        tmp = t_1
    else if (b <= 2.3d-96) then
        tmp = t_3
    else if (b <= 7.9d-59) then
        tmp = t_1
    else if (b <= 3.8d-25) then
        tmp = t_3
    else if (b <= 5.5d+75) then
        tmp = (b + (x * (9.0d0 * y))) / (c_m * z)
    else if (b <= 6.7d+168) then
        tmp = ((b / c_m) + t_2) / z
    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 t_1 = (b - (4.0 * (a * (t * z)))) / (c_m * z);
	double t_2 = -4.0 * ((z / c_m) * (t * a));
	double t_3 = (t_2 + (x * (9.0 * (y / c_m)))) / z;
	double tmp;
	if (b <= -2.7e+52) {
		tmp = t_1;
	} else if (b <= 2.3e-96) {
		tmp = t_3;
	} else if (b <= 7.9e-59) {
		tmp = t_1;
	} else if (b <= 3.8e-25) {
		tmp = t_3;
	} else if (b <= 5.5e+75) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if (b <= 6.7e+168) {
		tmp = ((b / c_m) + t_2) / z;
	} 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):
	t_1 = (b - (4.0 * (a * (t * z)))) / (c_m * z)
	t_2 = -4.0 * ((z / c_m) * (t * a))
	t_3 = (t_2 + (x * (9.0 * (y / c_m)))) / z
	tmp = 0
	if b <= -2.7e+52:
		tmp = t_1
	elif b <= 2.3e-96:
		tmp = t_3
	elif b <= 7.9e-59:
		tmp = t_1
	elif b <= 3.8e-25:
		tmp = t_3
	elif b <= 5.5e+75:
		tmp = (b + (x * (9.0 * y))) / (c_m * z)
	elif b <= 6.7e+168:
		tmp = ((b / c_m) + t_2) / z
	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)
	t_1 = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / Float64(c_m * z))
	t_2 = Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a)))
	t_3 = Float64(Float64(t_2 + Float64(x * Float64(9.0 * Float64(y / c_m)))) / z)
	tmp = 0.0
	if (b <= -2.7e+52)
		tmp = t_1;
	elseif (b <= 2.3e-96)
		tmp = t_3;
	elseif (b <= 7.9e-59)
		tmp = t_1;
	elseif (b <= 3.8e-25)
		tmp = t_3;
	elseif (b <= 5.5e+75)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(c_m * z));
	elseif (b <= 6.7e+168)
		tmp = Float64(Float64(Float64(b / c_m) + t_2) / z);
	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)
	t_1 = (b - (4.0 * (a * (t * z)))) / (c_m * z);
	t_2 = -4.0 * ((z / c_m) * (t * a));
	t_3 = (t_2 + (x * (9.0 * (y / c_m)))) / z;
	tmp = 0.0;
	if (b <= -2.7e+52)
		tmp = t_1;
	elseif (b <= 2.3e-96)
		tmp = t_3;
	elseif (b <= 7.9e-59)
		tmp = t_1;
	elseif (b <= 3.8e-25)
		tmp = t_3;
	elseif (b <= 5.5e+75)
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	elseif (b <= 6.7e+168)
		tmp = ((b / c_m) + t_2) / z;
	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_] := Block[{t$95$1 = N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(x * N[(9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, N[(c$95$s * If[LessEqual[b, -2.7e+52], t$95$1, If[LessEqual[b, 2.3e-96], t$95$3, If[LessEqual[b, 7.9e-59], t$95$1, If[LessEqual[b, 3.8e-25], t$95$3, If[LessEqual[b, 5.5e+75], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.7e+168], N[(N[(N[(b / c$95$m), $MachinePrecision] + t$95$2), $MachinePrecision] / z), $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 5 regimes

2. if b < -2.7e52 or 2.3e-96 < b < 7.89999999999999985e-59

   1. Initial program 78.1%

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

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 80.9%

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

      4. *-commutative 80.9%

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

      5. associate-+l- 80.9%

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

      6. associate-*l* 80.9%

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

      7. associate-*l* 79.4%

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

      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 0 70.0%

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

   if -2.7e52 < b < 2.3e-96 or 7.89999999999999985e-59 < b < 3.7999999999999998e-25

   1. Initial program 76.9%

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

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 77.7%

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

      4. *-commutative 77.7%

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

      5. associate-+l- 77.7%

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

      6. associate-*l* 77.7%

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

      7. associate-*l* 78.5%

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

      8. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in z around 0 82.3%

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

      1. associate-/l* 81.0%

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

      2. associate-*r/ 82.5%

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

      3. associate-*r* 84.7%

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

   7. Applied egg-rr 84.7%

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

   8. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 80.9%

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

      3. associate-*r* 80.9%

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

      4. *-commutative 80.9%

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

   10. Simplified 80.9%

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

   if 3.7999999999999998e-25 < b < 5.5000000000000001e75

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-+l- 90.3%

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

      6. associate-*l* 90.3%

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

      7. associate-*l* 90.3%

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

      8. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. associate-*r* 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 85.3%

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

   7. Simplified 85.3%

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

   if 5.5000000000000001e75 < b < 6.7000000000000003e168

   1. Initial program 49.1%

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

      1. associate-+l- 49.1%

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

      2. *-commutative 49.1%

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

      3. associate-*r* 54.7%

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

      4. *-commutative 54.7%

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

      5. associate-+l- 54.7%

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

      6. associate-*l* 54.7%

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

      7. associate-*l* 54.9%

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

      8. *-commutative 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. associate-/l* 61.2%

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

      2. associate-*r/ 78.0%

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

      3. associate-*r* 83.9%

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

   7. Applied egg-rr 83.9%

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

   8. Taylor expanded in x around 0 78.5%

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

   if 6.7000000000000003e168 < b

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*r* 89.2%

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

      4. *-commutative 89.2%

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

      5. associate-+l- 89.2%

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

      6. associate-*l* 89.2%

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

      7. associate-*l* 82.0%

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

      8. *-commutative 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 85.8%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+52}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{-4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right) + x \cdot \left(9 \cdot \frac{y}{c}\right)}{z}\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{-59}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{-4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right) + x \cdot \left(9 \cdot \frac{y}{c}\right)}{z}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c\_m \leq 1.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}}{z}\\ \mathbf{elif}\;c\_m \leq 1.15 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c\_m \leq 2.7 \cdot 10^{+179}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;c\_m \leq 2.15 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right) + x \cdot \left(9 \cdot \frac{y}{c\_m}\right)}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (- (* x (* 9.0 y)) (* (* t a) (* z 4.0)))) (* c_m z))))
   (*
    c_s
    (if (<= c_m 1.55e+83)
      t_1
      (if (<= c_m 1.7e+104)
        (/ (+ (/ b c_m) (* 9.0 (/ (* x y) c_m))) z)
        (if (<= c_m 1.15e+166)
          t_1
          (if (<= c_m 2.7e+179)
            (* -4.0 (* t (/ a c_m)))
            (if (<= c_m 2.15e+209)
              t_1
              (/
               (+ (* -4.0 (* (/ z c_m) (* t a))) (* x (* 9.0 (/ 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 t_1 = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	double tmp;
	if (c_m <= 1.55e+83) {
		tmp = t_1;
	} else if (c_m <= 1.7e+104) {
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z;
	} else if (c_m <= 1.15e+166) {
		tmp = t_1;
	} else if (c_m <= 2.7e+179) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (c_m <= 2.15e+209) {
		tmp = t_1;
	} else {
		tmp = ((-4.0 * ((z / c_m) * (t * a))) + (x * (9.0 * (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) :: t_1
    real(8) :: tmp
    t_1 = (b + ((x * (9.0d0 * y)) - ((t * a) * (z * 4.0d0)))) / (c_m * z)
    if (c_m <= 1.55d+83) then
        tmp = t_1
    else if (c_m <= 1.7d+104) then
        tmp = ((b / c_m) + (9.0d0 * ((x * y) / c_m))) / z
    else if (c_m <= 1.15d+166) then
        tmp = t_1
    else if (c_m <= 2.7d+179) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (c_m <= 2.15d+209) then
        tmp = t_1
    else
        tmp = (((-4.0d0) * ((z / c_m) * (t * a))) + (x * (9.0d0 * (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 t_1 = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	double tmp;
	if (c_m <= 1.55e+83) {
		tmp = t_1;
	} else if (c_m <= 1.7e+104) {
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z;
	} else if (c_m <= 1.15e+166) {
		tmp = t_1;
	} else if (c_m <= 2.7e+179) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (c_m <= 2.15e+209) {
		tmp = t_1;
	} else {
		tmp = ((-4.0 * ((z / c_m) * (t * a))) + (x * (9.0 * (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):
	t_1 = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z)
	tmp = 0
	if c_m <= 1.55e+83:
		tmp = t_1
	elif c_m <= 1.7e+104:
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z
	elif c_m <= 1.15e+166:
		tmp = t_1
	elif c_m <= 2.7e+179:
		tmp = -4.0 * (t * (a / c_m))
	elif c_m <= 2.15e+209:
		tmp = t_1
	else:
		tmp = ((-4.0 * ((z / c_m) * (t * a))) + (x * (9.0 * (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)
	t_1 = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(t * a) * Float64(z * 4.0)))) / Float64(c_m * z))
	tmp = 0.0
	if (c_m <= 1.55e+83)
		tmp = t_1;
	elseif (c_m <= 1.7e+104)
		tmp = Float64(Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / c_m))) / z);
	elseif (c_m <= 1.15e+166)
		tmp = t_1;
	elseif (c_m <= 2.7e+179)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (c_m <= 2.15e+209)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a))) + Float64(x * Float64(9.0 * Float64(y / 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 = (b + ((x * (9.0 * y)) - ((t * a) * (z * 4.0)))) / (c_m * z);
	tmp = 0.0;
	if (c_m <= 1.55e+83)
		tmp = t_1;
	elseif (c_m <= 1.7e+104)
		tmp = ((b / c_m) + (9.0 * ((x * y) / c_m))) / z;
	elseif (c_m <= 1.15e+166)
		tmp = t_1;
	elseif (c_m <= 2.7e+179)
		tmp = -4.0 * (t * (a / c_m));
	elseif (c_m <= 2.15e+209)
		tmp = t_1;
	else
		tmp = ((-4.0 * ((z / c_m) * (t * a))) + (x * (9.0 * (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_] := Block[{t$95$1 = N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[c$95$m, 1.55e+83], t$95$1, If[LessEqual[c$95$m, 1.7e+104], N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[c$95$m, 1.15e+166], t$95$1, If[LessEqual[c$95$m, 2.7e+179], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c$95$m, 2.15e+209], t$95$1, N[(N[(N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if c < 1.54999999999999996e83 or 1.6999999999999998e104 < c < 1.15000000000000004e166 or 2.69999999999999982e179 < c < 2.14999999999999994e209

   1. Initial program 79.8%

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

      1. associate-+l- 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-*r* 82.7%

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

      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* 82.7%

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

      7. associate-*l* 82.7%

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

      8. *-commutative 82.7%

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

   3. Simplified 82.7%

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

   if 1.54999999999999996e83 < c < 1.6999999999999998e104

   1. Initial program 81.0%

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

      1. associate-+l- 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r* 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-+l- 81.0%

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

      6. associate-*l* 81.0%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. fma-define 100.0%

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

      2. associate-/l* 100.0%

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

      3. associate-/l* 100.0%

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

      4. fma-define 100.0%

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

      5. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around 0 100.0%

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

   if 1.15000000000000004e166 < c < 2.69999999999999982e179

   1. Initial program 66.1%

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

      1. associate-+l- 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*r* 66.1%

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

      4. *-commutative 66.1%

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

      5. associate-+l- 66.1%

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

      6. associate-*l* 65.6%

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

      7. associate-*l* 34.4%

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

      8. *-commutative 34.4%

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

   3. Simplified 34.4%

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

   5. Taylor expanded in z around 0 68.3%

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

      1. associate-*r/ 68.3%

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

      2. *-commutative 68.3%

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

   7. Applied egg-rr 68.3%

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

   8. Taylor expanded in a around inf 5.2%

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

      1. associate-*r/ 5.2%

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

      2. associate-*r* 5.2%

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

      3. associate-*l/ 68.1%

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

      4. associate-*r/ 68.1%

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

      5. associate-*l* 68.1%

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

   10. Simplified 68.1%

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

   if 2.14999999999999994e209 < c

   1. Initial program 45.3%

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

      1. associate-+l- 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*r* 40.9%

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

      4. *-commutative 40.9%

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

      5. associate-+l- 40.9%

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

      6. associate-*l* 40.8%

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

      7. associate-*l* 36.0%

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

      8. *-commutative 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in z around 0 69.6%

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

      1. associate-/l* 74.4%

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

      2. associate-*r/ 79.3%

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

      3. associate-*r* 69.1%

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

   7. Applied egg-rr 69.1%

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

   8. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-/l* 64.7%

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

      3. associate-*r* 64.8%

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

      4. *-commutative 64.8%

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

   10. Simplified 64.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}}{z}\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+166}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+179}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+209}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(t \cdot a\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right) + x \cdot \left(9 \cdot \frac{y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c\_m} + -4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right)}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-136}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 215000000:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 c_m) (* -4.0 (* (/ z c_m) (* t a)))) z)))
   (*
    c_s
    (if (<= z -2.6e+67)
      t_1
      (if (<= z 6e-136)
        (/ (+ b (* x (* 9.0 y))) (* c_m z))
        (if (<= z 215000000.0)
          (/ (- (* 9.0 (* x y)) (* 4.0 (* a (* t z)))) (* c_m z))
          (if (<= z 1.7e+142) t_1 (* a (/ (* t -4.0) 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 t_1 = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	double tmp;
	if (z <= -2.6e+67) {
		tmp = t_1;
	} else if (z <= 6e-136) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if (z <= 215000000.0) {
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (t * z)))) / (c_m * z);
	} else if (z <= 1.7e+142) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / 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) :: t_1
    real(8) :: tmp
    t_1 = ((b / c_m) + ((-4.0d0) * ((z / c_m) * (t * a)))) / z
    if (z <= (-2.6d+67)) then
        tmp = t_1
    else if (z <= 6d-136) then
        tmp = (b + (x * (9.0d0 * y))) / (c_m * z)
    else if (z <= 215000000.0d0) then
        tmp = ((9.0d0 * (x * y)) - (4.0d0 * (a * (t * z)))) / (c_m * z)
    else if (z <= 1.7d+142) then
        tmp = t_1
    else
        tmp = a * ((t * (-4.0d0)) / 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 t_1 = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	double tmp;
	if (z <= -2.6e+67) {
		tmp = t_1;
	} else if (z <= 6e-136) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if (z <= 215000000.0) {
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (t * z)))) / (c_m * z);
	} else if (z <= 1.7e+142) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / 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):
	t_1 = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z
	tmp = 0
	if z <= -2.6e+67:
		tmp = t_1
	elif z <= 6e-136:
		tmp = (b + (x * (9.0 * y))) / (c_m * z)
	elif z <= 215000000.0:
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (t * z)))) / (c_m * z)
	elif z <= 1.7e+142:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / 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)
	t_1 = Float64(Float64(Float64(b / c_m) + Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a)))) / z)
	tmp = 0.0
	if (z <= -2.6e+67)
		tmp = t_1;
	elseif (z <= 6e-136)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(c_m * z));
	elseif (z <= 215000000.0)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) - Float64(4.0 * Float64(a * Float64(t * z)))) / Float64(c_m * z));
	elseif (z <= 1.7e+142)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / 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)
	t_1 = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / z;
	tmp = 0.0;
	if (z <= -2.6e+67)
		tmp = t_1;
	elseif (z <= 6e-136)
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	elseif (z <= 215000000.0)
		tmp = ((9.0 * (x * y)) - (4.0 * (a * (t * z)))) / (c_m * z);
	elseif (z <= 1.7e+142)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / 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_] := Block[{t$95$1 = N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -2.6e+67], t$95$1, If[LessEqual[z, 6e-136], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 215000000.0], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+142], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e67 or 2.15e8 < z < 1.6999999999999999e142

   1. Initial program 63.1%

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

      1. associate-+l- 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-*r* 66.8%

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

      4. *-commutative 66.8%

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

      5. associate-+l- 66.8%

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

      6. associate-*l* 66.7%

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

      7. associate-*l* 69.5%

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

      8. *-commutative 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 64.4%

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

      2. associate-*r/ 70.4%

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

      3. associate-*r* 75.2%

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

   7. Applied egg-rr 75.2%

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

   8. Taylor expanded in x around 0 68.1%

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

   if -2.6e67 < z < 5.9999999999999996e-136

   1. Initial program 91.4%

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

      1. associate-+l- 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-*r* 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-+l- 93.0%

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

      6. associate-*l* 93.0%

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

      7. associate-*l* 89.4%

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

      8. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 82.5%

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

      1. associate-*r* 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 82.5%

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

   7. Simplified 82.5%

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

   if 5.9999999999999996e-136 < z < 2.15e8

   1. Initial program 94.3%

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

      1. associate-+l- 94.3%

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

      2. *-commutative 94.3%

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

      3. associate-*r* 94.2%

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

      4. *-commutative 94.2%

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

      5. associate-+l- 94.2%

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

      6. associate-*l* 94.2%

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

      7. associate-*l* 91.6%

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

      8. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in b around 0 77.5%

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

   if 1.6999999999999999e142 < z

   1. Initial program 45.3%

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

      1. associate-+l- 45.3%

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

      2. *-commutative 45.3%

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

      3. associate-*r* 49.0%

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

      4. *-commutative 49.0%

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

      5. associate-+l- 49.0%

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

      6. associate-*l* 49.0%

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

      7. associate-*l* 51.3%

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

      8. *-commutative 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in z around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-/l* 63.4%

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

      3. associate-*r* 63.4%

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

      4. associate-*l/ 63.4%

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

   7. Simplified 63.4%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-136}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 215000000:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot \frac{y}{c\_m}}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-111}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 c_m)) z))))
   (*
    c_s
    (if (<= a -1.1e-111)
      (* -4.0 (/ (* t a) c_m))
      (if (<= a 6.5e-235)
        t_1
        (if (<= a 8.6e-82)
          (/ (/ b c_m) z)
          (if (<= a 1.6e-25)
            t_1
            (if (<= a 7.2e-20) (/ b (* 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 t_1 = 9.0 * ((x * (y / c_m)) / z);
	double tmp;
	if (a <= -1.1e-111) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 6.5e-235) {
		tmp = t_1;
	} else if (a <= 8.6e-82) {
		tmp = (b / c_m) / z;
	} else if (a <= 1.6e-25) {
		tmp = t_1;
	} else if (a <= 7.2e-20) {
		tmp = b / (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) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((x * (y / c_m)) / z)
    if (a <= (-1.1d-111)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (a <= 6.5d-235) then
        tmp = t_1
    else if (a <= 8.6d-82) then
        tmp = (b / c_m) / z
    else if (a <= 1.6d-25) then
        tmp = t_1
    else if (a <= 7.2d-20) then
        tmp = b / (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 t_1 = 9.0 * ((x * (y / c_m)) / z);
	double tmp;
	if (a <= -1.1e-111) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 6.5e-235) {
		tmp = t_1;
	} else if (a <= 8.6e-82) {
		tmp = (b / c_m) / z;
	} else if (a <= 1.6e-25) {
		tmp = t_1;
	} else if (a <= 7.2e-20) {
		tmp = b / (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):
	t_1 = 9.0 * ((x * (y / c_m)) / z)
	tmp = 0
	if a <= -1.1e-111:
		tmp = -4.0 * ((t * a) / c_m)
	elif a <= 6.5e-235:
		tmp = t_1
	elif a <= 8.6e-82:
		tmp = (b / c_m) / z
	elif a <= 1.6e-25:
		tmp = t_1
	elif a <= 7.2e-20:
		tmp = b / (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)
	t_1 = Float64(9.0 * Float64(Float64(x * Float64(y / c_m)) / z))
	tmp = 0.0
	if (a <= -1.1e-111)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (a <= 6.5e-235)
		tmp = t_1;
	elseif (a <= 8.6e-82)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (a <= 1.6e-25)
		tmp = t_1;
	elseif (a <= 7.2e-20)
		tmp = Float64(b / 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)
	t_1 = 9.0 * ((x * (y / c_m)) / z);
	tmp = 0.0;
	if (a <= -1.1e-111)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (a <= 6.5e-235)
		tmp = t_1;
	elseif (a <= 8.6e-82)
		tmp = (b / c_m) / z;
	elseif (a <= 1.6e-25)
		tmp = t_1;
	elseif (a <= 7.2e-20)
		tmp = b / (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_] := Block[{t$95$1 = N[(9.0 * N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1.1e-111], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-235], t$95$1, If[LessEqual[a, 8.6e-82], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.6e-25], t$95$1, If[LessEqual[a, 7.2e-20], N[(b / 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 5 regimes

2. if a < -1.1e-111

   1. Initial program 78.9%

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

      1. associate-+l- 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 80.7%

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

      4. *-commutative 80.7%

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

      5. associate-+l- 80.7%

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

      6. associate-*l* 80.7%

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

      7. associate-*l* 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 z around inf 45.8%

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

      1. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   if -1.1e-111 < a < 6.49999999999999973e-235 or 8.60000000000000037e-82 < a < 1.6000000000000001e-25

   1. Initial program 79.2%

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

      1. associate-+l- 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*r* 87.3%

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

      4. *-commutative 87.3%

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

      5. associate-+l- 87.3%

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

      6. associate-*l* 87.3%

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

      7. associate-*l* 87.3%

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

      8. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around inf 47.9%

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

      1. associate-/r* 46.8%

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

      2. associate-/l* 49.3%

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

   7. Simplified 49.3%

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

   if 6.49999999999999973e-235 < a < 8.60000000000000037e-82

   1. Initial program 75.9%

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

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-+l- 78.8%

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

      6. associate-*l* 78.7%

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

      7. associate-*l* 78.7%

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

      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 b around inf 38.0%

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

      1. associate-/r* 49.9%

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

   7. Simplified 49.9%

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

   if 1.6000000000000001e-25 < a < 7.19999999999999948e-20

   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* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 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 inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 7.19999999999999948e-20 < a

   1. Initial program 70.2%

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

      1. associate-+l- 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.5%

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

      7. associate-*l* 68.3%

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

      8. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around 0 77.6%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Applied egg-rr 75.6%

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

   8. Taylor expanded in a around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. associate-*r* 51.6%

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

      3. associate-*l/ 66.1%

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

      4. associate-*r/ 66.1%

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

      5. associate-*l* 66.1%

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

   10. Simplified 66.1%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-111}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-235}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-235}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c\_m}}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;\left(9 \cdot \frac{y}{c\_m}\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a -1.7e-116)
    (* -4.0 (/ (* t a) c_m))
    (if (<= a 5.1e-235)
      (* 9.0 (/ (* x (/ y c_m)) z))
      (if (<= a 1.1e-81)
        (/ (/ b c_m) z)
        (if (<= a 4.5e-30)
          (* (* 9.0 (/ y c_m)) (/ x z))
          (if (<= a 5.8e-17) (/ b (* 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 (a <= -1.7e-116) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 5.1e-235) {
		tmp = 9.0 * ((x * (y / c_m)) / z);
	} else if (a <= 1.1e-81) {
		tmp = (b / c_m) / z;
	} else if (a <= 4.5e-30) {
		tmp = (9.0 * (y / c_m)) * (x / z);
	} else if (a <= 5.8e-17) {
		tmp = b / (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 (a <= (-1.7d-116)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (a <= 5.1d-235) then
        tmp = 9.0d0 * ((x * (y / c_m)) / z)
    else if (a <= 1.1d-81) then
        tmp = (b / c_m) / z
    else if (a <= 4.5d-30) then
        tmp = (9.0d0 * (y / c_m)) * (x / z)
    else if (a <= 5.8d-17) then
        tmp = b / (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 (a <= -1.7e-116) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 5.1e-235) {
		tmp = 9.0 * ((x * (y / c_m)) / z);
	} else if (a <= 1.1e-81) {
		tmp = (b / c_m) / z;
	} else if (a <= 4.5e-30) {
		tmp = (9.0 * (y / c_m)) * (x / z);
	} else if (a <= 5.8e-17) {
		tmp = b / (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 a <= -1.7e-116:
		tmp = -4.0 * ((t * a) / c_m)
	elif a <= 5.1e-235:
		tmp = 9.0 * ((x * (y / c_m)) / z)
	elif a <= 1.1e-81:
		tmp = (b / c_m) / z
	elif a <= 4.5e-30:
		tmp = (9.0 * (y / c_m)) * (x / z)
	elif a <= 5.8e-17:
		tmp = b / (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 (a <= -1.7e-116)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (a <= 5.1e-235)
		tmp = Float64(9.0 * Float64(Float64(x * Float64(y / c_m)) / z));
	elseif (a <= 1.1e-81)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (a <= 4.5e-30)
		tmp = Float64(Float64(9.0 * Float64(y / c_m)) * Float64(x / z));
	elseif (a <= 5.8e-17)
		tmp = Float64(b / 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 (a <= -1.7e-116)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (a <= 5.1e-235)
		tmp = 9.0 * ((x * (y / c_m)) / z);
	elseif (a <= 1.1e-81)
		tmp = (b / c_m) / z;
	elseif (a <= 4.5e-30)
		tmp = (9.0 * (y / c_m)) * (x / z);
	elseif (a <= 5.8e-17)
		tmp = b / (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[a, -1.7e-116], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e-235], N[(9.0 * N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-81], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 4.5e-30], N[(N[(9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-17], N[(b / 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 6 regimes

2. if a < -1.69999999999999996e-116

   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* 80.9%

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

      4. *-commutative 80.9%

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

      5. associate-+l- 80.9%

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

      6. associate-*l* 80.9%

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

      7. associate-*l* 77.0%

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

      8. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 46.3%

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

      1. *-commutative 46.3%

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

   7. Simplified 46.3%

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

   if -1.69999999999999996e-116 < a < 5.09999999999999993e-235

   1. Initial program 78.5%

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

      1. associate-+l- 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 88.7%

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

      4. *-commutative 88.7%

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

      5. associate-+l- 88.7%

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

      6. associate-*l* 88.7%

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

      7. associate-*l* 88.6%

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

      8. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. associate-/r* 48.7%

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

      2. associate-/l* 50.3%

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

   7. Simplified 50.3%

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

   if 5.09999999999999993e-235 < a < 1.1e-81

   1. Initial program 75.9%

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

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-+l- 78.8%

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

      6. associate-*l* 78.7%

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

      7. associate-*l* 78.7%

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

      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 b around inf 38.0%

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

      1. associate-/r* 49.9%

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

   7. Simplified 49.9%

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

   if 1.1e-81 < a < 4.49999999999999967e-30

   1. Initial program 78.1%

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

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r* 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-+l- 78.1%

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

      6. associate-*l* 78.2%

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

      7. associate-*l* 78.2%

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

      8. *-commutative 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. associate-*r* 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*r* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in x around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*r* 47.8%

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

   10. Simplified 47.8%

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

       1. times-frac 55.2%

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

       2. *-commutative 55.2%

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

       3. *-un-lft-identity 55.2%

          \[\leadsto \frac{x}{z} \cdot \frac{9 \cdot y}{\color{blue}{1 \cdot c}} \]

       4. times-frac 55.3%

          \[\leadsto \frac{x}{z} \cdot \color{blue}{\left(\frac{9}{1} \cdot \frac{y}{c}\right)} \]

       5. metadata-eval 55.3%

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

   12. Applied egg-rr 55.3%

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

   if 4.49999999999999967e-30 < a < 5.8000000000000006e-17

   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* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate-*l* 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 inf 66.8%

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

      1. *-commutative 66.8%

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

   7. Simplified 66.8%

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

   if 5.8000000000000006e-17 < a

   1. Initial program 70.2%

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

      1. associate-+l- 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.5%

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

      7. associate-*l* 68.3%

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

      8. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around 0 77.6%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Applied egg-rr 75.6%

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

   8. Taylor expanded in a around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. associate-*r* 51.6%

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

      3. associate-*l/ 66.1%

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

      4. associate-*r/ 66.1%

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

      5. associate-*l* 66.1%

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

   10. Simplified 66.1%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-116}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-235}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+185} \lor \neg \left(a \leq 1.2 \cdot 10^{+279}\right):\\ \;\;\;\;\frac{\frac{b}{c\_m} + -4 \cdot \left(\frac{z}{c\_m} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a 1.4e-6)
    (/ (+ b (* x (* 9.0 y))) (* c_m z))
    (if (or (<= a 5.1e+185) (not (<= a 1.2e+279)))
      (/ (+ (/ b c_m) (* -4.0 (* (/ z c_m) (* t a)))) 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 (a <= 1.4e-6) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if ((a <= 5.1e+185) || !(a <= 1.2e+279)) {
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / 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 (a <= 1.4d-6) then
        tmp = (b + (x * (9.0d0 * y))) / (c_m * z)
    else if ((a <= 5.1d+185) .or. (.not. (a <= 1.2d+279))) then
        tmp = ((b / c_m) + ((-4.0d0) * ((z / c_m) * (t * a)))) / 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 (a <= 1.4e-6) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if ((a <= 5.1e+185) || !(a <= 1.2e+279)) {
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / 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 a <= 1.4e-6:
		tmp = (b + (x * (9.0 * y))) / (c_m * z)
	elif (a <= 5.1e+185) or not (a <= 1.2e+279):
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / 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 (a <= 1.4e-6)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(c_m * z));
	elseif ((a <= 5.1e+185) || !(a <= 1.2e+279))
		tmp = Float64(Float64(Float64(b / c_m) + Float64(-4.0 * Float64(Float64(z / c_m) * Float64(t * a)))) / 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 (a <= 1.4e-6)
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	elseif ((a <= 5.1e+185) || ~((a <= 1.2e+279)))
		tmp = ((b / c_m) + (-4.0 * ((z / c_m) * (t * a)))) / 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[a, 1.4e-6], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5.1e+185], N[Not[LessEqual[a, 1.2e+279]], $MachinePrecision]], N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(-4.0 * N[(N[(z / c$95$m), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if a < 1.39999999999999994e-6

   1. Initial program 78.9%

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

      1. associate-+l- 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 83.1%

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

      4. *-commutative 83.1%

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

      5. associate-+l- 83.1%

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

      6. associate-*l* 83.1%

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

      7. associate-*l* 81.2%

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

      8. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. associate-*r* 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-*r* 65.6%

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

   7. Simplified 65.6%

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

   if 1.39999999999999994e-6 < a < 5.09999999999999996e185 or 1.2e279 < a

   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* 62.4%

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

      4. *-commutative 62.4%

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

      5. associate-+l- 62.4%

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

      6. associate-*l* 62.4%

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

      7. associate-*l* 65.0%

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

      8. *-commutative 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in z around 0 78.4%

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

      1. associate-/l* 78.5%

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

      2. associate-*r/ 78.4%

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

      3. associate-*r* 75.7%

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

   7. Applied egg-rr 75.7%

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

   8. Taylor expanded in x around 0 70.9%

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

   if 5.09999999999999996e185 < a < 1.2e279

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 65.1%

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

      4. *-commutative 65.1%

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

      5. associate-+l- 65.1%

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

      6. associate-*l* 65.1%

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

      7. associate-*l* 72.4%

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

      8. *-commutative 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around 0 72.3%

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

      1. associate-*r/ 72.2%

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

      2. *-commutative 72.2%

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

   7. Applied egg-rr 72.2%

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

   8. Taylor expanded in a around inf 66.1%

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

      1. associate-*r/ 66.1%

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

      2. associate-*r* 66.1%

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

      3. associate-*l/ 86.3%

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

      4. associate-*r/ 86.3%

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

      5. associate-*l* 86.3%

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

   10. Simplified 86.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+185} \lor \neg \left(a \leq 1.2 \cdot 10^{+279}\right):\\ \;\;\;\;\frac{\frac{b}{c} + -4 \cdot \left(\frac{z}{c} \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 9.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c\_m \cdot z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{b}{c\_m} + 9 \cdot \frac{x \cdot y}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a 9.6e-120)
    (/ (+ b (* x (* 9.0 y))) (* c_m z))
    (if (<= a 2.9e+24)
      (/ (+ (/ b c_m) (* 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 (a <= 9.6e-120) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if (a <= 2.9e+24) {
		tmp = ((b / c_m) + (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 (a <= 9.6d-120) then
        tmp = (b + (x * (9.0d0 * y))) / (c_m * z)
    else if (a <= 2.9d+24) then
        tmp = ((b / c_m) + (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 (a <= 9.6e-120) {
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	} else if (a <= 2.9e+24) {
		tmp = ((b / c_m) + (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 a <= 9.6e-120:
		tmp = (b + (x * (9.0 * y))) / (c_m * z)
	elif a <= 2.9e+24:
		tmp = ((b / c_m) + (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 (a <= 9.6e-120)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(c_m * z));
	elseif (a <= 2.9e+24)
		tmp = Float64(Float64(Float64(b / c_m) + Float64(9.0 * Float64(Float64(x * y) / 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 (a <= 9.6e-120)
		tmp = (b + (x * (9.0 * y))) / (c_m * z);
	elseif (a <= 2.9e+24)
		tmp = ((b / c_m) + (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[a, 9.6e-120], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+24], N[(N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if a < 9.5999999999999998e-120

   1. Initial program 78.9%

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

      1. associate-+l- 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r* 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* 81.7%

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

      8. *-commutative 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in x around inf 65.9%

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

      1. associate-*r* 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-*r* 65.9%

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

   7. Simplified 65.9%

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

   if 9.5999999999999998e-120 < a < 2.89999999999999979e24

   1. Initial program 79.4%

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

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

      6. associate-*l* 79.4%

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

      7. associate-*l* 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 z around 0 78.4%

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

      1. fma-define 78.4%

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

      2. associate-/l* 72.3%

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

      3. associate-/l* 75.5%

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

      4. fma-define 75.5%

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

      5. associate-/l* 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in a around 0 72.5%

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

   if 2.89999999999999979e24 < a

   1. Initial program 67.3%

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

      1. associate-+l- 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*r* 60.8%

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

      4. *-commutative 60.8%

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

      5. associate-+l- 60.8%

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

      6. associate-*l* 60.8%

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

      7. associate-*l* 65.1%

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

      8. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in z around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. *-commutative 74.1%

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

   7. Applied egg-rr 74.1%

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

   8. Taylor expanded in a around inf 57.0%

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

      1. associate-*r/ 57.0%

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

      2. associate-*r* 57.0%

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

      3. associate-*l/ 73.8%

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

      4. associate-*r/ 73.8%

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

      5. associate-*l* 73.7%

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

   10. Simplified 73.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.6 \cdot 10^{-120}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{b}{c} + 9 \cdot \frac{x \cdot y}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-70}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-235}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a -9.2e-70)
    (* -4.0 (/ (* t a) c_m))
    (if (<= a 9e-235)
      (* 9.0 (* x (/ y (* c_m z))))
      (if (<= a 1.2e-19) (/ (/ b 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 (a <= -9.2e-70) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 9e-235) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (a <= 1.2e-19) {
		tmp = (b / 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 (a <= (-9.2d-70)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (a <= 9d-235) then
        tmp = 9.0d0 * (x * (y / (c_m * z)))
    else if (a <= 1.2d-19) then
        tmp = (b / 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 (a <= -9.2e-70) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 9e-235) {
		tmp = 9.0 * (x * (y / (c_m * z)));
	} else if (a <= 1.2e-19) {
		tmp = (b / 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 a <= -9.2e-70:
		tmp = -4.0 * ((t * a) / c_m)
	elif a <= 9e-235:
		tmp = 9.0 * (x * (y / (c_m * z)))
	elif a <= 1.2e-19:
		tmp = (b / 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 (a <= -9.2e-70)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (a <= 9e-235)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))));
	elseif (a <= 1.2e-19)
		tmp = Float64(Float64(b / 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 (a <= -9.2e-70)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (a <= 9e-235)
		tmp = 9.0 * (x * (y / (c_m * z)));
	elseif (a <= 1.2e-19)
		tmp = (b / 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[a, -9.2e-70], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-235], N[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-19], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if a < -9.20000000000000002e-70

   1. Initial program 80.6%

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

      1. associate-+l- 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-+l- 82.6%

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

      6. associate-*l* 82.6%

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

      7. associate-*l* 78.1%

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

      8. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in z around inf 46.9%

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

      1. *-commutative 46.9%

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

   7. Simplified 46.9%

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

   if -9.20000000000000002e-70 < a < 8.9999999999999996e-235

   1. Initial program 76.9%

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

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 85.4%

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

      4. *-commutative 85.4%

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

      5. associate-+l- 85.4%

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

      6. associate-*l* 85.4%

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

      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. Taylor expanded in x around inf 46.5%

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

      1. associate-/l* 49.2%

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

      2. associate-/r* 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in x around 0 46.5%

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

      1. associate-/l* 49.2%

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

   10. Simplified 49.2%

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

   if 8.9999999999999996e-235 < a < 1.20000000000000011e-19

   1. Initial program 78.0%

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

      1. associate-+l- 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-+l- 79.9%

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

      6. associate-*l* 79.9%

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

      7. associate-*l* 79.9%

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

      8. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in b around inf 38.4%

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

      1. associate-/r* 46.5%

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

   7. Simplified 46.5%

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

   if 1.20000000000000011e-19 < a

   1. Initial program 70.2%

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

      1. associate-+l- 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.5%

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

      7. associate-*l* 68.3%

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

      8. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around 0 77.6%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Applied egg-rr 75.6%

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

   8. Taylor expanded in a around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. associate-*r* 51.6%

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

      3. associate-*l/ 66.1%

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

      4. associate-*r/ 66.1%

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

      5. associate-*l* 66.1%

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

   10. Simplified 66.1%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-70}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-235}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-162} \lor \neg \left(a \leq 7.5 \cdot 10^{-17}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a -4.8e-162) (not (<= a 7.5e-17)))
    (* -4.0 (* t (/ a 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 ((a <= -4.8e-162) || !(a <= 7.5e-17)) {
		tmp = -4.0 * (t * (a / 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 ((a <= (-4.8d-162)) .or. (.not. (a <= 7.5d-17))) then
        tmp = (-4.0d0) * (t * (a / 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 ((a <= -4.8e-162) || !(a <= 7.5e-17)) {
		tmp = -4.0 * (t * (a / 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 (a <= -4.8e-162) or not (a <= 7.5e-17):
		tmp = -4.0 * (t * (a / 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 ((a <= -4.8e-162) || !(a <= 7.5e-17))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	else
		tmp = Float64(Float64(b / 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 ((a <= -4.8e-162) || ~((a <= 7.5e-17)))
		tmp = -4.0 * (t * (a / 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[Or[LessEqual[a, -4.8e-162], N[Not[LessEqual[a, 7.5e-17]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000004e-162 or 7.49999999999999984e-17 < a

   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* 76.2%

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

      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* 75.1%

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

      8. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around 0 76.3%

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

      1. associate-*r/ 77.4%

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

      2. *-commutative 77.4%

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

   7. Applied egg-rr 77.4%

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

   8. Taylor expanded in a around inf 48.7%

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

      1. associate-*r/ 48.7%

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

      2. associate-*r* 48.7%

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

      3. associate-*l/ 54.7%

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

      4. associate-*r/ 54.7%

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

      5. associate-*l* 54.6%

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

   10. Simplified 54.6%

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

   if -4.8000000000000004e-162 < a < 7.49999999999999984e-17

   1. Initial program 77.9%

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

      1. associate-+l- 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

      6. associate-*l* 84.1%

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

      7. associate-*l* 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 b around inf 42.8%

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

      1. associate-/r* 44.9%

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

   7. Simplified 44.9%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-162} \lor \neg \left(a \leq 7.5 \cdot 10^{-17}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a -4.4e-162)
    (* a (/ (* t -4.0) c_m))
    (if (<= a 5.4e-16) (/ (/ b 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 (a <= -4.4e-162) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 5.4e-16) {
		tmp = (b / 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 (a <= (-4.4d-162)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (a <= 5.4d-16) then
        tmp = (b / 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 (a <= -4.4e-162) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (a <= 5.4e-16) {
		tmp = (b / 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 a <= -4.4e-162:
		tmp = a * ((t * -4.0) / c_m)
	elif a <= 5.4e-16:
		tmp = (b / 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 (a <= -4.4e-162)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (a <= 5.4e-16)
		tmp = Float64(Float64(b / 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 (a <= -4.4e-162)
		tmp = a * ((t * -4.0) / c_m);
	elseif (a <= 5.4e-16)
		tmp = (b / 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[a, -4.4e-162], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-16], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if a < -4.3999999999999998e-162

   1. Initial program 79.4%

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

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-+l- 81.9%

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

      6. associate-*l* 81.9%

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

      7. associate-*l* 78.4%

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

      8. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-/l* 46.4%

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

      3. associate-*r* 46.4%

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

      4. associate-*l/ 46.4%

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

   7. Simplified 46.4%

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

   if -4.3999999999999998e-162 < a < 5.39999999999999999e-16

   1. Initial program 77.9%

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

      1. associate-+l- 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

      6. associate-*l* 84.1%

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

      7. associate-*l* 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 b around inf 42.8%

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

      1. associate-/r* 44.9%

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

   7. Simplified 44.9%

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

   if 5.39999999999999999e-16 < a

   1. Initial program 70.2%

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

      1. associate-+l- 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.5%

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

      7. associate-*l* 68.3%

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

      8. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around 0 77.6%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

   7. Applied egg-rr 75.6%

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

   8. Taylor expanded in a around inf 51.6%

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

      1. associate-*r/ 51.6%

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

      2. associate-*r* 51.6%

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

      3. associate-*l/ 66.1%

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

      4. associate-*r/ 66.1%

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

      5. associate-*l* 66.1%

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

   10. Simplified 66.1%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-162}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a -4.8e-162)
    (* -4.0 (/ (* t a) c_m))
    (if (<= a 6e-19) (/ (/ b 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 (a <= -4.8e-162) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 6e-19) {
		tmp = (b / 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 (a <= (-4.8d-162)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (a <= 6d-19) then
        tmp = (b / 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 (a <= -4.8e-162) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 6e-19) {
		tmp = (b / 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 a <= -4.8e-162:
		tmp = -4.0 * ((t * a) / c_m)
	elif a <= 6e-19:
		tmp = (b / 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 (a <= -4.8e-162)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (a <= 6e-19)
		tmp = Float64(Float64(b / 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 (a <= -4.8e-162)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (a <= 6e-19)
		tmp = (b / 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[a, -4.8e-162], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-19], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if a < -4.8000000000000004e-162

   1. Initial program 79.4%

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

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-*r* 81.9%

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

      4. *-commutative 81.9%

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

      5. associate-+l- 81.9%

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

      6. associate-*l* 81.9%

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

      7. associate-*l* 78.4%

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

      8. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 47.3%

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

      1. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if -4.8000000000000004e-162 < a < 5.99999999999999985e-19

   1. Initial program 77.9%

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

      1. associate-+l- 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

      6. associate-*l* 84.1%

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

      7. associate-*l* 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 b around inf 42.8%

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

      1. associate-/r* 44.9%

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

   7. Simplified 44.9%

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

   if 5.99999999999999985e-19 < a

   1. Initial program 70.2%

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

      1. associate-+l- 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. associate-*l* 64.5%

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

      7. associate-*l* 68.3%

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

      8. *-commutative 68.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 77.6%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 75.6%

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{c}\right)} + \frac{b}{c}\right)}{z} \]

      2. *-commutative 75.6%

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(\frac{y}{c} \cdot x\right)} + \frac{b}{c}\right)}{z} \]

   7. Applied egg-rr 75.6%

      \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(\frac{y}{c} \cdot x\right)} + \frac{b}{c}\right)}{z} \]

   8. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*r/ 51.6%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 51.6%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 66.1%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. associate-*r/ 66.1%

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \cdot t \]

      5. associate-*l* 66.1%

         \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   10. Simplified 66.1%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-162}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a 2.9e+24)
    (/ (+ 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 (a <= 2.9e+24) {
		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 (a <= 2.9d+24) 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 (a <= 2.9e+24) {
		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 a <= 2.9e+24:
		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 (a <= 2.9e+24)
		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 (a <= 2.9e+24)
		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[a, 2.9e+24], 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 2 regimes

2. if a < 2.89999999999999979e24

   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* 83.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.1%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if 2.89999999999999979e24 < a

   1. Initial program 67.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 67.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 67.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 60.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 65.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 65.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 74.1%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.1%

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{c}\right)} + \frac{b}{c}\right)}{z} \]

      2. *-commutative 74.1%

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(\frac{y}{c} \cdot x\right)} + \frac{b}{c}\right)}{z} \]

   7. Applied egg-rr 74.1%

      \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(\frac{y}{c} \cdot x\right)} + \frac{b}{c}\right)}{z} \]

   8. Taylor expanded in a around inf 57.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*r/ 57.0%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 57.0%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 73.8%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. associate-*r/ 73.8%

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \cdot t \]

      5. associate-*l* 73.7%

         \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   10. Simplified 73.7%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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 (<= a 2.9e+24)
    (/ (+ b (* x (* 9.0 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 (a <= 2.9e+24) {
		tmp = (b + (x * (9.0 * 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 (a <= 2.9d+24) then
        tmp = (b + (x * (9.0d0 * 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 (a <= 2.9e+24) {
		tmp = (b + (x * (9.0 * 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 a <= 2.9e+24:
		tmp = (b + (x * (9.0 * 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 (a <= 2.9e+24)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * 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 (a <= 2.9e+24)
		tmp = (b + (x * (9.0 * 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[a, 2.9e+24], N[(N[(b + N[(x * N[(9.0 * 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 2 regimes

2. if a < 2.89999999999999979e24

   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* 83.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 81.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.1%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 66.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 66.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 66.1%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 66.1%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 2.89999999999999979e24 < a

   1. Initial program 67.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 67.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 67.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 60.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 60.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 60.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 65.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 65.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 65.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 74.1%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.1%

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(x \cdot \frac{y}{c}\right)} + \frac{b}{c}\right)}{z} \]

      2. *-commutative 74.1%

         \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(\frac{y}{c} \cdot x\right)} + \frac{b}{c}\right)}{z} \]

   7. Applied egg-rr 74.1%

      \[\leadsto \frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \color{blue}{\left(\frac{y}{c} \cdot x\right)} + \frac{b}{c}\right)}{z} \]

   8. Taylor expanded in a around inf 57.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   9. Step-by-step derivation

      1. associate-*r/ 57.0%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. associate-*r* 57.0%

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

      3. associate-*l/ 73.8%

         \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

      4. associate-*r/ 73.8%

         \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \cdot t \]

      5. associate-*l* 73.7%

         \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   10. Simplified 73.7%

       \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.9% 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 #s(literal 1 binary64) 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 76.9%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 76.9%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 76.9%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.2%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 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* 78.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 78.5%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 36.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 36.1%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 36.1%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 36.1%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Alternative 20: 34.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{\frac{b}{c\_m}}{z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) 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(Float64(b / 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[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.9%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 76.9%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 76.9%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.2%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 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* 78.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 78.5%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 78.5%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 36.1%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. associate-/r* 37.2%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

7. Simplified 37.2%

   \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

8. Final simplification 37.2%

   \[\leadsto \frac{\frac{b}{c}}{z} \]
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 2024071 
(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)))