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

Percentage Accurate: 79.6% → 88.8%

Time: 21.8s

Alternatives: 21

Speedup: 0.7×

• 37.3% 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: 79.6% 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: 88.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -2e-234)
      t_1
      (if (<= t_1 0.0)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)))
         z)
        (if (<= t_1 INFINITY)
          (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* z c_m))
          (- (* -4.0 (* t (/ a 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 t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-234) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (z * c_m);
	} else {
		tmp = (-4.0 * (t * (a / 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)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -2e-234)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) - Float64(-9.0 * Float64(x * Float64(Float64(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_] := Block[{t$95$1 = 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$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-234], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $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)) < -1.9999999999999999e-234

   1. Initial program 91.2%

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

   if -1.9999999999999999e-234 < (/.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)) < 0.0

   1. Initial program 46.1%

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

      1. +-commutative 46.1%

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

      2. associate-+r- 46.1%

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

      3. *-commutative 46.1%

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

      4. associate-*r* 39.9%

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

      5. *-commutative 39.9%

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

      6. associate-+r- 39.9%

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

      7. +-commutative 39.9%

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

      8. associate-*l* 39.9%

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

      9. associate-*l* 46.1%

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

      10. *-commutative 46.1%

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

   3. Simplified 46.1%

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

   5. Taylor expanded in z around 0 99.7%

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

   if 0.0 < (/.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)) < +inf.0

   1. Initial program 94.9%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   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. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 5.6%

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

      5. *-commutative 5.6%

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

      6. associate-+r- 5.6%

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

      7. +-commutative 5.6%

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

      8. associate-*l* 5.6%

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

      9. associate-*l* 5.6%

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

      10. *-commutative 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in y around inf 22.4%

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

   6. Taylor expanded in z around -inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-/l* 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-/l* 83.6%

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

      7. mul-1-neg 83.6%

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

      8. unsub-neg 83.6%

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

      9. associate-*r/ 83.9%

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

      10. *-commutative 83.9%

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

      11. associate-/l* 84.0%

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

      12. associate-/r* 84.0%

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

   8. Simplified 84.0%

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

   9. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 58.8%

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

       2. associate-/r* 86.2%

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

   11. Simplified 86.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-234}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-196}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) - \frac{\left(x \cdot y\right) \cdot -9}{z}}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -2e-234)
      t_1
      (if (<= t_1 2e-196)
        (/ (- (* -4.0 (* t a)) (/ (* (* x y) -9.0) z)) c_m)
        (if (<= t_1 INFINITY)
          t_1
          (- (* -4.0 (* t (/ a 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 t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-234) {
		tmp = t_1;
	} else if (t_1 <= 2e-196) {
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)));
	}
	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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-234) {
		tmp = t_1;
	} else if (t_1 <= 2e-196) {
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) - (-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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	tmp = 0
	if t_1 <= -2e-234:
		tmp = t_1
	elif t_1 <= 2e-196:
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (-4.0 * (t * (a / 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)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -2e-234)
		tmp = t_1;
	elseif (t_1 <= 2e-196)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) - Float64(Float64(Float64(x * y) * -9.0) / z)) / c_m);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) - Float64(-9.0 * Float64(x * Float64(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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -2e-234)
		tmp = t_1;
	elseif (t_1 <= 2e-196)
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (-4.0 * (t * (a / c_m))) - (-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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-234], t$95$1, If[LessEqual[t$95$1, 2e-196], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * y), $MachinePrecision] * -9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 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)) < -1.9999999999999999e-234 or 2.0000000000000001e-196 < (/.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 93.0%

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

   if -1.9999999999999999e-234 < (/.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)) < 2.0000000000000001e-196

   1. Initial program 51.8%

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

      1. +-commutative 51.8%

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

      2. associate-+r- 51.8%

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

      3. *-commutative 51.8%

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

      4. associate-*r* 46.3%

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

      5. *-commutative 46.3%

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

      6. associate-+r- 46.3%

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

      7. +-commutative 46.3%

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

      8. associate-*l* 46.1%

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

      9. associate-*l* 51.6%

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

      10. *-commutative 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in y around inf 74.9%

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

   6. Taylor expanded in z around -inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-/l* 89.5%

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

      5. *-commutative 89.5%

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

      6. associate-/l* 84.5%

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

      7. mul-1-neg 84.5%

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

      8. unsub-neg 84.5%

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

      9. associate-*r/ 84.6%

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

      10. *-commutative 84.6%

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

      11. associate-/l* 84.5%

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

      12. associate-/r* 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in c around 0 84.2%

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

   10. Taylor expanded in y around inf 79.9%

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

       1. *-commutative 79.9%

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

   12. Simplified 79.9%

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

   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. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 5.6%

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

      5. *-commutative 5.6%

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

      6. associate-+r- 5.6%

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

      7. +-commutative 5.6%

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

      8. associate-*l* 5.6%

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

      9. associate-*l* 5.6%

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

      10. *-commutative 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in y around inf 22.4%

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

   6. Taylor expanded in z around -inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-/l* 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-/l* 83.6%

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

      7. mul-1-neg 83.6%

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

      8. unsub-neg 83.6%

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

      9. associate-*r/ 83.9%

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

      10. *-commutative 83.9%

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

      11. associate-/l* 84.0%

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

      12. associate-/r* 84.0%

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

   8. Simplified 84.0%

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

   9. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 58.8%

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

       2. associate-/r* 86.2%

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

   11. Simplified 86.2%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-234}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{-196}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) - \frac{\left(x \cdot y\right) \cdot -9}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -2e-71)
      t_1
      (if (<= t_1 2e-91)
        (/ (+ (* -4.0 (* t a)) (/ (* y (- (/ b y) (* x -9.0))) z)) c_m)
        (if (<= t_1 INFINITY)
          t_1
          (- (* -4.0 (* t (/ a 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 t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-71) {
		tmp = t_1;
	} else if (t_1 <= 2e-91) {
		tmp = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)));
	}
	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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-71) {
		tmp = t_1;
	} else if (t_1 <= 2e-91) {
		tmp = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) - (-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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	tmp = 0
	if t_1 <= -2e-71:
		tmp = t_1
	elif t_1 <= 2e-91:
		tmp = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (-4.0 * (t * (a / 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)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -2e-71)
		tmp = t_1;
	elseif (t_1 <= 2e-91)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(y * Float64(Float64(b / y) - Float64(x * -9.0))) / z)) / c_m);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) - Float64(-9.0 * Float64(x * Float64(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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -2e-71)
		tmp = t_1;
	elseif (t_1 <= 2e-91)
		tmp = ((-4.0 * (t * a)) + ((y * ((b / y) - (x * -9.0))) / z)) / c_m;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (-4.0 * (t * (a / c_m))) - (-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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-71], t$95$1, If[LessEqual[t$95$1, 2e-91], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(b / y), $MachinePrecision] - N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 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)) < -1.9999999999999998e-71 or 2.00000000000000004e-91 < (/.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 93.0%

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

   if -1.9999999999999998e-71 < (/.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)) < 2.00000000000000004e-91

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-+r- 69.2%

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

      3. *-commutative 69.2%

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

      4. associate-*r* 66.9%

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

      5. *-commutative 66.9%

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

      6. associate-+r- 66.9%

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

      7. +-commutative 66.9%

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

      8. associate-*l* 66.8%

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

      9. associate-*l* 72.1%

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

      10. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around inf 64.8%

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

   6. Taylor expanded in z around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. *-commutative 76.4%

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

      4. associate-/l* 74.4%

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

      5. *-commutative 74.4%

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

      6. associate-/l* 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

      9. associate-*r/ 77.3%

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

      10. *-commutative 77.3%

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

      11. associate-/l* 77.2%

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

      12. associate-/r* 71.7%

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

   8. Simplified 71.7%

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

   9. Taylor expanded in c around 0 90.8%

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

   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. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 5.6%

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

      5. *-commutative 5.6%

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

      6. associate-+r- 5.6%

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

      7. +-commutative 5.6%

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

      8. associate-*l* 5.6%

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

      9. associate-*l* 5.6%

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

      10. *-commutative 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in y around inf 22.4%

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

   6. Taylor expanded in z around -inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-/l* 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-/l* 83.6%

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

      7. mul-1-neg 83.6%

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

      8. unsub-neg 83.6%

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

      9. associate-*r/ 83.9%

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

      10. *-commutative 83.9%

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

      11. associate-/l* 84.0%

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

      12. associate-/r* 84.0%

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

   8. Simplified 84.0%

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

   9. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 58.8%

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

       2. associate-/r* 86.2%

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

   11. Simplified 86.2%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-71}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{-91}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y \cdot \left(\frac{b}{y} - x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-174}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -2e-234)
      t_1
      (if (<= t_1 2e-174)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)))
         z)
        (if (<= t_1 INFINITY)
          t_1
          (- (* -4.0 (* t (/ a 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 t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-234) {
		tmp = t_1;
	} else if (t_1 <= 2e-174) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)));
	}
	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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	double tmp;
	if (t_1 <= -2e-234) {
		tmp = t_1;
	} else if (t_1 <= 2e-174) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) - (-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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m)
	tmp = 0
	if t_1 <= -2e-234:
		tmp = t_1
	elif t_1 <= 2e-174:
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (-4.0 * (t * (a / 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)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -2e-234)
		tmp = t_1;
	elseif (t_1 <= 2e-174)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m))) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) - Float64(-9.0 * Float64(x * Float64(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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -2e-234)
		tmp = t_1;
	elseif (t_1 <= 2e-174)
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((9.0 * ((x * y) / c_m)) + (b / c_m))) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (-4.0 * (t * (a / c_m))) - (-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[(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$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-234], t$95$1, If[LessEqual[t$95$1, 2e-174], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 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)) < -1.9999999999999999e-234 or 2e-174 < (/.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 93.0%

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

   if -1.9999999999999999e-234 < (/.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)) < 2e-174

   1. Initial program 54.2%

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

      1. +-commutative 54.2%

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

      2. associate-+r- 54.2%

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

      3. *-commutative 54.2%

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

      4. associate-*r* 45.6%

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

      5. *-commutative 45.6%

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

      6. associate-+r- 45.6%

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

      7. +-commutative 45.6%

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

      8. associate-*l* 45.5%

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

      9. associate-*l* 54.0%

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

      10. *-commutative 54.0%

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

   3. Simplified 54.0%

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

   5. Taylor expanded in z around 0 95.1%

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

   if +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. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 5.6%

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

      5. *-commutative 5.6%

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

      6. associate-+r- 5.6%

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

      7. +-commutative 5.6%

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

      8. associate-*l* 5.6%

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

      9. associate-*l* 5.6%

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

      10. *-commutative 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in y around inf 22.4%

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

   6. Taylor expanded in z around -inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-/l* 79.1%

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

      5. *-commutative 79.1%

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

      6. associate-/l* 83.6%

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

      7. mul-1-neg 83.6%

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

      8. unsub-neg 83.6%

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

      9. associate-*r/ 83.9%

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

      10. *-commutative 83.9%

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

      11. associate-/l* 84.0%

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

      12. associate-/r* 84.0%

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

   8. Simplified 84.0%

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

   9. Taylor expanded in x around inf 48.4%

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

       1. associate-/l* 58.8%

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

       2. associate-/r* 86.2%

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

   11. Simplified 86.2%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-234}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{-174}:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c\_m}\\ t_2 := 9 \cdot \frac{x \cdot y}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* -4.0 (/ (* t a) c_m))) (t_2 (* 9.0 (/ (* x y) (* z c_m)))))
   (*
    c_s
    (if (<= z -1.25e+111)
      (* -4.0 (* t (/ a c_m)))
      (if (<= z -2.25e+62)
        t_2
        (if (<= z -4.1e-60)
          t_1
          (if (<= z -1.05e-220)
            (* b (/ 1.0 (* z c_m)))
            (if (<= z 1.02e-198)
              t_2
              (if (<= z 3.4e-34)
                (/ b (* z c_m))
                (if (<= z 0.36) t_2 t_1))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * ((t * a) / c_m);
	double t_2 = 9.0 * ((x * y) / (z * c_m));
	double tmp;
	if (z <= -1.25e+111) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -2.25e+62) {
		tmp = t_2;
	} else if (z <= -4.1e-60) {
		tmp = t_1;
	} else if (z <= -1.05e-220) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 1.02e-198) {
		tmp = t_2;
	} else if (z <= 3.4e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) / c_m)
    t_2 = 9.0d0 * ((x * y) / (z * c_m))
    if (z <= (-1.25d+111)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-2.25d+62)) then
        tmp = t_2
    else if (z <= (-4.1d-60)) then
        tmp = t_1
    else if (z <= (-1.05d-220)) then
        tmp = b * (1.0d0 / (z * c_m))
    else if (z <= 1.02d-198) then
        tmp = t_2
    else if (z <= 3.4d-34) then
        tmp = b / (z * c_m)
    else if (z <= 0.36d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * ((t * a) / c_m);
	double t_2 = 9.0 * ((x * y) / (z * c_m));
	double tmp;
	if (z <= -1.25e+111) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -2.25e+62) {
		tmp = t_2;
	} else if (z <= -4.1e-60) {
		tmp = t_1;
	} else if (z <= -1.05e-220) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 1.02e-198) {
		tmp = t_2;
	} else if (z <= 3.4e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * ((t * a) / c_m)
	t_2 = 9.0 * ((x * y) / (z * c_m))
	tmp = 0
	if z <= -1.25e+111:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -2.25e+62:
		tmp = t_2
	elif z <= -4.1e-60:
		tmp = t_1
	elif z <= -1.05e-220:
		tmp = b * (1.0 / (z * c_m))
	elif z <= 1.02e-198:
		tmp = t_2
	elif z <= 3.4e-34:
		tmp = b / (z * c_m)
	elif z <= 0.36:
		tmp = t_2
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) / c_m))
	t_2 = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c_m)))
	tmp = 0.0
	if (z <= -1.25e+111)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -2.25e+62)
		tmp = t_2;
	elseif (z <= -4.1e-60)
		tmp = t_1;
	elseif (z <= -1.05e-220)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	elseif (z <= 1.02e-198)
		tmp = t_2;
	elseif (z <= 3.4e-34)
		tmp = Float64(b / Float64(z * c_m));
	elseif (z <= 0.36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * ((t * a) / c_m);
	t_2 = 9.0 * ((x * y) / (z * c_m));
	tmp = 0.0;
	if (z <= -1.25e+111)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -2.25e+62)
		tmp = t_2;
	elseif (z <= -4.1e-60)
		tmp = t_1;
	elseif (z <= -1.05e-220)
		tmp = b * (1.0 / (z * c_m));
	elseif (z <= 1.02e-198)
		tmp = t_2;
	elseif (z <= 3.4e-34)
		tmp = b / (z * c_m);
	elseif (z <= 0.36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.25e+111], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e+62], t$95$2, If[LessEqual[z, -4.1e-60], t$95$1, If[LessEqual[z, -1.05e-220], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-198], t$95$2, If[LessEqual[z, 3.4e-34], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.36], t$95$2, t$95$1]]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2499999999999999e111

   1. Initial program 57.3%

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

      1. +-commutative 57.3%

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

      2. associate-+r- 57.3%

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

      3. *-commutative 57.3%

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

      4. associate-*r* 57.7%

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

      5. *-commutative 57.7%

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

      6. associate-+r- 57.7%

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

      7. +-commutative 57.7%

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

      8. associate-*l* 57.7%

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

      9. associate-*l* 59.9%

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

      10. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in z around 0 57.2%

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

   6. Taylor expanded in a around inf 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-/l* 61.9%

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

   8. Simplified 61.9%

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

   if -1.2499999999999999e111 < z < -2.24999999999999999e62 or -1.04999999999999996e-220 < z < 1.01999999999999997e-198 or 3.4000000000000001e-34 < z < 0.35999999999999999

   1. Initial program 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-+r- 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*r* 92.4%

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

      5. *-commutative 92.4%

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

      6. associate-+r- 92.4%

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

      7. +-commutative 92.4%

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

      8. associate-*l* 92.4%

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

      9. associate-*l* 90.8%

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

      10. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 66.5%

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

   if -2.24999999999999999e62 < z < -4.10000000000000013e-60 or 0.35999999999999999 < z

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-+r- 68.2%

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

      3. *-commutative 68.2%

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

      4. associate-*r* 69.7%

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

      5. *-commutative 69.7%

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

      6. associate-+r- 69.7%

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

      7. +-commutative 69.7%

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

      8. associate-*l* 69.8%

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

      9. associate-*l* 74.4%

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

      10. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in z around inf 62.2%

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

   if -4.10000000000000013e-60 < z < -1.04999999999999996e-220

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-+r- 94.6%

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

      7. +-commutative 94.6%

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

      8. associate-*l* 94.6%

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

      9. associate-*l* 90.2%

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

      10. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

      1. div-inv 64.4%

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

   9. Applied egg-rr 64.4%

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

   if 1.01999999999999997e-198 < z < 3.4000000000000001e-34

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*r* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-+r- 97.5%

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

      7. +-commutative 97.5%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 95.0%

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

      10. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+62}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-198}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z \cdot c\_m}\\ t_2 := -4 \cdot \frac{t \cdot a}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{\frac{9 \cdot y}{c\_m}}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 9:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

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) (* z c_m)))) (t_2 (* -4.0 (/ (* t a) c_m))))
   (*
    c_s
    (if (<= z -1.85e+141)
      (* -4.0 (* t (/ a c_m)))
      (if (<= z -1.45e+41)
        (* x (/ (/ (* 9.0 y) c_m) z))
        (if (<= z -7e-61)
          t_2
          (if (<= z -1.95e-222)
            (* b (/ 1.0 (* z c_m)))
            (if (<= z 4.4e-198)
              t_1
              (if (<= z 3.6e-34)
                (/ b (* z c_m))
                (if (<= z 9.0) t_1 t_2))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x * y) / (z * c_m));
	double t_2 = -4.0 * ((t * a) / c_m);
	double tmp;
	if (z <= -1.85e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.45e+41) {
		tmp = x * (((9.0 * y) / c_m) / z);
	} else if (z <= -7e-61) {
		tmp = t_2;
	} else if (z <= -1.95e-222) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 4.4e-198) {
		tmp = t_1;
	} else if (z <= 3.6e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 9.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((x * y) / (z * c_m))
    t_2 = (-4.0d0) * ((t * a) / c_m)
    if (z <= (-1.85d+141)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.45d+41)) then
        tmp = x * (((9.0d0 * y) / c_m) / z)
    else if (z <= (-7d-61)) then
        tmp = t_2
    else if (z <= (-1.95d-222)) then
        tmp = b * (1.0d0 / (z * c_m))
    else if (z <= 4.4d-198) then
        tmp = t_1
    else if (z <= 3.6d-34) then
        tmp = b / (z * c_m)
    else if (z <= 9.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x * y) / (z * c_m));
	double t_2 = -4.0 * ((t * a) / c_m);
	double tmp;
	if (z <= -1.85e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.45e+41) {
		tmp = x * (((9.0 * y) / c_m) / z);
	} else if (z <= -7e-61) {
		tmp = t_2;
	} else if (z <= -1.95e-222) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 4.4e-198) {
		tmp = t_1;
	} else if (z <= 3.6e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 9.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((x * y) / (z * c_m))
	t_2 = -4.0 * ((t * a) / c_m)
	tmp = 0
	if z <= -1.85e+141:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.45e+41:
		tmp = x * (((9.0 * y) / c_m) / z)
	elif z <= -7e-61:
		tmp = t_2
	elif z <= -1.95e-222:
		tmp = b * (1.0 / (z * c_m))
	elif z <= 4.4e-198:
		tmp = t_1
	elif z <= 3.6e-34:
		tmp = b / (z * c_m)
	elif z <= 9.0:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c_m)))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) / c_m))
	tmp = 0.0
	if (z <= -1.85e+141)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.45e+41)
		tmp = Float64(x * Float64(Float64(Float64(9.0 * y) / c_m) / z));
	elseif (z <= -7e-61)
		tmp = t_2;
	elseif (z <= -1.95e-222)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	elseif (z <= 4.4e-198)
		tmp = t_1;
	elseif (z <= 3.6e-34)
		tmp = Float64(b / Float64(z * c_m));
	elseif (z <= 9.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((x * y) / (z * c_m));
	t_2 = -4.0 * ((t * a) / c_m);
	tmp = 0.0;
	if (z <= -1.85e+141)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.45e+41)
		tmp = x * (((9.0 * y) / c_m) / z);
	elseif (z <= -7e-61)
		tmp = t_2;
	elseif (z <= -1.95e-222)
		tmp = b * (1.0 / (z * c_m));
	elseif (z <= 4.4e-198)
		tmp = t_1;
	elseif (z <= 3.6e-34)
		tmp = b / (z * c_m);
	elseif (z <= 9.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.85e+141], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e+41], N[(x * N[(N[(N[(9.0 * y), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-61], t$95$2, If[LessEqual[z, -1.95e-222], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-198], t$95$1, If[LessEqual[z, 3.6e-34], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.0], t$95$1, t$95$2]]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8500000000000001e141

   1. Initial program 51.7%

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

      1. +-commutative 51.7%

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

      2. associate-+r- 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*r* 52.1%

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

      5. *-commutative 52.1%

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

      6. associate-+r- 52.1%

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

      7. +-commutative 52.1%

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

      8. associate-*l* 52.1%

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

      9. associate-*l* 54.8%

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

      10. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around 0 51.7%

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

   6. Taylor expanded in a around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if -1.8500000000000001e141 < z < -1.44999999999999994e41

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r- 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*r* 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-+r- 70.0%

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

      7. +-commutative 70.0%

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

      8. associate-*l* 69.9%

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

      9. associate-*l* 74.1%

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

      10. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in y around inf 66.2%

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

   6. Taylor expanded in z around -inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. associate-/l* 86.9%

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

      5. *-commutative 86.9%

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

      6. associate-/l* 91.6%

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

      7. mul-1-neg 91.6%

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

      8. unsub-neg 91.6%

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

      9. associate-*r/ 91.6%

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

      10. *-commutative 91.6%

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

      11. associate-/l* 91.7%

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

      12. associate-/r* 87.2%

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

   8. Simplified 87.2%

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

   9. Taylor expanded in x around inf 47.6%

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

       1. *-commutative 47.6%

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

       2. associate-/l* 41.3%

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

       3. associate-*r* 41.3%

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

       4. associate-/r* 49.7%

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

       5. associate-*l/ 49.5%

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

       6. associate-*l/ 49.6%

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

   11. Simplified 49.6%

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

   if -1.44999999999999994e41 < z < -7.0000000000000006e-61 or 9 < z

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-+r- 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*r* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-+r- 71.4%

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

      7. +-commutative 71.4%

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

      8. associate-*l* 71.5%

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

      9. associate-*l* 76.4%

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

      10. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -7.0000000000000006e-61 < z < -1.95e-222

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-+r- 94.6%

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

      7. +-commutative 94.6%

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

      8. associate-*l* 94.6%

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

      9. associate-*l* 90.2%

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

      10. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

      1. div-inv 64.4%

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

   9. Applied egg-rr 64.4%

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

   if -1.95e-222 < z < 4.4000000000000001e-198 or 3.60000000000000008e-34 < z < 9

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+r- 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*r* 98.6%

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

      5. *-commutative 98.6%

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

      6. associate-+r- 98.6%

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

      7. +-commutative 98.6%

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

      8. associate-*l* 98.6%

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

      9. associate-*l* 94.6%

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

      10. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 68.4%

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

   if 4.4000000000000001e-198 < z < 3.60000000000000008e-34

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*r* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-+r- 97.5%

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

      7. +-commutative 97.5%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 95.0%

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

      10. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{\frac{9 \cdot y}{c}}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-61}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-198}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 9:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{c\_m} \cdot \frac{9}{z}\\ t_2 := -4 \cdot \frac{t \cdot a}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{\frac{9 \cdot y}{c\_m}}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-223}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

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 (* (/ (* x y) c_m) (/ 9.0 z))) (t_2 (* -4.0 (/ (* t a) c_m))))
   (*
    c_s
    (if (<= z -4.1e+141)
      (* -4.0 (* t (/ a c_m)))
      (if (<= z -1.15e+41)
        (* x (/ (/ (* 9.0 y) c_m) z))
        (if (<= z -8.4e-60)
          t_2
          (if (<= z -7.8e-223)
            (* b (/ 1.0 (* z c_m)))
            (if (<= z 1.02e-198)
              t_1
              (if (<= z 3.4e-34)
                (/ b (* z c_m))
                (if (<= z 0.65) t_1 t_2))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x * y) / c_m) * (9.0 / z);
	double t_2 = -4.0 * ((t * a) / c_m);
	double tmp;
	if (z <= -4.1e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.15e+41) {
		tmp = x * (((9.0 * y) / c_m) / z);
	} else if (z <= -8.4e-60) {
		tmp = t_2;
	} else if (z <= -7.8e-223) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 1.02e-198) {
		tmp = t_1;
	} else if (z <= 3.4e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) / c_m) * (9.0d0 / z)
    t_2 = (-4.0d0) * ((t * a) / c_m)
    if (z <= (-4.1d+141)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.15d+41)) then
        tmp = x * (((9.0d0 * y) / c_m) / z)
    else if (z <= (-8.4d-60)) then
        tmp = t_2
    else if (z <= (-7.8d-223)) then
        tmp = b * (1.0d0 / (z * c_m))
    else if (z <= 1.02d-198) then
        tmp = t_1
    else if (z <= 3.4d-34) then
        tmp = b / (z * c_m)
    else if (z <= 0.65d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x * y) / c_m) * (9.0 / z);
	double t_2 = -4.0 * ((t * a) / c_m);
	double tmp;
	if (z <= -4.1e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.15e+41) {
		tmp = x * (((9.0 * y) / c_m) / z);
	} else if (z <= -8.4e-60) {
		tmp = t_2;
	} else if (z <= -7.8e-223) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 1.02e-198) {
		tmp = t_1;
	} else if (z <= 3.4e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((x * y) / c_m) * (9.0 / z)
	t_2 = -4.0 * ((t * a) / c_m)
	tmp = 0
	if z <= -4.1e+141:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.15e+41:
		tmp = x * (((9.0 * y) / c_m) / z)
	elif z <= -8.4e-60:
		tmp = t_2
	elif z <= -7.8e-223:
		tmp = b * (1.0 / (z * c_m))
	elif z <= 1.02e-198:
		tmp = t_1
	elif z <= 3.4e-34:
		tmp = b / (z * c_m)
	elif z <= 0.65:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(x * y) / c_m) * Float64(9.0 / z))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) / c_m))
	tmp = 0.0
	if (z <= -4.1e+141)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.15e+41)
		tmp = Float64(x * Float64(Float64(Float64(9.0 * y) / c_m) / z));
	elseif (z <= -8.4e-60)
		tmp = t_2;
	elseif (z <= -7.8e-223)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	elseif (z <= 1.02e-198)
		tmp = t_1;
	elseif (z <= 3.4e-34)
		tmp = Float64(b / Float64(z * c_m));
	elseif (z <= 0.65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((x * y) / c_m) * (9.0 / z);
	t_2 = -4.0 * ((t * a) / c_m);
	tmp = 0.0;
	if (z <= -4.1e+141)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.15e+41)
		tmp = x * (((9.0 * y) / c_m) / z);
	elseif (z <= -8.4e-60)
		tmp = t_2;
	elseif (z <= -7.8e-223)
		tmp = b * (1.0 / (z * c_m));
	elseif (z <= 1.02e-198)
		tmp = t_1;
	elseif (z <= 3.4e-34)
		tmp = b / (z * c_m);
	elseif (z <= 0.65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -4.1e+141], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e+41], N[(x * N[(N[(N[(9.0 * y), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.4e-60], t$95$2, If[LessEqual[z, -7.8e-223], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-198], t$95$1, If[LessEqual[z, 3.4e-34], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], t$95$1, t$95$2]]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.10000000000000022e141

   1. Initial program 51.7%

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

      1. +-commutative 51.7%

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

      2. associate-+r- 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*r* 52.1%

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

      5. *-commutative 52.1%

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

      6. associate-+r- 52.1%

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

      7. +-commutative 52.1%

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

      8. associate-*l* 52.1%

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

      9. associate-*l* 54.8%

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

      10. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around 0 51.7%

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

   6. Taylor expanded in a around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if -4.10000000000000022e141 < z < -1.1499999999999999e41

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r- 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*r* 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-+r- 70.0%

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

      7. +-commutative 70.0%

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

      8. associate-*l* 69.9%

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

      9. associate-*l* 74.1%

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

      10. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in y around inf 66.2%

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

   6. Taylor expanded in z around -inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

      3. *-commutative 91.3%

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

      4. associate-/l* 86.9%

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

      5. *-commutative 86.9%

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

      6. associate-/l* 91.6%

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

      7. mul-1-neg 91.6%

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

      8. unsub-neg 91.6%

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

      9. associate-*r/ 91.6%

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

      10. *-commutative 91.6%

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

      11. associate-/l* 91.7%

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

      12. associate-/r* 87.2%

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

   8. Simplified 87.2%

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

   9. Taylor expanded in x around inf 47.6%

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

       1. *-commutative 47.6%

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

       2. associate-/l* 41.3%

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

       3. associate-*r* 41.3%

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

       4. associate-/r* 49.7%

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

       5. associate-*l/ 49.5%

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

       6. associate-*l/ 49.6%

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

   11. Simplified 49.6%

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

   if -1.1499999999999999e41 < z < -8.39999999999999964e-60 or 0.650000000000000022 < z

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-+r- 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*r* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-+r- 71.4%

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

      7. +-commutative 71.4%

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

      8. associate-*l* 71.5%

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

      9. associate-*l* 76.4%

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

      10. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -8.39999999999999964e-60 < z < -7.79999999999999924e-223

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-+r- 94.6%

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

      7. +-commutative 94.6%

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

      8. associate-*l* 94.6%

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

      9. associate-*l* 90.2%

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

      10. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

      1. div-inv 64.4%

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

   9. Applied egg-rr 64.4%

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

   if -7.79999999999999924e-223 < z < 1.01999999999999997e-198 or 3.4000000000000001e-34 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+r- 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*r* 98.6%

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

      5. *-commutative 98.6%

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

      6. associate-+r- 98.6%

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

      7. +-commutative 98.6%

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

      8. associate-*l* 98.6%

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

      9. associate-*l* 94.6%

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

      10. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. associate-*r* 68.4%

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

      3. *-commutative 68.4%

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

   7. Simplified 68.4%

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

      1. associate-*l* 68.4%

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

      2. times-frac 69.8%

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

   9. Applied egg-rr 69.8%

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

   if 1.01999999999999997e-198 < z < 3.4000000000000001e-34

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*r* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-+r- 97.5%

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

      7. +-commutative 97.5%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 95.0%

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

      10. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{\frac{9 \cdot y}{c}}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-223}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-198}:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y}{c\_m} \cdot \frac{9}{z}\\ t_2 := -4 \cdot \frac{t \cdot a}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot 9}{c\_m} \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

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 (* (/ (* x y) c_m) (/ 9.0 z))) (t_2 (* -4.0 (/ (* t a) c_m))))
   (*
    c_s
    (if (<= z -1.05e+141)
      (* -4.0 (* t (/ a c_m)))
      (if (<= z -1.15e+41)
        (* (/ (* x 9.0) c_m) (/ y z))
        (if (<= z -9.6e-60)
          t_2
          (if (<= z -3.7e-222)
            (* b (/ 1.0 (* z c_m)))
            (if (<= z 3.4e-198)
              t_1
              (if (<= z 3.2e-34)
                (/ b (* z c_m))
                (if (<= z 0.62) t_1 t_2))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x * y) / c_m) * (9.0 / z);
	double t_2 = -4.0 * ((t * a) / c_m);
	double tmp;
	if (z <= -1.05e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.15e+41) {
		tmp = ((x * 9.0) / c_m) * (y / z);
	} else if (z <= -9.6e-60) {
		tmp = t_2;
	} else if (z <= -3.7e-222) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 3.4e-198) {
		tmp = t_1;
	} else if (z <= 3.2e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) / c_m) * (9.0d0 / z)
    t_2 = (-4.0d0) * ((t * a) / c_m)
    if (z <= (-1.05d+141)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.15d+41)) then
        tmp = ((x * 9.0d0) / c_m) * (y / z)
    else if (z <= (-9.6d-60)) then
        tmp = t_2
    else if (z <= (-3.7d-222)) then
        tmp = b * (1.0d0 / (z * c_m))
    else if (z <= 3.4d-198) then
        tmp = t_1
    else if (z <= 3.2d-34) then
        tmp = b / (z * c_m)
    else if (z <= 0.62d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x * y) / c_m) * (9.0 / z);
	double t_2 = -4.0 * ((t * a) / c_m);
	double tmp;
	if (z <= -1.05e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.15e+41) {
		tmp = ((x * 9.0) / c_m) * (y / z);
	} else if (z <= -9.6e-60) {
		tmp = t_2;
	} else if (z <= -3.7e-222) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 3.4e-198) {
		tmp = t_1;
	} else if (z <= 3.2e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((x * y) / c_m) * (9.0 / z)
	t_2 = -4.0 * ((t * a) / c_m)
	tmp = 0
	if z <= -1.05e+141:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.15e+41:
		tmp = ((x * 9.0) / c_m) * (y / z)
	elif z <= -9.6e-60:
		tmp = t_2
	elif z <= -3.7e-222:
		tmp = b * (1.0 / (z * c_m))
	elif z <= 3.4e-198:
		tmp = t_1
	elif z <= 3.2e-34:
		tmp = b / (z * c_m)
	elif z <= 0.62:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(x * y) / c_m) * Float64(9.0 / z))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) / c_m))
	tmp = 0.0
	if (z <= -1.05e+141)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.15e+41)
		tmp = Float64(Float64(Float64(x * 9.0) / c_m) * Float64(y / z));
	elseif (z <= -9.6e-60)
		tmp = t_2;
	elseif (z <= -3.7e-222)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	elseif (z <= 3.4e-198)
		tmp = t_1;
	elseif (z <= 3.2e-34)
		tmp = Float64(b / Float64(z * c_m));
	elseif (z <= 0.62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((x * y) / c_m) * (9.0 / z);
	t_2 = -4.0 * ((t * a) / c_m);
	tmp = 0.0;
	if (z <= -1.05e+141)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.15e+41)
		tmp = ((x * 9.0) / c_m) * (y / z);
	elseif (z <= -9.6e-60)
		tmp = t_2;
	elseif (z <= -3.7e-222)
		tmp = b * (1.0 / (z * c_m));
	elseif (z <= 3.4e-198)
		tmp = t_1;
	elseif (z <= 3.2e-34)
		tmp = b / (z * c_m);
	elseif (z <= 0.62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.05e+141], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e+41], N[(N[(N[(x * 9.0), $MachinePrecision] / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.6e-60], t$95$2, If[LessEqual[z, -3.7e-222], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-198], t$95$1, If[LessEqual[z, 3.2e-34], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.62], t$95$1, t$95$2]]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.0499999999999999e141

   1. Initial program 51.7%

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

      1. +-commutative 51.7%

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

      2. associate-+r- 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*r* 52.1%

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

      5. *-commutative 52.1%

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

      6. associate-+r- 52.1%

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

      7. +-commutative 52.1%

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

      8. associate-*l* 52.1%

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

      9. associate-*l* 54.8%

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

      10. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around 0 51.7%

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

   6. Taylor expanded in a around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if -1.0499999999999999e141 < z < -1.1499999999999999e41

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r- 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*r* 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-+r- 70.0%

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

      7. +-commutative 70.0%

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

      8. associate-*l* 69.9%

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

      9. associate-*l* 74.1%

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

      10. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf 47.6%

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

      1. associate-*r/ 47.6%

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

      2. associate-*r* 47.6%

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

      3. *-commutative 47.6%

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

   7. Simplified 47.6%

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

      1. *-commutative 47.6%

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

      2. times-frac 62.1%

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

      3. *-commutative 62.1%

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

   9. Applied egg-rr 62.1%

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

   if -1.1499999999999999e41 < z < -9.60000000000000038e-60 or 0.619999999999999996 < z

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-+r- 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*r* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-+r- 71.4%

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

      7. +-commutative 71.4%

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

      8. associate-*l* 71.5%

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

      9. associate-*l* 76.4%

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

      10. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -9.60000000000000038e-60 < z < -3.6999999999999999e-222

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-+r- 94.6%

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

      7. +-commutative 94.6%

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

      8. associate-*l* 94.6%

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

      9. associate-*l* 90.2%

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

      10. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

      1. div-inv 64.4%

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

   9. Applied egg-rr 64.4%

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

   if -3.6999999999999999e-222 < z < 3.3999999999999998e-198 or 3.20000000000000003e-34 < z < 0.619999999999999996

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+r- 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*r* 98.6%

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

      5. *-commutative 98.6%

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

      6. associate-+r- 98.6%

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

      7. +-commutative 98.6%

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

      8. associate-*l* 98.6%

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

      9. associate-*l* 94.6%

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

      10. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 68.4%

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

      1. associate-*r/ 68.4%

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

      2. associate-*r* 68.4%

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

      3. *-commutative 68.4%

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

   7. Simplified 68.4%

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

      1. associate-*l* 68.4%

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

      2. times-frac 69.8%

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

   9. Applied egg-rr 69.8%

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

   if 3.3999999999999998e-198 < z < 3.20000000000000003e-34

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*r* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-+r- 97.5%

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

      7. +-commutative 97.5%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 95.0%

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

      10. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot 9}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-198}:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c\_m}\\ t_2 := \frac{x \cdot y}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot 9}{c\_m} \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-198}:\\ \;\;\;\;\frac{9 \cdot t\_2}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 0.115:\\ \;\;\;\;t\_2 \cdot \frac{9}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* -4.0 (/ (* t a) c_m))) (t_2 (/ (* x y) c_m)))
   (*
    c_s
    (if (<= z -8.2e+140)
      (* -4.0 (* t (/ a c_m)))
      (if (<= z -1.36e+41)
        (* (/ (* x 9.0) c_m) (/ y z))
        (if (<= z -6.2e-61)
          t_1
          (if (<= z -1.72e-221)
            (* b (/ 1.0 (* z c_m)))
            (if (<= z 1.35e-198)
              (/ (* 9.0 t_2) z)
              (if (<= z 3.8e-34)
                (/ b (* z c_m))
                (if (<= z 0.115) (* t_2 (/ 9.0 z)) t_1))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * ((t * a) / c_m);
	double t_2 = (x * y) / c_m;
	double tmp;
	if (z <= -8.2e+140) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.36e+41) {
		tmp = ((x * 9.0) / c_m) * (y / z);
	} else if (z <= -6.2e-61) {
		tmp = t_1;
	} else if (z <= -1.72e-221) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 1.35e-198) {
		tmp = (9.0 * t_2) / z;
	} else if (z <= 3.8e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.115) {
		tmp = t_2 * (9.0 / z);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) / c_m)
    t_2 = (x * y) / c_m
    if (z <= (-8.2d+140)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.36d+41)) then
        tmp = ((x * 9.0d0) / c_m) * (y / z)
    else if (z <= (-6.2d-61)) then
        tmp = t_1
    else if (z <= (-1.72d-221)) then
        tmp = b * (1.0d0 / (z * c_m))
    else if (z <= 1.35d-198) then
        tmp = (9.0d0 * t_2) / z
    else if (z <= 3.8d-34) then
        tmp = b / (z * c_m)
    else if (z <= 0.115d0) then
        tmp = t_2 * (9.0d0 / z)
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = -4.0 * ((t * a) / c_m);
	double t_2 = (x * y) / c_m;
	double tmp;
	if (z <= -8.2e+140) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.36e+41) {
		tmp = ((x * 9.0) / c_m) * (y / z);
	} else if (z <= -6.2e-61) {
		tmp = t_1;
	} else if (z <= -1.72e-221) {
		tmp = b * (1.0 / (z * c_m));
	} else if (z <= 1.35e-198) {
		tmp = (9.0 * t_2) / z;
	} else if (z <= 3.8e-34) {
		tmp = b / (z * c_m);
	} else if (z <= 0.115) {
		tmp = t_2 * (9.0 / z);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = -4.0 * ((t * a) / c_m)
	t_2 = (x * y) / c_m
	tmp = 0
	if z <= -8.2e+140:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.36e+41:
		tmp = ((x * 9.0) / c_m) * (y / z)
	elif z <= -6.2e-61:
		tmp = t_1
	elif z <= -1.72e-221:
		tmp = b * (1.0 / (z * c_m))
	elif z <= 1.35e-198:
		tmp = (9.0 * t_2) / z
	elif z <= 3.8e-34:
		tmp = b / (z * c_m)
	elif z <= 0.115:
		tmp = t_2 * (9.0 / z)
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) / c_m))
	t_2 = Float64(Float64(x * y) / c_m)
	tmp = 0.0
	if (z <= -8.2e+140)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.36e+41)
		tmp = Float64(Float64(Float64(x * 9.0) / c_m) * Float64(y / z));
	elseif (z <= -6.2e-61)
		tmp = t_1;
	elseif (z <= -1.72e-221)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	elseif (z <= 1.35e-198)
		tmp = Float64(Float64(9.0 * t_2) / z);
	elseif (z <= 3.8e-34)
		tmp = Float64(b / Float64(z * c_m));
	elseif (z <= 0.115)
		tmp = Float64(t_2 * Float64(9.0 / z));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = -4.0 * ((t * a) / c_m);
	t_2 = (x * y) / c_m;
	tmp = 0.0;
	if (z <= -8.2e+140)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.36e+41)
		tmp = ((x * 9.0) / c_m) * (y / z);
	elseif (z <= -6.2e-61)
		tmp = t_1;
	elseif (z <= -1.72e-221)
		tmp = b * (1.0 / (z * c_m));
	elseif (z <= 1.35e-198)
		tmp = (9.0 * t_2) / z;
	elseif (z <= 3.8e-34)
		tmp = b / (z * c_m);
	elseif (z <= 0.115)
		tmp = t_2 * (9.0 / z);
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -8.2e+140], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.36e+41], N[(N[(N[(x * 9.0), $MachinePrecision] / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-61], t$95$1, If[LessEqual[z, -1.72e-221], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-198], N[(N[(9.0 * t$95$2), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.8e-34], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.115], N[(t$95$2 * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 7 regimes

2. if z < -8.1999999999999998e140

   1. Initial program 51.7%

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

      1. +-commutative 51.7%

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

      2. associate-+r- 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*r* 52.1%

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

      5. *-commutative 52.1%

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

      6. associate-+r- 52.1%

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

      7. +-commutative 52.1%

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

      8. associate-*l* 52.1%

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

      9. associate-*l* 54.8%

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

      10. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around 0 51.7%

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

   6. Taylor expanded in a around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if -8.1999999999999998e140 < z < -1.35999999999999995e41

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r- 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*r* 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-+r- 70.0%

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

      7. +-commutative 70.0%

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

      8. associate-*l* 69.9%

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

      9. associate-*l* 74.1%

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

      10. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf 47.6%

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

      1. associate-*r/ 47.6%

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

      2. associate-*r* 47.6%

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

      3. *-commutative 47.6%

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

   7. Simplified 47.6%

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

      1. *-commutative 47.6%

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

      2. times-frac 62.1%

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

      3. *-commutative 62.1%

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

   9. Applied egg-rr 62.1%

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

   if -1.35999999999999995e41 < z < -6.1999999999999999e-61 or 0.115000000000000005 < z

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-+r- 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*r* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-+r- 71.4%

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

      7. +-commutative 71.4%

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

      8. associate-*l* 71.5%

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

      9. associate-*l* 76.4%

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

      10. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -6.1999999999999999e-61 < z < -1.71999999999999997e-221

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r- 96.0%

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

      3. *-commutative 96.0%

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

      4. associate-*r* 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-+r- 94.6%

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

      7. +-commutative 94.6%

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

      8. associate-*l* 94.6%

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

      9. associate-*l* 90.2%

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

      10. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

      1. div-inv 64.4%

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

   9. Applied egg-rr 64.4%

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

   if -1.71999999999999997e-221 < z < 1.3500000000000001e-198

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. *-commutative 98.2%

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

      4. associate-*r* 98.2%

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

      5. *-commutative 98.2%

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

      6. associate-+r- 98.2%

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

      7. +-commutative 98.2%

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

      8. associate-*l* 98.3%

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

      9. associate-*l* 92.9%

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

      10. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around inf 61.5%

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

   6. Taylor expanded in z around 0 86.4%

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

   7. Taylor expanded in y around inf 72.7%

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

   if 1.3500000000000001e-198 < z < 3.8000000000000001e-34

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-+r- 97.5%

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

      3. *-commutative 97.5%

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

      4. associate-*r* 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-+r- 97.5%

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

      7. +-commutative 97.5%

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

      8. associate-*l* 97.5%

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

      9. associate-*l* 95.0%

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

      10. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 65.2%

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

      1. *-commutative 65.2%

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

   7. Simplified 65.2%

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

   if 3.8000000000000001e-34 < z < 0.115000000000000005

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*r* 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-+r- 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-*l* 99.7%

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

      9. associate-*l* 99.7%

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

      10. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 60.8%

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

      1. associate-*r/ 60.8%

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

      2. associate-*r* 61.0%

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

      3. *-commutative 61.0%

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

   7. Simplified 61.0%

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

      1. associate-*l* 60.8%

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

      2. times-frac 61.1%

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

   9. Applied egg-rr 61.1%

      \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot 9}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-61}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-198}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.115:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot 9}{c\_m} \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87} \lor \neg \left(z \leq 0.058\right):\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

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 (<= z -8.2e+140)
    (* -4.0 (* t (/ a c_m)))
    (if (<= z -1.45e+41)
      (* (/ (* x 9.0) c_m) (/ y z))
      (if (or (<= z -8e-87) (not (<= z 0.058)))
        (/ (- (/ b z) (* a (* 4.0 t))) c_m)
        (/ (+ b (* x (* 9.0 y))) (* z c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -8.2e+140) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.45e+41) {
		tmp = ((x * 9.0) / c_m) * (y / z);
	} else if ((z <= -8e-87) || !(z <= 0.058)) {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-8.2d+140)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.45d+41)) then
        tmp = ((x * 9.0d0) / c_m) * (y / z)
    else if ((z <= (-8d-87)) .or. (.not. (z <= 0.058d0))) then
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    else
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -8.2e+140) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.45e+41) {
		tmp = ((x * 9.0) / c_m) * (y / z);
	} else if ((z <= -8e-87) || !(z <= 0.058)) {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -8.2e+140:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.45e+41:
		tmp = ((x * 9.0) / c_m) * (y / z)
	elif (z <= -8e-87) or not (z <= 0.058):
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	else:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -8.2e+140)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.45e+41)
		tmp = Float64(Float64(Float64(x * 9.0) / c_m) * Float64(y / z));
	elseif ((z <= -8e-87) || !(z <= 0.058))
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -8.2e+140)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.45e+41)
		tmp = ((x * 9.0) / c_m) * (y / z);
	elseif ((z <= -8e-87) || ~((z <= 0.058)))
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	else
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -8.2e+140], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e+41], N[(N[(N[(x * 9.0), $MachinePrecision] / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8e-87], N[Not[LessEqual[z, 0.058]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -8.1999999999999998e140

   1. Initial program 51.7%

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

      1. +-commutative 51.7%

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

      2. associate-+r- 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*r* 52.1%

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

      5. *-commutative 52.1%

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

      6. associate-+r- 52.1%

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

      7. +-commutative 52.1%

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

      8. associate-*l* 52.1%

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

      9. associate-*l* 54.8%

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

      10. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in z around 0 51.7%

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

   6. Taylor expanded in a around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if -8.1999999999999998e140 < z < -1.44999999999999994e41

   1. Initial program 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r- 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*r* 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-+r- 70.0%

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

      7. +-commutative 70.0%

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

      8. associate-*l* 69.9%

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

      9. associate-*l* 74.1%

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

      10. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf 47.6%

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

      1. associate-*r/ 47.6%

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

      2. associate-*r* 47.6%

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

      3. *-commutative 47.6%

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

   7. Simplified 47.6%

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

      1. *-commutative 47.6%

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

      2. times-frac 62.1%

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

      3. *-commutative 62.1%

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

   9. Applied egg-rr 62.1%

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

   if -1.44999999999999994e41 < z < -8.00000000000000014e-87 or 0.0580000000000000029 < z

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-+r- 73.3%

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

      3. *-commutative 73.3%

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

      4. associate-*r* 74.7%

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

      5. *-commutative 74.7%

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

      6. associate-+r- 74.7%

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

      7. +-commutative 74.7%

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

      8. associate-*l* 74.7%

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

      9. associate-*l* 77.7%

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

      10. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around inf 65.6%

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

   6. Taylor expanded in z around -inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. unsub-neg 68.9%

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

      3. *-commutative 68.9%

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

      4. associate-/l* 70.3%

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

      5. *-commutative 70.3%

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

      6. associate-/l* 71.4%

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

      7. mul-1-neg 71.4%

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

      8. unsub-neg 71.4%

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

      9. associate-*r/ 71.3%

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

      10. *-commutative 71.3%

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

      11. associate-/l* 71.3%

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

      12. associate-/r* 74.3%

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

   8. Simplified 74.3%

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

   9. Taylor expanded in x around 0 72.6%

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

       1. mul-1-neg 72.6%

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

       2. associate-/r* 69.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 69.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 69.1%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   12. Taylor expanded in c around -inf 76.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]
   13. Step-by-step derivation

       1. mul-1-neg 76.6%

          \[\leadsto \color{blue}{-\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]

       2. distribute-neg-frac2 76.6%

          \[\leadsto \color{blue}{\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{-c}} \]

       3. *-commutative 76.6%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot 4} - \frac{b}{z}}{-c} \]

       4. associate-*r* 76.6%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot 4\right)} - \frac{b}{z}}{-c} \]

   14. Simplified 76.6%

       \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot 4\right) - \frac{b}{z}}{-c}} \]

   if -8.00000000000000014e-87 < z < 0.0580000000000000029

   1. Initial program 97.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot 9}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87} \lor \neg \left(z \leq 0.058\right):\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}}{z}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-88} \lor \neg \left(z \leq 0.007\right):\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

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 (<= z -4e+141)
    (* -4.0 (* t (/ a c_m)))
    (if (<= z -1.45e+41)
      (/ (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)) z)
      (if (or (<= z -6.6e-88) (not (<= z 0.007)))
        (/ (- (/ b z) (* a (* 4.0 t))) c_m)
        (/ (+ b (* x (* 9.0 y))) (* z c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -4e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.45e+41) {
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	} else if ((z <= -6.6e-88) || !(z <= 0.007)) {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-4d+141)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.45d+41)) then
        tmp = ((9.0d0 * ((x * y) / c_m)) + (b / c_m)) / z
    else if ((z <= (-6.6d-88)) .or. (.not. (z <= 0.007d0))) then
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    else
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -4e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.45e+41) {
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	} else if ((z <= -6.6e-88) || !(z <= 0.007)) {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -4e+141:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.45e+41:
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z
	elif (z <= -6.6e-88) or not (z <= 0.007):
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	else:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -4e+141)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.45e+41)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m)) / z);
	elseif ((z <= -6.6e-88) || !(z <= 0.007))
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -4e+141)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.45e+41)
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	elseif ((z <= -6.6e-88) || ~((z <= 0.007)))
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	else
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -4e+141], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e+41], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, -6.6e-88], N[Not[LessEqual[z, 0.007]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -4.00000000000000007e141

   1. Initial program 51.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 51.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 51.7%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 51.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 52.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 52.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 52.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 52.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 52.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 54.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 54.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 51.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 57.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 67.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 67.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -4.00000000000000007e141 < z < -1.44999999999999994e41

   1. Initial program 74.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 74.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 74.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 70.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 70.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 70.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 70.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 69.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 74.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 74.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around 0 68.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]

   if -1.44999999999999994e41 < z < -6.59999999999999987e-88 or 0.00700000000000000015 < z

   1. Initial program 73.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 73.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 73.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 74.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 74.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 74.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 74.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 74.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 77.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 77.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 68.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 68.9%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 68.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 68.9%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 70.3%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 70.3%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 71.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 71.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 71.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 71.3%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 71.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 71.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 74.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 74.3%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 72.6%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 72.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 69.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 69.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 69.1%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   12. Taylor expanded in c around -inf 76.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]
   13. Step-by-step derivation

       1. mul-1-neg 76.6%

          \[\leadsto \color{blue}{-\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]

       2. distribute-neg-frac2 76.6%

          \[\leadsto \color{blue}{\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{-c}} \]

       3. *-commutative 76.6%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot 4} - \frac{b}{z}}{-c} \]

       4. associate-*r* 76.6%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot 4\right)} - \frac{b}{z}}{-c} \]

   14. Simplified 76.6%

       \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot 4\right) - \frac{b}{z}}{-c}} \]

   if -6.59999999999999987e-88 < z < 0.00700000000000000015

   1. Initial program 97.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-88} \lor \neg \left(z \leq 0.007\right):\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \end{array} \end{array} \end{array} \]

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 (* x (* 9.0 y))) (* z c_m)))
        (t_2 (* -4.0 (* t (/ a c_m)))))
   (*
    c_s
    (if (<= z -9.2e+140)
      t_2
      (if (<= z -8.2e+35)
        t_1
        (if (<= z -8e-87)
          t_2
          (if (<= z 4e+80) t_1 (* -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 = (b + (x * (9.0 * y))) / (z * c_m);
	double t_2 = -4.0 * (t * (a / c_m));
	double tmp;
	if (z <= -9.2e+140) {
		tmp = t_2;
	} else if (z <= -8.2e+35) {
		tmp = t_1;
	} else if (z <= -8e-87) {
		tmp = t_2;
	} else if (z <= 4e+80) {
		tmp = t_1;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b + (x * (9.0d0 * y))) / (z * c_m)
    t_2 = (-4.0d0) * (t * (a / c_m))
    if (z <= (-9.2d+140)) then
        tmp = t_2
    else if (z <= (-8.2d+35)) then
        tmp = t_1
    else if (z <= (-8d-87)) then
        tmp = t_2
    else if (z <= 4d+80) then
        tmp = t_1
    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 = (b + (x * (9.0 * y))) / (z * c_m);
	double t_2 = -4.0 * (t * (a / c_m));
	double tmp;
	if (z <= -9.2e+140) {
		tmp = t_2;
	} else if (z <= -8.2e+35) {
		tmp = t_1;
	} else if (z <= -8e-87) {
		tmp = t_2;
	} else if (z <= 4e+80) {
		tmp = t_1;
	} 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 = (b + (x * (9.0 * y))) / (z * c_m)
	t_2 = -4.0 * (t * (a / c_m))
	tmp = 0
	if z <= -9.2e+140:
		tmp = t_2
	elif z <= -8.2e+35:
		tmp = t_1
	elif z <= -8e-87:
		tmp = t_2
	elif z <= 4e+80:
		tmp = t_1
	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(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c_m)))
	tmp = 0.0
	if (z <= -9.2e+140)
		tmp = t_2;
	elseif (z <= -8.2e+35)
		tmp = t_1;
	elseif (z <= -8e-87)
		tmp = t_2;
	elseif (z <= 4e+80)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(Float64(t * 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 = (b + (x * (9.0 * y))) / (z * c_m);
	t_2 = -4.0 * (t * (a / c_m));
	tmp = 0.0;
	if (z <= -9.2e+140)
		tmp = t_2;
	elseif (z <= -8.2e+35)
		tmp = t_1;
	elseif (z <= -8e-87)
		tmp = t_2;
	elseif (z <= 4e+80)
		tmp = t_1;
	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[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -9.2e+140], t$95$2, If[LessEqual[z, -8.2e+35], t$95$1, If[LessEqual[z, -8e-87], t$95$2, If[LessEqual[z, 4e+80], t$95$1, N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999961e140 or -8.1999999999999997e35 < z < -8.00000000000000014e-87

   1. Initial program 67.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 67.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 67.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 70.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 70.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 70.5%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 70.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 70.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 70.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 70.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 65.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 58.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 58.0%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 64.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 64.1%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -9.19999999999999961e140 < z < -8.1999999999999997e35 or -8.00000000000000014e-87 < z < 4e80

   1. Initial program 93.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 93.5%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 93.5%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 93.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 92.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 92.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 92.5%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 92.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 92.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 90.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 90.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.1%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 82.1%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 82.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 82.1%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 82.1%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 4e80 < z

   1. Initial program 57.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 57.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 57.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 54.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 54.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 54.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 54.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 54.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 63.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 63.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+80}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87}:\\ \;\;\;\;\frac{b - \left(z \cdot t\right) \cdot \left(4 \cdot a\right)}{z \cdot c\_m}\\ \mathbf{elif}\;z \leq 0.096:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \end{array} \end{array} \]

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 (<= z -3.6e+141)
    (* -4.0 (* t (/ a c_m)))
    (if (<= z -1.35e+41)
      (/ (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)) z)
      (if (<= z -8e-87)
        (/ (- b (* (* z t) (* 4.0 a))) (* z c_m))
        (if (<= z 0.096)
          (/ (+ b (* x (* 9.0 y))) (* z c_m))
          (/ (- (/ b z) (* a (* 4.0 t))) c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -3.6e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.35e+41) {
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	} else if (z <= -8e-87) {
		tmp = (b - ((z * t) * (4.0 * a))) / (z * c_m);
	} else if (z <= 0.096) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-3.6d+141)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= (-1.35d+41)) then
        tmp = ((9.0d0 * ((x * y) / c_m)) + (b / c_m)) / z
    else if (z <= (-8d-87)) then
        tmp = (b - ((z * t) * (4.0d0 * a))) / (z * c_m)
    else if (z <= 0.096d0) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    else
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -3.6e+141) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= -1.35e+41) {
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	} else if (z <= -8e-87) {
		tmp = (b - ((z * t) * (4.0 * a))) / (z * c_m);
	} else if (z <= 0.096) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -3.6e+141:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= -1.35e+41:
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z
	elif z <= -8e-87:
		tmp = (b - ((z * t) * (4.0 * a))) / (z * c_m)
	elif z <= 0.096:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	else:
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -3.6e+141)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= -1.35e+41)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m)) / z);
	elseif (z <= -8e-87)
		tmp = Float64(Float64(b - Float64(Float64(z * t) * Float64(4.0 * a))) / Float64(z * c_m));
	elseif (z <= 0.096)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -3.6e+141)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= -1.35e+41)
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	elseif (z <= -8e-87)
		tmp = (b - ((z * t) * (4.0 * a))) / (z * c_m);
	elseif (z <= 0.096)
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	else
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -3.6e+141], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e+41], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8e-87], N[(N[(b - N[(N[(z * t), $MachinePrecision] * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.096], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if z < -3.6000000000000001e141

   1. Initial program 51.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 51.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 51.7%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 51.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 52.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 52.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 52.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 52.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 52.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 54.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 54.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 51.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 57.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 67.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 67.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -3.6000000000000001e141 < z < -1.35e41

   1. Initial program 74.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 74.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 74.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 70.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 70.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 70.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 70.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 69.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 74.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 74.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around 0 68.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]

   if -1.35e41 < z < -8.00000000000000014e-87

   1. Initial program 89.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 89.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 89.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 89.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 92.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 92.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r* 74.7%

         \[\leadsto \frac{b - \color{blue}{\left(4 \cdot a\right) \cdot \left(t \cdot z\right)}}{c \cdot z} \]

      2. *-commutative 74.7%

         \[\leadsto \frac{b - \left(4 \cdot a\right) \cdot \left(t \cdot z\right)}{\color{blue}{z \cdot c}} \]

   7. Simplified 74.7%

      \[\leadsto \color{blue}{\frac{b - \left(4 \cdot a\right) \cdot \left(t \cdot z\right)}{z \cdot c}} \]

   if -8.00000000000000014e-87 < z < 0.096000000000000002

   1. Initial program 97.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 0.096000000000000002 < z

   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. +-commutative 63.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 63.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 63.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 60.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 60.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 68.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 65.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 65.3%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 65.3%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 65.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 67.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 67.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 71.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 71.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 71.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 74.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 74.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 71.3%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 71.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 65.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 65.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 65.6%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   12. Taylor expanded in c around -inf 78.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]
   13. Step-by-step derivation

       1. mul-1-neg 78.0%

          \[\leadsto \color{blue}{-\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]

       2. distribute-neg-frac2 78.0%

          \[\leadsto \color{blue}{\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{-c}} \]

       3. *-commutative 78.0%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot 4} - \frac{b}{z}}{-c} \]

       4. associate-*r* 78.0%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot 4\right)} - \frac{b}{z}}{-c} \]

   14. Simplified 78.0%

       \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot 4\right) - \frac{b}{z}}{-c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87}:\\ \;\;\;\;\frac{b - \left(z \cdot t\right) \cdot \left(4 \cdot a\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 0.096:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right) + \frac{\frac{b}{c\_m}}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+41}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c\_m} + \frac{b}{c\_m}}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.78:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \end{array} \end{array} \end{array} \]

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 (+ (* -4.0 (* t (/ a c_m))) (/ (/ b c_m) z))))
   (*
    c_s
    (if (<= z -8.2e+140)
      t_1
      (if (<= z -1.08e+41)
        (/ (+ (* 9.0 (/ (* x y) c_m)) (/ b c_m)) z)
        (if (<= z -8e-87)
          t_1
          (if (<= z 0.78)
            (/ (+ b (* x (* 9.0 y))) (* z c_m))
            (/ (- (/ b z) (* a (* 4.0 t))) c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	double tmp;
	if (z <= -8.2e+140) {
		tmp = t_1;
	} else if (z <= -1.08e+41) {
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	} else if (z <= -8e-87) {
		tmp = t_1;
	} else if (z <= 0.78) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * (a / c_m))) + ((b / c_m) / z)
    if (z <= (-8.2d+140)) then
        tmp = t_1
    else if (z <= (-1.08d+41)) then
        tmp = ((9.0d0 * ((x * y) / c_m)) + (b / c_m)) / z
    else if (z <= (-8d-87)) then
        tmp = t_1
    else if (z <= 0.78d0) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    else
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	double tmp;
	if (z <= -8.2e+140) {
		tmp = t_1;
	} else if (z <= -1.08e+41) {
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	} else if (z <= -8e-87) {
		tmp = t_1;
	} else if (z <= 0.78) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z)
	tmp = 0
	if z <= -8.2e+140:
		tmp = t_1
	elif z <= -1.08e+41:
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z
	elif z <= -8e-87:
		tmp = t_1
	elif z <= 0.78:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	else:
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) + Float64(Float64(b / c_m) / z))
	tmp = 0.0
	if (z <= -8.2e+140)
		tmp = t_1;
	elseif (z <= -1.08e+41)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / c_m)) + Float64(b / c_m)) / z);
	elseif (z <= -8e-87)
		tmp = t_1;
	elseif (z <= 0.78)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	tmp = 0.0;
	if (z <= -8.2e+140)
		tmp = t_1;
	elseif (z <= -1.08e+41)
		tmp = ((9.0 * ((x * y) / c_m)) + (b / c_m)) / z;
	elseif (z <= -8e-87)
		tmp = t_1;
	elseif (z <= 0.78)
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	else
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -8.2e+140], t$95$1, If[LessEqual[z, -1.08e+41], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8e-87], t$95$1, If[LessEqual[z, 0.78], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -8.1999999999999998e140 or -1.08000000000000004e41 < z < -8.00000000000000014e-87

   1. Initial program 67.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 67.8%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 67.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 71.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 71.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 71.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 71.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 71.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 71.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 71.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 69.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 69.9%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 69.9%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 69.9%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 75.8%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 75.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 75.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 75.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 75.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 75.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 75.8%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 75.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 75.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 75.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 73.9%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 73.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 75.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 75.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 75.3%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   if -8.1999999999999998e140 < z < -1.08000000000000004e41

   1. Initial program 74.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 74.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 74.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 70.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 70.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 70.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 70.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 69.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 74.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 74.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around 0 68.7%

      \[\leadsto \color{blue}{\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}} \]

   if -8.00000000000000014e-87 < z < 0.78000000000000003

   1. Initial program 97.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 0.78000000000000003 < z

   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. +-commutative 63.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 63.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 63.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 60.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 60.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 68.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 65.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 65.3%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 65.3%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 65.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 67.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 67.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 71.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 71.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 71.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 74.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 74.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 71.3%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 71.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 65.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 65.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 65.6%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   12. Taylor expanded in c around -inf 78.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]
   13. Step-by-step derivation

       1. mul-1-neg 78.0%

          \[\leadsto \color{blue}{-\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]

       2. distribute-neg-frac2 78.0%

          \[\leadsto \color{blue}{\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{-c}} \]

       3. *-commutative 78.0%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot 4} - \frac{b}{z}}{-c} \]

       4. associate-*r* 78.0%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot 4\right)} - \frac{b}{z}}{-c} \]

   14. Simplified 78.0%

       \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot 4\right) - \frac{b}{z}}{-c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+41}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-87}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 0.78:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c\_m}\right) + \frac{\frac{b}{c\_m}}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot \frac{x}{c\_m} + \frac{b}{y \cdot c\_m}\right)}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.01:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \end{array} \end{array} \end{array} \]

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 (+ (* -4.0 (* t (/ a c_m))) (/ (/ b c_m) z))))
   (*
    c_s
    (if (<= z -6.8e+137)
      t_1
      (if (<= z -1.4e+41)
        (/ (* y (+ (* 9.0 (/ x c_m)) (/ b (* y c_m)))) z)
        (if (<= z -1.25e-87)
          t_1
          (if (<= z 0.01)
            (/ (+ b (* x (* 9.0 y))) (* z c_m))
            (/ (- (/ b z) (* a (* 4.0 t))) c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	double tmp;
	if (z <= -6.8e+137) {
		tmp = t_1;
	} else if (z <= -1.4e+41) {
		tmp = (y * ((9.0 * (x / c_m)) + (b / (y * c_m)))) / z;
	} else if (z <= -1.25e-87) {
		tmp = t_1;
	} else if (z <= 0.01) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * (t * (a / c_m))) + ((b / c_m) / z)
    if (z <= (-6.8d+137)) then
        tmp = t_1
    else if (z <= (-1.4d+41)) then
        tmp = (y * ((9.0d0 * (x / c_m)) + (b / (y * c_m)))) / z
    else if (z <= (-1.25d-87)) then
        tmp = t_1
    else if (z <= 0.01d0) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    else
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	double tmp;
	if (z <= -6.8e+137) {
		tmp = t_1;
	} else if (z <= -1.4e+41) {
		tmp = (y * ((9.0 * (x / c_m)) + (b / (y * c_m)))) / z;
	} else if (z <= -1.25e-87) {
		tmp = t_1;
	} else if (z <= 0.01) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z)
	tmp = 0
	if z <= -6.8e+137:
		tmp = t_1
	elif z <= -1.4e+41:
		tmp = (y * ((9.0 * (x / c_m)) + (b / (y * c_m)))) / z
	elif z <= -1.25e-87:
		tmp = t_1
	elif z <= 0.01:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	else:
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) + Float64(Float64(b / c_m) / z))
	tmp = 0.0
	if (z <= -6.8e+137)
		tmp = t_1;
	elseif (z <= -1.4e+41)
		tmp = Float64(Float64(y * Float64(Float64(9.0 * Float64(x / c_m)) + Float64(b / Float64(y * c_m)))) / z);
	elseif (z <= -1.25e-87)
		tmp = t_1;
	elseif (z <= 0.01)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	tmp = 0.0;
	if (z <= -6.8e+137)
		tmp = t_1;
	elseif (z <= -1.4e+41)
		tmp = (y * ((9.0 * (x / c_m)) + (b / (y * c_m)))) / z;
	elseif (z <= -1.25e-87)
		tmp = t_1;
	elseif (z <= 0.01)
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	else
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -6.8e+137], t$95$1, If[LessEqual[z, -1.4e+41], N[(N[(y * N[(N[(9.0 * N[(x / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(y * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.25e-87], t$95$1, If[LessEqual[z, 0.01], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999973e137 or -1.4e41 < z < -1.25000000000000011e-87

   1. Initial program 68.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 68.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 68.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 68.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 71.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 71.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 71.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 71.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 71.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 71.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 71.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 70.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 70.3%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 70.3%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 70.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 76.2%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 76.2%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 76.1%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 76.1%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 76.1%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 76.2%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 76.2%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 76.2%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 76.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 76.3%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 74.3%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 74.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 75.7%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 75.7%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 75.7%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   if -6.79999999999999973e137 < z < -1.4e41

   1. Initial program 73.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 73.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 73.0%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 73.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 68.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 68.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 68.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 68.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 68.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 72.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 72.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around 0 76.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(9 \cdot \frac{x}{c} + \frac{b}{c \cdot y}\right)}{z}} \]

   if -1.25000000000000011e-87 < z < 0.0100000000000000002

   1. Initial program 97.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 87.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if 0.0100000000000000002 < z

   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. +-commutative 63.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 63.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 63.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 60.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 60.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 68.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 65.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 65.3%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 65.3%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 65.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 67.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 67.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 71.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 71.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 71.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 71.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 74.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 74.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 71.3%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 71.3%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 65.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 65.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 65.6%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   12. Taylor expanded in c around -inf 78.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]
   13. Step-by-step derivation

       1. mul-1-neg 78.0%

          \[\leadsto \color{blue}{-\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]

       2. distribute-neg-frac2 78.0%

          \[\leadsto \color{blue}{\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{-c}} \]

       3. *-commutative 78.0%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot 4} - \frac{b}{z}}{-c} \]

       4. associate-*r* 78.0%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot 4\right)} - \frac{b}{z}}{-c} \]

   14. Simplified 78.0%

       \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot 4\right) - \frac{b}{z}}{-c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+137}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot \frac{x}{c} + \frac{b}{y \cdot c}\right)}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-87}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 0.01:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+86}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c\_m}}{z}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+164}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c\_m}\\ \end{array} \end{array} \]

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 (<= z -1e+86)
    (- (* -4.0 (* t (/ a c_m))) (* -9.0 (* x (/ (/ y c_m) z))))
    (if (<= z 7.2e+164)
      (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))
      (/ (- (/ b z) (* a (* 4.0 t))) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1e+86) {
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)));
	} else if (z <= 7.2e+164) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-1d+86)) then
        tmp = ((-4.0d0) * (t * (a / c_m))) - ((-9.0d0) * (x * ((y / c_m) / z)))
    else if (z <= 7.2d+164) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c_m)
    else
        tmp = ((b / z) - (a * (4.0d0 * t))) / c_m
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1e+86) {
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)));
	} else if (z <= 7.2e+164) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -1e+86:
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)))
	elif z <= 7.2e+164:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m)
	else:
		tmp = ((b / z) - (a * (4.0 * t))) / c_m
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -1e+86)
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) - Float64(-9.0 * Float64(x * Float64(Float64(y / c_m) / z))));
	elseif (z <= 7.2e+164)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(b / z) - Float64(a * Float64(4.0 * t))) / c_m);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -1e+86)
		tmp = (-4.0 * (t * (a / c_m))) - (-9.0 * (x * ((y / c_m) / z)));
	elseif (z <= 7.2e+164)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	else
		tmp = ((b / z) - (a * (4.0 * t))) / c_m;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -1e+86], N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * N[(N[(y / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+164], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] - N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1e86

   1. Initial program 56.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 56.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 56.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 56.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 56.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 56.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 56.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 56.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 56.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 58.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 58.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 58.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.8%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 73.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 73.1%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 73.1%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 73.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 78.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 78.7%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 80.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 80.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 80.9%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 81.1%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 81.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 81.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 77.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 77.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around inf 62.3%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 66.7%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

       2. associate-/r* 70.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{c}}{z}}\right) \]

   11. Simplified 70.4%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)} \]

   if -1e86 < z < 7.19999999999999981e164

   1. Initial program 93.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 93.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 93.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 93.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 93.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 93.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 93.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 93.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 93.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 91.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 91.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   if 7.19999999999999981e164 < z

   1. Initial program 51.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 51.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 51.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 47.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 47.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 47.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 47.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 47.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 59.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 59.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 59.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.5%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 59.5%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 59.5%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 59.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 59.6%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 59.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 59.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 59.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 59.1%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 59.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 59.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 63.2%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 63.2%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 73.9%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 73.9%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 68.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 68.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 68.0%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   12. Taylor expanded in c around -inf 85.9%

       \[\leadsto \color{blue}{-1 \cdot \frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]
   13. Step-by-step derivation

       1. mul-1-neg 85.9%

          \[\leadsto \color{blue}{-\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{c}} \]

       2. distribute-neg-frac2 85.9%

          \[\leadsto \color{blue}{\frac{4 \cdot \left(a \cdot t\right) - \frac{b}{z}}{-c}} \]

       3. *-commutative 85.9%

          \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot 4} - \frac{b}{z}}{-c} \]

       4. associate-*r* 85.9%

          \[\leadsto \frac{\color{blue}{a \cdot \left(t \cdot 4\right)} - \frac{b}{z}}{-c} \]

   14. Simplified 85.9%

       \[\leadsto \color{blue}{\frac{a \cdot \left(t \cdot 4\right) - \frac{b}{z}}{-c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+86}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) - -9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+164}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - a \cdot \left(4 \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c\_m}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) - \frac{\left(x \cdot y\right) \cdot -9}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) + \frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

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 (<= b -4.5e-41)
    (/ (+ b (* x (* 9.0 y))) (* z c_m))
    (if (<= b 1.2e+91)
      (/ (- (* -4.0 (* t a)) (/ (* (* x y) -9.0) z)) c_m)
      (+ (* -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 (b <= -4.5e-41) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else if (b <= 1.2e+91) {
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (b <= (-4.5d-41)) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c_m)
    else if (b <= 1.2d+91) then
        tmp = (((-4.0d0) * (t * a)) - (((x * y) * (-9.0d0)) / z)) / c_m
    else
        tmp = ((-4.0d0) * (t * (a / c_m))) + ((b / c_m) / z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -4.5e-41) {
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	} else if (b <= 1.2e+91) {
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -4.5e-41:
		tmp = (b + (x * (9.0 * y))) / (z * c_m)
	elif b <= 1.2e+91:
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m
	else:
		tmp = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -4.5e-41)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c_m));
	elseif (b <= 1.2e+91)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) - Float64(Float64(Float64(x * y) * -9.0) / z)) / c_m);
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) + 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 (b <= -4.5e-41)
		tmp = (b + (x * (9.0 * y))) / (z * c_m);
	elseif (b <= 1.2e+91)
		tmp = ((-4.0 * (t * a)) - (((x * y) * -9.0) / z)) / c_m;
	else
		tmp = (-4.0 * (t * (a / c_m))) + ((b / c_m) / z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -4.5e-41], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+91], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * y), $MachinePrecision] * -9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -4.5e-41

   1. Initial program 87.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 87.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 87.0%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 87.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 82.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 82.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 82.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 82.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 82.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 87.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 87.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.3%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 81.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y + b}{z \cdot c} \]

      3. associate-*r* 81.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   7. Simplified 81.4%

      \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z \cdot c} \]

   if -4.5e-41 < b < 1.19999999999999991e91

   1. Initial program 80.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 80.9%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 80.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 83.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 83.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 83.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 83.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 83.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 82.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 82.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 82.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 82.0%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 82.0%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 82.0%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 80.8%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 80.8%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 79.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 79.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 79.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 79.4%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 79.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 79.4%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 79.6%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 79.6%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in c around 0 92.2%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{y \cdot \left(-9 \cdot x - \frac{b}{y}\right)}{z}}{c}} \]

   10. Taylor expanded in y around inf 84.1%

       \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(x \cdot y\right)}}{z}}{c} \]
   11. Step-by-step derivation

       1. *-commutative 84.1%

          \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \color{blue}{\left(y \cdot x\right)}}{z}}{c} \]

   12. Simplified 84.1%

       \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(y \cdot x\right)}}{z}}{c} \]

   if 1.19999999999999991e91 < b

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 80.0%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 80.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 78.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 78.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 78.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 78.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 78.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 73.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 73.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 56.0%

      \[\leadsto \color{blue}{y \cdot \left(\left(9 \cdot \frac{x}{c \cdot z} + \frac{b}{c \cdot \left(y \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot y}\right)} \]

   6. Taylor expanded in z around -inf 62.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.4%

         \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\left(-\frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}\right)} \]

      2. unsub-neg 62.4%

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z}} \]

      3. *-commutative 62.4%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      4. associate-/l* 68.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} - \frac{y \cdot \left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right)}{z} \]

      5. *-commutative 68.1%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \frac{\color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot y}}{z} \]

      6. associate-/l* 70.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} + -1 \cdot \frac{b}{c \cdot y}\right) \cdot \frac{y}{z}} \]

      7. mul-1-neg 70.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-9 \cdot \frac{x}{c} + \color{blue}{\left(-\frac{b}{c \cdot y}\right)}\right) \cdot \frac{y}{z} \]

      8. unsub-neg 70.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-9 \cdot \frac{x}{c} - \frac{b}{c \cdot y}\right)} \cdot \frac{y}{z} \]

      9. associate-*r/ 70.0%

         \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{\frac{-9 \cdot x}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      10. *-commutative 70.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\frac{\color{blue}{x \cdot -9}}{c} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      11. associate-/l* 70.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(\color{blue}{x \cdot \frac{-9}{c}} - \frac{b}{c \cdot y}\right) \cdot \frac{y}{z} \]

      12. associate-/r* 70.0%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \color{blue}{\frac{\frac{b}{c}}{y}}\right) \cdot \frac{y}{z} \]

   8. Simplified 70.0%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(x \cdot \frac{-9}{c} - \frac{\frac{b}{c}}{y}\right) \cdot \frac{y}{z}} \]

   9. Taylor expanded in x around 0 85.1%

      \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{-1 \cdot \frac{b}{c \cdot z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 85.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\left(-\frac{b}{c \cdot z}\right)} \]

       2. associate-/r* 82.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \left(-\color{blue}{\frac{\frac{b}{c}}{z}}\right) \]

       3. distribute-neg-frac2 82.1%

          \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]

   11. Simplified 82.1%

       \[\leadsto -4 \cdot \left(t \cdot \frac{a}{c}\right) - \color{blue}{\frac{\frac{b}{c}}{-z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) - \frac{\left(x \cdot y\right) \cdot -9}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-60} \lor \neg \left(z \leq 12.5\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \end{array} \end{array} \]

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 (<= z -1.9e-60) (not (<= z 12.5)))
    (* -4.0 (* t (/ a c_m)))
    (/ b (* z c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1.9e-60) || !(z <= 12.5)) {
		tmp = -4.0 * (t * (a / c_m));
	} else {
		tmp = b / (z * c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((z <= (-1.9d-60)) .or. (.not. (z <= 12.5d0))) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else
        tmp = b / (z * c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1.9e-60) || !(z <= 12.5)) {
		tmp = -4.0 * (t * (a / c_m));
	} else {
		tmp = b / (z * c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -1.9e-60) or not (z <= 12.5):
		tmp = -4.0 * (t * (a / c_m))
	else:
		tmp = b / (z * c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -1.9e-60) || !(z <= 12.5))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	else
		tmp = Float64(b / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -1.9e-60) || ~((z <= 12.5)))
		tmp = -4.0 * (t * (a / c_m));
	else
		tmp = b / (z * 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[Or[LessEqual[z, -1.9e-60], N[Not[LessEqual[z, 12.5]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999997e-60 or 12.5 < z

   1. Initial program 65.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 65.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 65.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 65.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 65.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 65.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 65.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 65.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 65.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 69.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-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 63.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 55.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 55.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 55.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 55.1%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.89999999999999997e-60 < z < 12.5

   1. Initial program 97.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 56.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 56.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-60} \lor \neg \left(z \leq 12.5\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 49.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-61}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq 0.002:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \end{array} \end{array} \]

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 (<= z -7.5e-61)
    (* -4.0 (* t (/ a c_m)))
    (if (<= z 0.002) (/ b (* z c_m)) (* -4.0 (/ (* t a) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -7.5e-61) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= 0.002) {
		tmp = b / (z * c_m);
	} else {
		tmp = -4.0 * ((t * a) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-7.5d-61)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= 0.002d0) then
        tmp = b / (z * c_m)
    else
        tmp = (-4.0d0) * ((t * a) / c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -7.5e-61) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= 0.002) {
		tmp = b / (z * c_m);
	} else {
		tmp = -4.0 * ((t * a) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -7.5e-61:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= 0.002:
		tmp = b / (z * c_m)
	else:
		tmp = -4.0 * ((t * a) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -7.5e-61)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= 0.002)
		tmp = Float64(b / Float64(z * c_m));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -7.5e-61)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= 0.002)
		tmp = b / (z * c_m);
	else
		tmp = -4.0 * ((t * a) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -7.5e-61], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.002], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000047e-61

   1. Initial program 66.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 66.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 66.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 66.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 67.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 67.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 67.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 67.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 67.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 70.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 70.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 50.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 50.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 53.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 53.1%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -7.50000000000000047e-61 < z < 2e-3

   1. Initial program 97.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 56.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 56.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 2e-3 < z

   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. +-commutative 63.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 63.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 63.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 60.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 60.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 68.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 63.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-61}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 0.002:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{elif}\;z \leq 1.75:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \end{array} \end{array} \]

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 (<= z -1.45e-60)
    (* -4.0 (* t (/ a c_m)))
    (if (<= z 1.75) (* b (/ 1.0 (* z c_m))) (* -4.0 (/ (* t a) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.45e-60) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= 1.75) {
		tmp = b * (1.0 / (z * c_m));
	} else {
		tmp = -4.0 * ((t * a) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-1.45d-60)) then
        tmp = (-4.0d0) * (t * (a / c_m))
    else if (z <= 1.75d0) then
        tmp = b * (1.0d0 / (z * c_m))
    else
        tmp = (-4.0d0) * ((t * a) / c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -1.45e-60) {
		tmp = -4.0 * (t * (a / c_m));
	} else if (z <= 1.75) {
		tmp = b * (1.0 / (z * c_m));
	} else {
		tmp = -4.0 * ((t * a) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -1.45e-60:
		tmp = -4.0 * (t * (a / c_m))
	elif z <= 1.75:
		tmp = b * (1.0 / (z * c_m))
	else:
		tmp = -4.0 * ((t * a) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -1.45e-60)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	elseif (z <= 1.75)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -1.45e-60)
		tmp = -4.0 * (t * (a / c_m));
	elseif (z <= 1.75)
		tmp = b * (1.0 / (z * c_m));
	else
		tmp = -4.0 * ((t * a) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -1.45e-60], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e-60

   1. Initial program 66.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 66.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 66.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 66.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 67.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 67.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 67.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 67.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 67.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 70.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 70.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \frac{a \cdot \left(t \cdot z\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}} \]

   6. Taylor expanded in a around inf 50.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 50.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 53.1%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 53.1%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]

   if -1.45e-60 < z < 1.75

   1. Initial program 97.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 97.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 97.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 97.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 96.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 96.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 96.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 96.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 96.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 93.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 93.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 56.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 56.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   8. Step-by-step derivation

      1. div-inv 57.6%

         \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   9. Applied egg-rr 57.6%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

   if 1.75 < z

   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. +-commutative 63.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 63.1%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 63.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 60.8%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 60.8%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 60.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 60.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 68.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 63.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 1.75:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 34.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{z \cdot c\_m} \end{array} \]

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 (* z 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) {
	return c_s * (b / (z * c_m));
}

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 / (z * c_m))
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 / (z * c_m));
}

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 / (z * c_m))

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(z * c_m)))
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 / (z * c_m));
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[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. +-commutative 82.3%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

   2. associate-+r- 82.3%

      \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

   3. *-commutative 82.3%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

   4. associate-*r* 82.1%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

   5. *-commutative 82.1%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

   6. associate-+r- 82.1%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

   7. +-commutative 82.1%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   8. associate-*l* 82.1%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   9. associate-*l* 82.0%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   10. *-commutative 82.0%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 82.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 40.4%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 40.4%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 40.4%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 40.4%

   \[\leadsto \frac{b}{z \cdot c} \]
9. Add Preprocessing

Developer target: 80.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024060 
(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)))