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

Percentage Accurate: 79.0% → 88.2%

Time: 16.6s

Alternatives: 19

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: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 240:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c\_m}\\ \mathbf{elif}\;c\_m \leq 7.5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(9, y \cdot \frac{\frac{x}{c\_m}}{z}, \mathsf{fma}\left(a \cdot \frac{t}{c\_m}, -4, \frac{b}{c\_m \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m} + \frac{x}{z} \cdot \left(\frac{b}{c\_m \cdot x} - -9 \cdot \frac{y}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 240.0)
    (/ (- (* -4.0 (* a t)) (/ (* x (- (* -9.0 y) (/ b x))) z)) c_m)
    (if (<= c_m 7.5e+131)
      (fma
       9.0
       (* y (/ (/ x c_m) z))
       (fma (* a (/ t c_m)) -4.0 (/ b (* c_m z))))
      (+
       (* a (/ (* -4.0 t) c_m))
       (* (/ x z) (- (/ b (* c_m x)) (* -9.0 (/ y c_m)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 240.0) {
		tmp = ((-4.0 * (a * t)) - ((x * ((-9.0 * y) - (b / x))) / z)) / c_m;
	} else if (c_m <= 7.5e+131) {
		tmp = fma(9.0, (y * ((x / c_m) / z)), fma((a * (t / c_m)), -4.0, (b / (c_m * z))));
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) + ((x / z) * ((b / (c_m * x)) - (-9.0 * (y / c_m))));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 240.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(x * Float64(Float64(-9.0 * y) - Float64(b / x))) / z)) / c_m);
	elseif (c_m <= 7.5e+131)
		tmp = fma(9.0, Float64(y * Float64(Float64(x / c_m) / z)), fma(Float64(a * Float64(t / c_m)), -4.0, Float64(b / Float64(c_m * z))));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) / c_m)) + Float64(Float64(x / z) * Float64(Float64(b / Float64(c_m * x)) - Float64(-9.0 * Float64(y / c_m)))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 240.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(-9.0 * y), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[c$95$m, 7.5e+131], N[(9.0 * N[(y * N[(N[(x / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(N[(b / N[(c$95$m * x), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if c < 240

   1. Initial program 82.9%

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

      1. associate-+l- 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*r* 85.1%

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

      4. *-commutative 85.1%

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

      5. associate-+l- 85.1%

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

      6. associate-*l* 85.1%

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

      7. associate-*l* 85.8%

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

      8. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 69.5%

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

   6. Taylor expanded in z around -inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r/ 73.6%

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

      4. associate-*r* 72.4%

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

      5. mul-1-neg 72.4%

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

      6. unsub-neg 72.4%

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

      7. associate-*r/ 72.4%

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

      8. *-commutative 72.4%

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

      9. associate-/l* 68.7%

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

      10. mul-1-neg 68.7%

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

      11. unsub-neg 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in c around 0 85.7%

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

   if 240 < c < 7.4999999999999995e131

   1. Initial program 71.8%

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

      1. associate-+l- 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-+l- 75.3%

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

      6. associate-*l* 75.3%

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

      7. associate-*l* 75.4%

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

      8. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in x around 0 86.0%

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

      1. associate--l+ 86.0%

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

      2. fma-define 85.9%

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

      3. *-commutative 85.9%

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

      4. *-commutative 85.9%

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

      5. associate-/l* 86.0%

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

      6. *-commutative 86.0%

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

      7. associate-/r* 86.1%

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

      8. cancel-sign-sub-inv 86.1%

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

      9. metadata-eval 86.1%

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

      10. +-commutative 86.1%

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

      11. *-commutative 86.1%

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

      12. fma-define 86.1%

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

      13. associate-/l* 92.6%

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

      14. *-commutative 92.6%

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

   7. Simplified 92.6%

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

   if 7.4999999999999995e131 < c

   1. Initial program 60.6%

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

      1. associate-+l- 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-*r* 60.7%

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

      4. *-commutative 60.7%

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

      5. associate-+l- 60.7%

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

      6. associate-*l* 60.6%

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

      7. associate-*l* 58.4%

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

      8. *-commutative 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in x around inf 54.4%

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

   6. Taylor expanded in z around -inf 78.9%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r/ 78.8%

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

      4. associate-*r* 85.4%

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

      5. mul-1-neg 85.4%

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

      6. unsub-neg 85.4%

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

      7. associate-*r/ 85.5%

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

      8. *-commutative 85.5%

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

      9. associate-/l* 75.0%

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

      10. mul-1-neg 75.0%

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

      11. unsub-neg 75.0%

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

   8. Simplified 75.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 240:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c}\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(9, y \cdot \frac{\frac{x}{c}}{z}, \mathsf{fma}\left(a \cdot \frac{t}{c}, -4, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} + \frac{x}{z} \cdot \left(\frac{b}{c \cdot x} - -9 \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c\_m}\\ t_2 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m} - x \cdot \frac{y \cdot \frac{-9}{c\_m}}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (- (* -4.0 (* a t)) (/ (* x (- (* -9.0 y) (/ b x))) z)) c_m))
        (t_2 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_2 (- INFINITY))
      t_1
      (if (<= t_2 -1e-13)
        t_2
        (if (<= t_2 2e+28)
          t_1
          (if (<= t_2 INFINITY)
            t_2
            (- (* a (/ (* -4.0 t) c_m)) (* x (/ (* y (/ -9.0 c_m)) z))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((-4.0 * (a * t)) - ((x * ((-9.0 * y) - (b / x))) / z)) / c_m;
	double t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-13) {
		tmp = t_2;
	} else if (t_2 <= 2e+28) {
		tmp = t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / 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 = ((-4.0 * (a * t)) - ((x * ((-9.0 * y) - (b / x))) / z)) / c_m;
	double t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-13) {
		tmp = t_2;
	} else if (t_2 <= 2e+28) {
		tmp = t_1;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((-4.0 * (a * t)) - ((x * ((-9.0 * y) - (b / x))) / z)) / c_m
	t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-13:
		tmp = t_2
	elif t_2 <= 2e+28:
		tmp = t_1
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(x * Float64(Float64(-9.0 * y) - Float64(b / x))) / z)) / c_m)
	t_2 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-13)
		tmp = t_2;
	elseif (t_2 <= 2e+28)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) / c_m)) - Float64(x * Float64(Float64(y * Float64(-9.0 / 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 = ((-4.0 * (a * t)) - ((x * ((-9.0 * y) - (b / x))) / z)) / c_m;
	t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-13)
		tmp = t_2;
	elseif (t_2 <= 2e+28)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(-9.0 * y), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-13], t$95$2, If[LessEqual[t$95$2, 2e+28], t$95$1, If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $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)) < -inf.0 or -1e-13 < (/.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)) < 1.99999999999999992e28

   1. Initial program 78.5%

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

      1. associate-+l- 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

      6. associate-*l* 79.7%

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

      7. associate-*l* 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around inf 75.4%

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

   6. Taylor expanded in z around -inf 79.1%

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

      1. associate-*r/ 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*r/ 79.0%

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

      4. associate-*r* 79.0%

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

      5. mul-1-neg 79.0%

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

      6. unsub-neg 79.0%

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

      7. associate-*r/ 79.0%

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

      8. *-commutative 79.0%

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

      9. associate-/l* 76.1%

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

      10. mul-1-neg 76.1%

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

      11. unsub-neg 76.1%

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

   8. Simplified 76.1%

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

   9. Taylor expanded in c around 0 92.0%

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

   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)) < -1e-13 or 1.99999999999999992e28 < (/.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 91.1%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 6.1%

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

      4. *-commutative 6.1%

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

      5. associate-+l- 6.1%

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

      6. associate-*l* 6.1%

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

      7. associate-*l* 6.1%

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

      8. *-commutative 6.1%

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

   3. Simplified 6.1%

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

   5. Taylor expanded in x around inf 29.1%

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

   6. Taylor expanded in z around -inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*r/ 68.3%

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

      4. associate-*r* 89.8%

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

      5. mul-1-neg 89.8%

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

      6. unsub-neg 89.8%

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

      7. associate-*r/ 89.8%

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

      8. *-commutative 89.8%

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

      9. associate-/l* 89.4%

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

      10. mul-1-neg 89.4%

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

      11. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   9. Taylor expanded in y around inf 54.4%

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

       1. *-commutative 54.4%

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

       2. associate-/l* 69.7%

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

       3. associate-*r* 69.7%

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

       4. *-commutative 69.7%

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

       5. associate-*r/ 69.7%

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

       6. associate-/r* 89.9%

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

       7. *-commutative 89.9%

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

       8. associate-/l* 89.9%

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

   11. Simplified 89.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -\infty:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -1 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 2 \cdot 10^{+28}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} - x \cdot \frac{y \cdot \frac{-9}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-146}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right)}{z}}{c\_m}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m} - x \cdot \frac{y \cdot \frac{-9}{c\_m}}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -1e-146)
      (/ (+ b (- (* x (* y 9.0)) (* (* a t) (* z 4.0)))) (* c_m z))
      (if (<= t_1 0.0)
        (/ (- (* -4.0 (* a t)) (/ (* -9.0 (* x y)) z)) c_m)
        (if (<= t_1 INFINITY)
          t_1
          (- (* a (/ (* -4.0 t) c_m)) (* x (/ (* y (/ -9.0 c_m)) z)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -1e-146) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / 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 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -1e-146) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_1 <= -1e-146:
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	elif t_1 <= 0.0:
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -1e-146)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(-9.0 * Float64(x * y)) / z)) / c_m);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) / c_m)) - Float64(x * Float64(Float64(y * Float64(-9.0 / c_m)) / z)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_1 <= -1e-146)
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e-146], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(-9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $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)) < -1.00000000000000003e-146

   1. Initial program 85.2%

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

      1. associate-+l- 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-*r* 84.2%

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

      4. *-commutative 84.2%

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

      5. associate-+l- 84.2%

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

      6. associate-*l* 84.3%

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

      7. associate-*l* 85.8%

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

      8. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   if -1.00000000000000003e-146 < (/.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 57.9%

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

      1. associate-+l- 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-*r* 61.5%

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

      4. *-commutative 61.5%

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

      5. associate-+l- 61.5%

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

      6. associate-*l* 61.5%

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

      7. associate-*l* 61.7%

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

      8. *-commutative 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in x around inf 69.1%

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

   6. Taylor expanded in z around -inf 91.9%

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

      1. associate-*r/ 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*r/ 91.7%

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

      4. associate-*r* 84.2%

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

      5. mul-1-neg 84.2%

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

      6. unsub-neg 84.2%

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

      7. associate-*r/ 84.2%

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

      8. *-commutative 84.2%

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

      9. associate-/l* 84.4%

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

      10. mul-1-neg 84.4%

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

      11. unsub-neg 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in c around 0 95.6%

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

   10. Taylor expanded in x around inf 80.6%

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

   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 91.1%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 6.1%

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

      4. *-commutative 6.1%

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

      5. associate-+l- 6.1%

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

      6. associate-*l* 6.1%

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

      7. associate-*l* 6.1%

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

      8. *-commutative 6.1%

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

   3. Simplified 6.1%

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

   5. Taylor expanded in x around inf 29.1%

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

   6. Taylor expanded in z around -inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*r/ 68.3%

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

      4. associate-*r* 89.8%

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

      5. mul-1-neg 89.8%

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

      6. unsub-neg 89.8%

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

      7. associate-*r/ 89.8%

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

      8. *-commutative 89.8%

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

      9. associate-/l* 89.4%

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

      10. mul-1-neg 89.4%

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

      11. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   9. Taylor expanded in y around inf 54.4%

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

       1. *-commutative 54.4%

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

       2. associate-/l* 69.7%

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

       3. associate-*r* 69.7%

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

       4. *-commutative 69.7%

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

       5. associate-*r/ 69.7%

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

       6. associate-/r* 89.9%

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

       7. *-commutative 89.9%

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

       8. associate-/l* 89.9%

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

   11. Simplified 89.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -1 \cdot 10^{-146}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} - x \cdot \frac{y \cdot \frac{-9}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+53}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+159} \lor \neg \left(y \leq 2 \cdot 10^{+207}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m} - -9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)}{c\_m}\\ \end{array} \end{array} \]

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 (<= y -9.8e-48)
    (* x (* (/ y c_m) (/ 9.0 z)))
    (if (<= y 1.55e+53)
      (+ (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z))
      (if (or (<= y 5.2e+159) (not (<= y 2e+207)))
        (- (* a (/ (* -4.0 t) c_m)) (* -9.0 (* x (/ y (* c_m z)))))
        (/ (* x (+ (* 9.0 (/ y z)) (/ b (* x 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 (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 1.55e+53) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else if ((y <= 5.2e+159) || !(y <= 2e+207)) {
		tmp = (a * ((-4.0 * t) / c_m)) - (-9.0 * (x * (y / (c_m * z))));
	} else {
		tmp = (x * ((9.0 * (y / z)) + (b / (x * 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 (y <= (-9.8d-48)) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else if (y <= 1.55d+53) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + ((b / c_m) / z)
    else if ((y <= 5.2d+159) .or. (.not. (y <= 2d+207))) then
        tmp = (a * (((-4.0d0) * t) / c_m)) - ((-9.0d0) * (x * (y / (c_m * z))))
    else
        tmp = (x * ((9.0d0 * (y / z)) + (b / (x * 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 (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 1.55e+53) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else if ((y <= 5.2e+159) || !(y <= 2e+207)) {
		tmp = (a * ((-4.0 * t) / c_m)) - (-9.0 * (x * (y / (c_m * z))));
	} else {
		tmp = (x * ((9.0 * (y / z)) + (b / (x * 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 y <= -9.8e-48:
		tmp = x * ((y / c_m) * (9.0 / z))
	elif y <= 1.55e+53:
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z)
	elif (y <= 5.2e+159) or not (y <= 2e+207):
		tmp = (a * ((-4.0 * t) / c_m)) - (-9.0 * (x * (y / (c_m * z))))
	else:
		tmp = (x * ((9.0 * (y / z)) + (b / (x * 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 (y <= -9.8e-48)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	elseif (y <= 1.55e+53)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(Float64(b / c_m) / z));
	elseif ((y <= 5.2e+159) || !(y <= 2e+207))
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) / c_m)) - Float64(-9.0 * Float64(x * Float64(y / Float64(c_m * z)))));
	else
		tmp = Float64(Float64(x * Float64(Float64(9.0 * Float64(y / z)) + Float64(b / Float64(x * 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 (y <= -9.8e-48)
		tmp = x * ((y / c_m) * (9.0 / z));
	elseif (y <= 1.55e+53)
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	elseif ((y <= 5.2e+159) || ~((y <= 2e+207)))
		tmp = (a * ((-4.0 * t) / c_m)) - (-9.0 * (x * (y / (c_m * z))));
	else
		tmp = (x * ((9.0 * (y / z)) + (b / (x * 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[y, -9.8e-48], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+53], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.2e+159], N[Not[LessEqual[y, 2e+207]], $MachinePrecision]], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -9.8000000000000005e-48

   1. Initial program 71.3%

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

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 72.9%

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

      8. *-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 x around inf 63.7%

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

      1. associate-*r* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in x around inf 48.6%

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

      1. associate-/l* 56.1%

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

      2. associate-*r* 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*r* 56.0%

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

      5. associate-*r/ 55.9%

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

      6. *-commutative 55.9%

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

      7. times-frac 60.7%

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

   10. Simplified 60.7%

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

   if -9.8000000000000005e-48 < y < 1.5500000000000001e53

   1. Initial program 81.8%

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

      1. associate-+l- 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r* 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-+l- 84.6%

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

      6. associate-*l* 84.6%

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

      7. associate-*l* 85.0%

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

      8. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around inf 69.4%

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

   6. Taylor expanded in z around inf 74.4%

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

   7. Taylor expanded in x around 0 74.9%

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

   if 1.5500000000000001e53 < y < 5.2000000000000001e159 or 2.0000000000000001e207 < y

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*r* 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-+l- 76.0%

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

      6. associate-*l* 76.0%

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

      7. associate-*l* 76.0%

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

      8. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around inf 57.0%

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

   6. Taylor expanded in z around -inf 72.9%

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

      1. associate-*r/ 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*r/ 72.9%

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

      4. associate-*r* 78.6%

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

      5. mul-1-neg 78.6%

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

      6. unsub-neg 78.6%

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

      7. associate-*r/ 78.6%

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

      8. *-commutative 78.6%

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

      9. associate-/l* 78.7%

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

      10. mul-1-neg 78.7%

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

      11. unsub-neg 78.7%

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

   8. Simplified 78.7%

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

   9. Taylor expanded in y around inf 74.7%

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

       1. associate-/l* 75.0%

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

   11. Simplified 75.0%

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

   if 5.2000000000000001e159 < y < 2.0000000000000001e207

   1. Initial program 77.8%

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

      1. associate-+l- 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r* 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-+l- 77.8%

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

      6. associate-*l* 77.6%

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

      7. associate-*l* 77.6%

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

      8. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around inf 77.8%

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

      1. associate-*r* 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in x around inf 78.1%

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

   9. Taylor expanded in c around 0 92.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+53}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+159} \lor \neg \left(y \leq 2 \cdot 10^{+207}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} - -9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{-4 \cdot t}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+52}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+159}:\\ \;\;\;\;t\_1 - -9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+207}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - x \cdot \frac{y \cdot \frac{-9}{c\_m}}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* a (/ (* -4.0 t) c_m))))
   (*
    c_s
    (if (<= y -9.8e-48)
      (* x (* (/ y c_m) (/ 9.0 z)))
      (if (<= y 8.8e+52)
        (+ (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z))
        (if (<= y 3.5e+159)
          (- t_1 (* -9.0 (* x (/ y (* c_m z)))))
          (if (<= y 1.8e+207)
            (/ (* x (+ (* 9.0 (/ y z)) (/ b (* x z)))) c_m)
            (- t_1 (* x (/ (* y (/ -9.0 c_m)) z))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = a * ((-4.0 * t) / c_m);
	double tmp;
	if (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 8.8e+52) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else if (y <= 3.5e+159) {
		tmp = t_1 - (-9.0 * (x * (y / (c_m * z))));
	} else if (y <= 1.8e+207) {
		tmp = (x * ((9.0 * (y / z)) + (b / (x * z)))) / c_m;
	} else {
		tmp = t_1 - (x * ((y * (-9.0 / c_m)) / z));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((-4.0d0) * t) / c_m)
    if (y <= (-9.8d-48)) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else if (y <= 8.8d+52) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + ((b / c_m) / z)
    else if (y <= 3.5d+159) then
        tmp = t_1 - ((-9.0d0) * (x * (y / (c_m * z))))
    else if (y <= 1.8d+207) then
        tmp = (x * ((9.0d0 * (y / z)) + (b / (x * z)))) / c_m
    else
        tmp = t_1 - (x * ((y * ((-9.0d0) / c_m)) / z))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = a * ((-4.0 * t) / c_m);
	double tmp;
	if (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 8.8e+52) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else if (y <= 3.5e+159) {
		tmp = t_1 - (-9.0 * (x * (y / (c_m * z))));
	} else if (y <= 1.8e+207) {
		tmp = (x * ((9.0 * (y / z)) + (b / (x * z)))) / c_m;
	} else {
		tmp = t_1 - (x * ((y * (-9.0 / c_m)) / z));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = a * ((-4.0 * t) / c_m)
	tmp = 0
	if y <= -9.8e-48:
		tmp = x * ((y / c_m) * (9.0 / z))
	elif y <= 8.8e+52:
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z)
	elif y <= 3.5e+159:
		tmp = t_1 - (-9.0 * (x * (y / (c_m * z))))
	elif y <= 1.8e+207:
		tmp = (x * ((9.0 * (y / z)) + (b / (x * z)))) / c_m
	else:
		tmp = t_1 - (x * ((y * (-9.0 / c_m)) / z))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(a * Float64(Float64(-4.0 * t) / c_m))
	tmp = 0.0
	if (y <= -9.8e-48)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	elseif (y <= 8.8e+52)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(Float64(b / c_m) / z));
	elseif (y <= 3.5e+159)
		tmp = Float64(t_1 - Float64(-9.0 * Float64(x * Float64(y / Float64(c_m * z)))));
	elseif (y <= 1.8e+207)
		tmp = Float64(Float64(x * Float64(Float64(9.0 * Float64(y / z)) + Float64(b / Float64(x * z)))) / c_m);
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(y * Float64(-9.0 / 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 = a * ((-4.0 * t) / c_m);
	tmp = 0.0;
	if (y <= -9.8e-48)
		tmp = x * ((y / c_m) * (9.0 / z));
	elseif (y <= 8.8e+52)
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	elseif (y <= 3.5e+159)
		tmp = t_1 - (-9.0 * (x * (y / (c_m * z))));
	elseif (y <= 1.8e+207)
		tmp = (x * ((9.0 * (y / z)) + (b / (x * z)))) / c_m;
	else
		tmp = t_1 - (x * ((y * (-9.0 / c_m)) / z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[y, -9.8e-48], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+52], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+159], N[(t$95$1 - N[(-9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+207], N[(N[(x * N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(y * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if y < -9.8000000000000005e-48

   1. Initial program 71.3%

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

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 72.9%

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

      8. *-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 x around inf 63.7%

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

      1. associate-*r* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in x around inf 48.6%

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

      1. associate-/l* 56.1%

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

      2. associate-*r* 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*r* 56.0%

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

      5. associate-*r/ 55.9%

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

      6. *-commutative 55.9%

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

      7. times-frac 60.7%

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

   10. Simplified 60.7%

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

   if -9.8000000000000005e-48 < y < 8.7999999999999999e52

   1. Initial program 81.8%

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

      1. associate-+l- 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r* 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-+l- 84.6%

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

      6. associate-*l* 84.6%

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

      7. associate-*l* 85.0%

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

      8. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around inf 69.4%

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

   6. Taylor expanded in z around inf 74.4%

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

   7. Taylor expanded in x around 0 74.9%

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

   if 8.7999999999999999e52 < y < 3.4999999999999999e159

   1. Initial program 76.3%

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

      1. associate-+l- 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 76.9%

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

      4. *-commutative 76.9%

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

      5. associate-+l- 76.9%

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

      6. associate-*l* 76.9%

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

      7. associate-*l* 76.8%

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

      8. *-commutative 76.8%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in x around inf 68.8%

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

   6. Taylor expanded in z around -inf 76.8%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r/ 76.8%

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

      4. associate-*r* 76.5%

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

      5. mul-1-neg 76.5%

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

      6. unsub-neg 76.5%

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

      7. associate-*r/ 76.4%

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

      8. *-commutative 76.4%

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

      9. associate-/l* 82.1%

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

      10. mul-1-neg 82.1%

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

      11. unsub-neg 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in y around inf 85.5%

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

       1. associate-/l* 85.6%

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

   11. Simplified 85.6%

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

   if 3.4999999999999999e159 < y < 1.80000000000000007e207

   1. Initial program 77.8%

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

      1. associate-+l- 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r* 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-+l- 77.8%

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

      6. associate-*l* 77.6%

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

      7. associate-*l* 77.6%

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

      8. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around inf 77.8%

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

      1. associate-*r* 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in x around inf 78.1%

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

   9. Taylor expanded in c around 0 92.1%

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

   if 1.80000000000000007e207 < y

   1. Initial program 75.1%

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

      1. associate-+l- 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-+l- 75.1%

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

      6. associate-*l* 75.1%

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

      7. associate-*l* 75.1%

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

      8. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around inf 44.4%

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

   6. Taylor expanded in z around -inf 68.9%

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

      1. associate-*r/ 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*r/ 68.9%

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

      4. associate-*r* 80.9%

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

      5. mul-1-neg 80.9%

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

      6. unsub-neg 80.9%

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

      7. associate-*r/ 80.9%

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

      8. *-commutative 80.9%

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

      9. associate-/l* 75.2%

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

      10. mul-1-neg 75.2%

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

      11. unsub-neg 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in y around inf 63.2%

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

       1. *-commutative 63.2%

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

       2. associate-/l* 63.8%

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

       3. associate-*r* 63.8%

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

       4. *-commutative 63.8%

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

       5. associate-*r/ 63.9%

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

       6. associate-/r* 63.9%

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

       7. *-commutative 63.9%

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

       8. associate-/l* 63.9%

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

   11. Simplified 63.9%

       \[\leadsto a \cdot \frac{t \cdot -4}{c} - \color{blue}{x \cdot \frac{y \cdot \frac{-9}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+52}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} - -9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+207}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} - x \cdot \frac{y \cdot \frac{-9}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 4.5 \cdot 10^{+48} \lor \neg \left(c\_m \leq 2.55 \cdot 10^{+190}\right) \land c\_m \leq 6 \cdot 10^{+221}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m} - x \cdot \frac{y \cdot \frac{-9}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= c_m 4.5e+48) (and (not (<= c_m 2.55e+190)) (<= c_m 6e+221)))
    (/ (+ b (- (* x (* y 9.0)) (* (* a t) (* z 4.0)))) (* c_m z))
    (- (* a (/ (* -4.0 t) c_m)) (* x (/ (* y (/ -9.0 c_m)) z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((c_m <= 4.5e+48) || (!(c_m <= 2.55e+190) && (c_m <= 6e+221))) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((c_m <= 4.5d+48) .or. (.not. (c_m <= 2.55d+190)) .and. (c_m <= 6d+221)) then
        tmp = (b + ((x * (y * 9.0d0)) - ((a * t) * (z * 4.0d0)))) / (c_m * z)
    else
        tmp = (a * (((-4.0d0) * t) / c_m)) - (x * ((y * ((-9.0d0) / c_m)) / z))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((c_m <= 4.5e+48) || (!(c_m <= 2.55e+190) && (c_m <= 6e+221))) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (c_m <= 4.5e+48) or (not (c_m <= 2.55e+190) and (c_m <= 6e+221)):
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	else:
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((c_m <= 4.5e+48) || (!(c_m <= 2.55e+190) && (c_m <= 6e+221)))
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) / c_m)) - Float64(x * Float64(Float64(y * Float64(-9.0 / 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 ((c_m <= 4.5e+48) || (~((c_m <= 2.55e+190)) && (c_m <= 6e+221)))
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	else
		tmp = (a * ((-4.0 * t) / c_m)) - (x * ((y * (-9.0 / c_m)) / z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[c$95$m, 4.5e+48], And[N[Not[LessEqual[c$95$m, 2.55e+190]], $MachinePrecision], LessEqual[c$95$m, 6e+221]]], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 4.49999999999999995e48 or 2.55000000000000015e190 < c < 6.0000000000000003e221

   1. Initial program 83.3%

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

      1. associate-+l- 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*r* 85.8%

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

      4. *-commutative 85.8%

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

      5. associate-+l- 85.8%

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

      6. associate-*l* 85.8%

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

      7. associate-*l* 86.9%

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

      8. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   if 4.49999999999999995e48 < c < 2.55000000000000015e190 or 6.0000000000000003e221 < c

   1. Initial program 57.6%

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

      1. associate-+l- 57.6%

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

      2. *-commutative 57.6%

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

      3. associate-*r* 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-+l- 57.7%

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

      6. associate-*l* 57.6%

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

      7. associate-*l* 54.2%

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

      8. *-commutative 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in x around inf 54.3%

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

   6. Taylor expanded in z around -inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r/ 76.0%

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

      4. associate-*r* 84.8%

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

      5. mul-1-neg 84.8%

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

      6. unsub-neg 84.8%

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

      7. associate-*r/ 84.9%

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

      8. *-commutative 84.9%

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

      9. associate-/l* 80.2%

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

      10. mul-1-neg 80.2%

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

      11. unsub-neg 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in y around inf 65.9%

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

       1. *-commutative 65.9%

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

       2. associate-/l* 71.8%

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

       3. associate-*r* 71.9%

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

       4. *-commutative 71.9%

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

       5. associate-*r/ 71.9%

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

       6. associate-/r* 70.1%

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

       7. *-commutative 70.1%

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

       8. associate-/l* 70.0%

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

   11. Simplified 70.0%

       \[\leadsto a \cdot \frac{t \cdot -4}{c} - \color{blue}{x \cdot \frac{y \cdot \frac{-9}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 4.5 \cdot 10^{+48} \lor \neg \left(c \leq 2.55 \cdot 10^{+190}\right) \land c \leq 6 \cdot 10^{+221}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} - x \cdot \frac{y \cdot \frac{-9}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+225}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{b}{c\_m \cdot x} + 9 \cdot \frac{y}{c\_m}\right)}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= y -9.8e-48)
    (* x (* (/ y c_m) (/ 9.0 z)))
    (if (<= y 1.5e+57)
      (+ (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z))
      (if (<= y 5.5e+225)
        (/ (- (* -4.0 (* a t)) (/ (* -9.0 (* x y)) z)) c_m)
        (/ (* x (+ (/ b (* c_m x)) (* 9.0 (/ y c_m)))) z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 1.5e+57) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else if (y <= 5.5e+225) {
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m;
	} else {
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (y <= (-9.8d-48)) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else if (y <= 1.5d+57) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + ((b / c_m) / z)
    else if (y <= 5.5d+225) then
        tmp = (((-4.0d0) * (a * t)) - (((-9.0d0) * (x * y)) / z)) / c_m
    else
        tmp = (x * ((b / (c_m * x)) + (9.0d0 * (y / c_m)))) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 1.5e+57) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else if (y <= 5.5e+225) {
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m;
	} else {
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if y <= -9.8e-48:
		tmp = x * ((y / c_m) * (9.0 / z))
	elif y <= 1.5e+57:
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z)
	elif y <= 5.5e+225:
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m
	else:
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (y <= -9.8e-48)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	elseif (y <= 1.5e+57)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(Float64(b / c_m) / z));
	elseif (y <= 5.5e+225)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(-9.0 * Float64(x * y)) / z)) / c_m);
	else
		tmp = Float64(Float64(x * Float64(Float64(b / Float64(c_m * x)) + Float64(9.0 * Float64(y / c_m)))) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (y <= -9.8e-48)
		tmp = x * ((y / c_m) * (9.0 / z));
	elseif (y <= 1.5e+57)
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	elseif (y <= 5.5e+225)
		tmp = ((-4.0 * (a * t)) - ((-9.0 * (x * y)) / z)) / c_m;
	else
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[y, -9.8e-48], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+57], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+225], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(-9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(x * N[(N[(b / N[(c$95$m * x), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -9.8000000000000005e-48

   1. Initial program 71.3%

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

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 72.9%

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

      8. *-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 x around inf 63.7%

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

      1. associate-*r* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in x around inf 48.6%

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

      1. associate-/l* 56.1%

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

      2. associate-*r* 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*r* 56.0%

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

      5. associate-*r/ 55.9%

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

      6. *-commutative 55.9%

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

      7. times-frac 60.7%

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

   10. Simplified 60.7%

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

   if -9.8000000000000005e-48 < y < 1.5e57

   1. Initial program 81.8%

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

      1. associate-+l- 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r* 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-+l- 84.6%

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

      6. associate-*l* 84.6%

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

      7. associate-*l* 85.0%

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

      8. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in x around inf 69.4%

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

   6. Taylor expanded in z around inf 74.4%

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

   7. Taylor expanded in x around 0 74.9%

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

   if 1.5e57 < y < 5.49999999999999985e225

   1. Initial program 71.8%

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

      1. associate-+l- 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-*r* 72.1%

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

      4. *-commutative 72.1%

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

      5. associate-+l- 72.1%

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

      6. associate-*l* 72.0%

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

      7. associate-*l* 72.0%

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

      8. *-commutative 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around inf 65.5%

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

   6. Taylor expanded in z around -inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 72.3%

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

      4. associate-*r* 77.5%

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

      5. mul-1-neg 77.5%

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

      6. unsub-neg 77.5%

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

      7. associate-*r/ 77.5%

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

      8. *-commutative 77.5%

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

      9. associate-/l* 82.9%

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

      10. mul-1-neg 82.9%

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

      11. unsub-neg 82.9%

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

   8. Simplified 82.9%

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

   9. Taylor expanded in c around 0 80.5%

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

   10. Taylor expanded in x around inf 77.6%

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

   if 5.49999999999999985e225 < y

   1. Initial program 90.6%

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

      1. associate-+l- 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*r* 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-+l- 90.6%

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

      6. associate-*l* 90.6%

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

      7. associate-*l* 90.6%

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

      8. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 54.8%

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

   6. Taylor expanded in z around 0 72.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+225}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{b}{c \cdot x} + 9 \cdot \frac{y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -9.475 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-231}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c_m) (/ x z)))))
   (*
    c_s
    (if (<= t -9.475e+155)
      (* -4.0 (* a (/ t c_m)))
      (if (<= t -1.05e+59)
        t_1
        (if (<= t -9.8e-231)
          (/ b (* c_m z))
          (if (<= t 3.5e-97) t_1 (* (/ a c_m) (* -4.0 t)))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((y / c_m) * (x / z));
	double tmp;
	if (t <= -9.475e+155) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -1.05e+59) {
		tmp = t_1;
	} else if (t <= -9.8e-231) {
		tmp = b / (c_m * z);
	} else if (t <= 3.5e-97) {
		tmp = t_1;
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / c_m) * (x / z))
    if (t <= (-9.475d+155)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= (-1.05d+59)) then
        tmp = t_1
    else if (t <= (-9.8d-231)) then
        tmp = b / (c_m * z)
    else if (t <= 3.5d-97) then
        tmp = t_1
    else
        tmp = (a / c_m) * ((-4.0d0) * t)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((y / c_m) * (x / z));
	double tmp;
	if (t <= -9.475e+155) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -1.05e+59) {
		tmp = t_1;
	} else if (t <= -9.8e-231) {
		tmp = b / (c_m * z);
	} else if (t <= 3.5e-97) {
		tmp = t_1;
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((y / c_m) * (x / z))
	tmp = 0
	if t <= -9.475e+155:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= -1.05e+59:
		tmp = t_1
	elif t <= -9.8e-231:
		tmp = b / (c_m * z)
	elif t <= 3.5e-97:
		tmp = t_1
	else:
		tmp = (a / c_m) * (-4.0 * t)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / z)))
	tmp = 0.0
	if (t <= -9.475e+155)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= -1.05e+59)
		tmp = t_1;
	elseif (t <= -9.8e-231)
		tmp = Float64(b / Float64(c_m * z));
	elseif (t <= 3.5e-97)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((y / c_m) * (x / z));
	tmp = 0.0;
	if (t <= -9.475e+155)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= -1.05e+59)
		tmp = t_1;
	elseif (t <= -9.8e-231)
		tmp = b / (c_m * z);
	elseif (t <= 3.5e-97)
		tmp = t_1;
	else
		tmp = (a / c_m) * (-4.0 * t);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t, -9.475e+155], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e+59], t$95$1, If[LessEqual[t, -9.8e-231], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-97], t$95$1, N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if t < -9.47500000000000055e155

   1. Initial program 62.6%

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

      1. associate-+l- 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*r* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-+l- 70.0%

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

      6. associate-*l* 70.0%

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

      7. associate-*l* 68.5%

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

      8. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/l* 68.4%

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

   7. Simplified 68.4%

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

   if -9.47500000000000055e155 < t < -1.04999999999999992e59 or -9.80000000000000007e-231 < t < 3.50000000000000019e-97

   1. Initial program 81.4%

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

      1. associate-+l- 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*r* 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-+l- 83.3%

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

      6. associate-*l* 83.3%

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

      7. associate-*l* 84.5%

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

      8. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in x around inf 78.3%

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

   6. Taylor expanded in z around -inf 85.4%

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

      1. associate-*r/ 85.4%

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

      2. *-commutative 85.4%

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

      3. associate-*r/ 85.3%

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

      4. associate-*r* 78.0%

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

      5. mul-1-neg 78.0%

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

      6. unsub-neg 78.0%

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

      7. associate-*r/ 78.0%

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

      8. *-commutative 78.0%

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

      9. associate-/l* 74.2%

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

      10. mul-1-neg 74.2%

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

      11. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   9. Taylor expanded in c around 0 82.9%

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

   10. Taylor expanded in x around inf 48.5%

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

       1. *-commutative 48.5%

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

       2. times-frac 48.5%

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

   12. Simplified 48.5%

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

   if -1.04999999999999992e59 < t < -9.80000000000000007e-231

   1. Initial program 88.0%

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

      1. associate-+l- 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-*r* 84.3%

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

      4. *-commutative 84.3%

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

      5. associate-+l- 84.3%

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

      6. associate-*l* 84.3%

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

      7. associate-*l* 88.0%

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

      8. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in b around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if 3.50000000000000019e-97 < t

   1. Initial program 75.9%

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

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-+l- 79.1%

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

      6. associate-*l* 79.1%

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

      7. associate-*l* 77.1%

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

      8. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around inf 67.2%

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

   6. Taylor expanded in z around -inf 75.1%

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

      1. associate-*r/ 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*r/ 75.1%

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

      4. associate-*r* 80.8%

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

      5. mul-1-neg 80.8%

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

      6. unsub-neg 80.8%

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

      7. associate-*r/ 80.9%

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

      8. *-commutative 80.9%

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

      9. associate-/l* 77.4%

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

      10. mul-1-neg 77.4%

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

      11. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

   9. Taylor expanded in c around 0 86.6%

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

   10. Taylor expanded in a around inf 43.2%

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

       1. associate-*r/ 43.2%

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

       2. associate-*r* 43.2%

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

       3. associate-*l/ 46.1%

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

       4. associate-*r/ 46.1%

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

       5. *-commutative 46.1%

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

       6. associate-*l* 46.1%

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

   12. Simplified 46.1%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.475 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-231}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-97}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -9.475 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+58}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-208}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -9.475e+155)
    (* -4.0 (* a (/ t c_m)))
    (if (<= t -6.8e+58)
      (* 9.0 (* (/ y c_m) (/ x z)))
      (if (<= t -3.9e-208)
        (/ b (* c_m z))
        (if (<= t 6e-95)
          (* x (* (/ y c_m) (/ 9.0 z)))
          (* (/ a c_m) (* -4.0 t))))))))

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 (t <= -9.475e+155) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -6.8e+58) {
		tmp = 9.0 * ((y / c_m) * (x / z));
	} else if (t <= -3.9e-208) {
		tmp = b / (c_m * z);
	} else if (t <= 6e-95) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 (t <= (-9.475d+155)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= (-6.8d+58)) then
        tmp = 9.0d0 * ((y / c_m) * (x / z))
    else if (t <= (-3.9d-208)) then
        tmp = b / (c_m * z)
    else if (t <= 6d-95) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else
        tmp = (a / c_m) * ((-4.0d0) * t)
    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 (t <= -9.475e+155) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= -6.8e+58) {
		tmp = 9.0 * ((y / c_m) * (x / z));
	} else if (t <= -3.9e-208) {
		tmp = b / (c_m * z);
	} else if (t <= 6e-95) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 t <= -9.475e+155:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= -6.8e+58:
		tmp = 9.0 * ((y / c_m) * (x / z))
	elif t <= -3.9e-208:
		tmp = b / (c_m * z)
	elif t <= 6e-95:
		tmp = x * ((y / c_m) * (9.0 / z))
	else:
		tmp = (a / c_m) * (-4.0 * t)
	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 (t <= -9.475e+155)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= -6.8e+58)
		tmp = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / z)));
	elseif (t <= -3.9e-208)
		tmp = Float64(b / Float64(c_m * z));
	elseif (t <= 6e-95)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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 (t <= -9.475e+155)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= -6.8e+58)
		tmp = 9.0 * ((y / c_m) * (x / z));
	elseif (t <= -3.9e-208)
		tmp = b / (c_m * z);
	elseif (t <= 6e-95)
		tmp = x * ((y / c_m) * (9.0 / z));
	else
		tmp = (a / c_m) * (-4.0 * t);
	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[t, -9.475e+155], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e+58], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-208], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-95], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -9.47500000000000055e155

   1. Initial program 62.6%

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

      1. associate-+l- 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*r* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-+l- 70.0%

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

      6. associate-*l* 70.0%

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

      7. associate-*l* 68.5%

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

      8. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-/l* 68.4%

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

   7. Simplified 68.4%

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

   if -9.47500000000000055e155 < t < -6.8000000000000001e58

   1. Initial program 66.2%

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

      1. associate-+l- 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-*r* 73.7%

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

      4. *-commutative 73.7%

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

      5. associate-+l- 73.7%

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

      6. associate-*l* 73.7%

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

      7. associate-*l* 70.0%

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

      8. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around inf 80.2%

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

   6. Taylor expanded in z around -inf 85.5%

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

      1. associate-*r/ 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*r/ 85.5%

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

      4. associate-*r* 74.5%

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

      5. mul-1-neg 74.5%

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

      6. unsub-neg 74.5%

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

      7. associate-*r/ 74.5%

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

      8. *-commutative 74.5%

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

      9. associate-/l* 74.2%

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

      10. mul-1-neg 74.2%

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

      11. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   9. Taylor expanded in c around 0 78.7%

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

   10. Taylor expanded in x around inf 42.8%

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

       1. *-commutative 42.8%

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

       2. times-frac 46.1%

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

   12. Simplified 46.1%

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

   if -6.8000000000000001e58 < t < -3.90000000000000004e-208

   1. Initial program 86.8%

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

      1. associate-+l- 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-+l- 82.6%

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

      6. associate-*l* 82.5%

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

      7. associate-*l* 86.8%

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

      8. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in b around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if -3.90000000000000004e-208 < t < 6e-95

   1. Initial program 90.2%

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

      1. associate-+l- 90.2%

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

      2. *-commutative 90.2%

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

      3. associate-*r* 89.3%

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

      4. *-commutative 89.3%

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

      5. associate-+l- 89.3%

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

      6. associate-*l* 89.3%

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

      7. associate-*l* 92.8%

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

      8. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around inf 81.1%

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

      1. associate-*r* 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in x around inf 52.4%

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

      1. associate-/l* 57.6%

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

      2. associate-*r* 57.6%

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

      3. *-commutative 57.6%

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

      4. associate-*r* 57.7%

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

      5. associate-*r/ 57.5%

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

      6. *-commutative 57.5%

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

      7. times-frac 55.9%

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

   10. Simplified 55.9%

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

   if 6e-95 < t

   1. Initial program 75.9%

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

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-*r* 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-+l- 79.1%

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

      6. associate-*l* 79.1%

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

      7. associate-*l* 77.1%

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

      8. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around inf 67.2%

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

   6. Taylor expanded in z around -inf 75.1%

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

      1. associate-*r/ 75.1%

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

      2. *-commutative 75.1%

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

      3. associate-*r/ 75.1%

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

      4. associate-*r* 80.8%

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

      5. mul-1-neg 80.8%

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

      6. unsub-neg 80.8%

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

      7. associate-*r/ 80.9%

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

      8. *-commutative 80.9%

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

      9. associate-/l* 77.4%

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

      10. mul-1-neg 77.4%

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

      11. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

   9. Taylor expanded in c around 0 86.6%

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

   10. Taylor expanded in a around inf 43.2%

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

       1. associate-*r/ 43.2%

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

       2. associate-*r* 43.2%

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

       3. associate-*l/ 46.1%

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

       4. associate-*r/ 46.1%

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

       5. *-commutative 46.1%

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

       6. associate-*l* 46.1%

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

   12. Simplified 46.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.475 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+58}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-208}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{x \cdot \left(\frac{b}{c\_m \cdot x} + 9 \cdot \frac{y}{c\_m}\right)}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.2e+46)
    (/ (+ b (- (* x (* y 9.0)) (* (* a t) (* z 4.0)))) (* c_m z))
    (+
     (* -4.0 (/ (* a t) c_m))
     (/ (* x (+ (/ b (* c_m x)) (* 9.0 (/ y c_m)))) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.2e+46) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else {
		tmp = (-4.0 * ((a * t) / c_m)) + ((x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (c_m <= 1.2d+46) then
        tmp = (b + ((x * (y * 9.0d0)) - ((a * t) * (z * 4.0d0)))) / (c_m * z)
    else
        tmp = ((-4.0d0) * ((a * t) / c_m)) + ((x * ((b / (c_m * x)) + (9.0d0 * (y / c_m)))) / z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.2e+46) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else {
		tmp = (-4.0 * ((a * t) / c_m)) + ((x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 1.2e+46:
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	else:
		tmp = (-4.0 * ((a * t) / c_m)) + ((x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.2e+46)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(Float64(x * Float64(Float64(b / Float64(c_m * x)) + Float64(9.0 * Float64(y / c_m)))) / z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 1.2e+46)
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	else
		tmp = (-4.0 * ((a * t) / c_m)) + ((x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.2e+46], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(b / N[(c$95$m * x), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.20000000000000004e46

   1. Initial program 83.0%

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

      1. associate-+l- 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-*r* 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-+l- 85.5%

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

      6. associate-*l* 85.5%

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

      7. associate-*l* 86.7%

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

      8. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   if 1.20000000000000004e46 < c

   1. Initial program 60.7%

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

      1. associate-+l- 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-*r* 60.7%

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

      4. *-commutative 60.7%

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

      5. associate-+l- 60.7%

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

      6. associate-*l* 60.7%

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

      7. associate-*l* 57.5%

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

      8. *-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in x around inf 57.6%

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

   6. Taylor expanded in z around inf 77.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{x \cdot \left(\frac{b}{c \cdot x} + 9 \cdot \frac{y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m} + \frac{x}{z} \cdot \left(\frac{b}{c\_m \cdot x} - -9 \cdot \frac{y}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.95e+46)
    (/ (+ b (- (* x (* y 9.0)) (* (* a t) (* z 4.0)))) (* c_m z))
    (+
     (* a (/ (* -4.0 t) c_m))
     (* (/ x z) (- (/ b (* c_m x)) (* -9.0 (/ y c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.95e+46) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) + ((x / z) * ((b / (c_m * x)) - (-9.0 * (y / c_m))));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (c_m <= 1.95d+46) then
        tmp = (b + ((x * (y * 9.0d0)) - ((a * t) * (z * 4.0d0)))) / (c_m * z)
    else
        tmp = (a * (((-4.0d0) * t) / c_m)) + ((x / z) * ((b / (c_m * x)) - ((-9.0d0) * (y / c_m))))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.95e+46) {
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	} else {
		tmp = (a * ((-4.0 * t) / c_m)) + ((x / z) * ((b / (c_m * x)) - (-9.0 * (y / c_m))));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if c_m <= 1.95e+46:
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z)
	else:
		tmp = (a * ((-4.0 * t) / c_m)) + ((x / z) * ((b / (c_m * x)) - (-9.0 * (y / c_m))))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.95e+46)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(y * 9.0)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(a * Float64(Float64(-4.0 * t) / c_m)) + Float64(Float64(x / z) * Float64(Float64(b / Float64(c_m * x)) - Float64(-9.0 * Float64(y / c_m)))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (c_m <= 1.95e+46)
		tmp = (b + ((x * (y * 9.0)) - ((a * t) * (z * 4.0)))) / (c_m * z);
	else
		tmp = (a * ((-4.0 * t) / c_m)) + ((x / z) * ((b / (c_m * x)) - (-9.0 * (y / c_m))));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.95e+46], N[(N[(b + N[(N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(N[(b / N[(c$95$m * x), $MachinePrecision]), $MachinePrecision] - N[(-9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.94999999999999997e46

   1. Initial program 83.0%

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

      1. associate-+l- 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-*r* 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-+l- 85.5%

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

      6. associate-*l* 85.5%

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

      7. associate-*l* 86.7%

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

      8. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   if 1.94999999999999997e46 < c

   1. Initial program 60.7%

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

      1. associate-+l- 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-*r* 60.7%

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

      4. *-commutative 60.7%

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

      5. associate-+l- 60.7%

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

      6. associate-*l* 60.7%

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

      7. associate-*l* 57.5%

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

      8. *-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in x around inf 57.6%

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

   6. Taylor expanded in z around -inf 77.8%

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

      1. associate-*r/ 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r/ 77.7%

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

      4. associate-*r* 85.8%

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

      5. mul-1-neg 85.8%

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

      6. unsub-neg 85.8%

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

      7. associate-*r/ 85.9%

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

      8. *-commutative 85.9%

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

      9. associate-/l* 79.9%

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

      10. mul-1-neg 79.9%

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

      11. unsub-neg 79.9%

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

   8. Simplified 79.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(y \cdot 9\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c} + \frac{x}{z} \cdot \left(\frac{b}{c \cdot x} - -9 \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{b}{c\_m \cdot x} + 9 \cdot \frac{y}{c\_m}\right)}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= y -9.8e-48)
    (* x (* (/ y c_m) (/ 9.0 z)))
    (if (<= y 2.8e+139)
      (+ (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z))
      (/ (* x (+ (/ b (* c_m x)) (* 9.0 (/ y c_m)))) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 2.8e+139) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else {
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (y <= (-9.8d-48)) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else if (y <= 2.8d+139) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + ((b / c_m) / z)
    else
        tmp = (x * ((b / (c_m * x)) + (9.0d0 * (y / c_m)))) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 2.8e+139) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else {
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if y <= -9.8e-48:
		tmp = x * ((y / c_m) * (9.0 / z))
	elif y <= 2.8e+139:
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z)
	else:
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (y <= -9.8e-48)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	elseif (y <= 2.8e+139)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(Float64(b / c_m) / z));
	else
		tmp = Float64(Float64(x * Float64(Float64(b / Float64(c_m * x)) + Float64(9.0 * Float64(y / c_m)))) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (y <= -9.8e-48)
		tmp = x * ((y / c_m) * (9.0 / z));
	elseif (y <= 2.8e+139)
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	else
		tmp = (x * ((b / (c_m * x)) + (9.0 * (y / c_m)))) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[y, -9.8e-48], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+139], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(b / N[(c$95$m * x), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -9.8000000000000005e-48

   1. Initial program 71.3%

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

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 72.9%

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

      4. *-commutative 72.9%

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

      5. associate-+l- 72.9%

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

      6. associate-*l* 72.9%

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

      7. associate-*l* 72.9%

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

      8. *-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 x around inf 63.7%

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

      1. associate-*r* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in x around inf 48.6%

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

      1. associate-/l* 56.1%

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

      2. associate-*r* 56.0%

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

      3. *-commutative 56.0%

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

      4. associate-*r* 56.0%

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

      5. associate-*r/ 55.9%

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

      6. *-commutative 55.9%

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

      7. times-frac 60.7%

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

   10. Simplified 60.7%

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

   if -9.8000000000000005e-48 < y < 2.7999999999999998e139

   1. Initial program 81.1%

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

      1. associate-+l- 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*r* 83.7%

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

      4. *-commutative 83.7%

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

      5. associate-+l- 83.7%

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

      6. associate-*l* 83.7%

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

      7. associate-*l* 84.0%

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

      8. *-commutative 84.0%

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

   3. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 69.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around inf 74.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{x \cdot \left(9 \cdot \frac{y}{c} + \frac{b}{c \cdot x}\right)}{z}} \]

   7. Taylor expanded in x around 0 72.3%

      \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if 2.7999999999999998e139 < y

   1. Initial program 77.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around 0 70.5%

      \[\leadsto \color{blue}{\frac{x \cdot \left(9 \cdot \frac{y}{c} + \frac{b}{c \cdot x}\right)}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{b}{c \cdot x} + 9 \cdot \frac{y}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c\_m} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m} + \frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{c\_m} \cdot \frac{x \cdot 9}{z}\\ \end{array} \end{array} \]

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 (<= y -9.8e-48)
    (* x (* (/ y c_m) (/ 9.0 z)))
    (if (<= y 1.15e+141)
      (+ (* -4.0 (/ (* a t) c_m)) (/ (/ b c_m) z))
      (* (/ y c_m) (/ (* x 9.0) 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 (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 1.15e+141) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else {
		tmp = (y / c_m) * ((x * 9.0) / 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 (y <= (-9.8d-48)) then
        tmp = x * ((y / c_m) * (9.0d0 / z))
    else if (y <= 1.15d+141) then
        tmp = ((-4.0d0) * ((a * t) / c_m)) + ((b / c_m) / z)
    else
        tmp = (y / c_m) * ((x * 9.0d0) / 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 (y <= -9.8e-48) {
		tmp = x * ((y / c_m) * (9.0 / z));
	} else if (y <= 1.15e+141) {
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	} else {
		tmp = (y / c_m) * ((x * 9.0) / 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 y <= -9.8e-48:
		tmp = x * ((y / c_m) * (9.0 / z))
	elif y <= 1.15e+141:
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z)
	else:
		tmp = (y / c_m) * ((x * 9.0) / 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 (y <= -9.8e-48)
		tmp = Float64(x * Float64(Float64(y / c_m) * Float64(9.0 / z)));
	elseif (y <= 1.15e+141)
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c_m)) + Float64(Float64(b / c_m) / z));
	else
		tmp = Float64(Float64(y / c_m) * Float64(Float64(x * 9.0) / 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 (y <= -9.8e-48)
		tmp = x * ((y / c_m) * (9.0 / z));
	elseif (y <= 1.15e+141)
		tmp = (-4.0 * ((a * t) / c_m)) + ((b / c_m) / z);
	else
		tmp = (y / c_m) * ((x * 9.0) / 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[y, -9.8e-48], N[(x * N[(N[(y / c$95$m), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+141], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / c$95$m), $MachinePrecision] * N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -9.8000000000000005e-48

   1. Initial program 71.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 72.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 72.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 72.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 72.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 72.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-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 x around inf 63.7%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 63.7%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 63.7%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   8. Taylor expanded in x around inf 48.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/l* 56.1%

         \[\leadsto 9 \cdot \color{blue}{\left(x \cdot \frac{y}{c \cdot z}\right)} \]

      2. associate-*r* 56.0%

         \[\leadsto \color{blue}{\left(9 \cdot x\right) \cdot \frac{y}{c \cdot z}} \]

      3. *-commutative 56.0%

         \[\leadsto \color{blue}{\left(x \cdot 9\right)} \cdot \frac{y}{c \cdot z} \]

      4. associate-*r* 56.0%

         \[\leadsto \color{blue}{x \cdot \left(9 \cdot \frac{y}{c \cdot z}\right)} \]

      5. associate-*r/ 55.9%

         \[\leadsto x \cdot \color{blue}{\frac{9 \cdot y}{c \cdot z}} \]

      6. *-commutative 55.9%

         \[\leadsto x \cdot \frac{9 \cdot y}{\color{blue}{z \cdot c}} \]

      7. times-frac 60.7%

         \[\leadsto x \cdot \color{blue}{\left(\frac{9}{z} \cdot \frac{y}{c}\right)} \]

   10. Simplified 60.7%

       \[\leadsto \color{blue}{x \cdot \left(\frac{9}{z} \cdot \frac{y}{c}\right)} \]

   if -9.8000000000000005e-48 < y < 1.1500000000000001e141

   1. Initial program 81.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 83.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 84.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 69.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around inf 74.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{x \cdot \left(9 \cdot \frac{y}{c} + \frac{b}{c \cdot x}\right)}{z}} \]

   7. Taylor expanded in x around 0 72.3%

      \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \frac{\color{blue}{\frac{b}{c}}}{z} \]

   if 1.1500000000000001e141 < y

   1. Initial program 77.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 77.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.7%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 60.7%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 60.7%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac 60.8%

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      4. associate-/l* 64.4%

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\left(x \cdot \frac{y}{c}\right)} \]

      5. associate-*r* 67.3%

         \[\leadsto \color{blue}{\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}} \]

   7. Simplified 67.3%

      \[\leadsto \color{blue}{\left(\frac{9}{z} \cdot x\right) \cdot \frac{y}{c}} \]
   8. Step-by-step derivation

      1. associate-*l/ 67.4%

         \[\leadsto \color{blue}{\frac{9 \cdot x}{z}} \cdot \frac{y}{c} \]

   9. Applied egg-rr 67.4%

      \[\leadsto \color{blue}{\frac{9 \cdot x}{z}} \cdot \frac{y}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-61}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -1.4e+148)
    (* -4.0 (* a (/ t c_m)))
    (if (<= t 1.95e-61)
      (/ (+ b (* y (* x 9.0))) (* c_m z))
      (* (/ a c_m) (* -4.0 t))))))

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 (t <= -1.4e+148) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= 1.95e-61) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 (t <= (-1.4d+148)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= 1.95d-61) then
        tmp = (b + (y * (x * 9.0d0))) / (c_m * z)
    else
        tmp = (a / c_m) * ((-4.0d0) * t)
    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 (t <= -1.4e+148) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= 1.95e-61) {
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 t <= -1.4e+148:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= 1.95e-61:
		tmp = (b + (y * (x * 9.0))) / (c_m * z)
	else:
		tmp = (a / c_m) * (-4.0 * t)
	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 (t <= -1.4e+148)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= 1.95e-61)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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 (t <= -1.4e+148)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= 1.95e-61)
		tmp = (b + (y * (x * 9.0))) / (c_m * z);
	else
		tmp = (a / c_m) * (-4.0 * t);
	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[t, -1.4e+148], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-61], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.3999999999999999e148

   1. Initial program 60.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 60.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 60.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 67.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 66.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 66.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 55.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 65.6%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 65.6%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -1.3999999999999999e148 < t < 1.95000000000000016e-61

   1. Initial program 84.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 84.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 84.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 84.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 84.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 86.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 86.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 74.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 74.6%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 74.6%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if 1.95000000000000016e-61 < t

   1. Initial program 75.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around -inf 74.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      2. *-commutative 74.0%

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4}}{c} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      3. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      4. associate-*r* 80.0%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      5. mul-1-neg 80.0%

         \[\leadsto a \cdot \left(t \cdot \frac{-4}{c}\right) + \color{blue}{\left(-\frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z}\right)} \]

      6. unsub-neg 80.0%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right) - \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z}} \]

      7. associate-*r/ 80.0%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} - \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      8. *-commutative 80.0%

         \[\leadsto a \cdot \frac{t \cdot -4}{c} - \frac{\color{blue}{\left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right) \cdot x}}{z} \]

      9. associate-/l* 77.5%

         \[\leadsto a \cdot \frac{t \cdot -4}{c} - \color{blue}{\left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right) \cdot \frac{x}{z}} \]

      10. mul-1-neg 77.5%

          \[\leadsto a \cdot \frac{t \cdot -4}{c} - \left(-9 \cdot \frac{y}{c} + \color{blue}{\left(-\frac{b}{c \cdot x}\right)}\right) \cdot \frac{x}{z} \]

      11. unsub-neg 77.5%

          \[\leadsto a \cdot \frac{t \cdot -4}{c} - \color{blue}{\left(-9 \cdot \frac{y}{c} - \frac{b}{c \cdot x}\right)} \cdot \frac{x}{z} \]

   8. Simplified 77.5%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c} - \left(-9 \cdot \frac{y}{c} - \frac{b}{c \cdot x}\right) \cdot \frac{x}{z}} \]

   9. Taylor expanded in c around 0 86.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c}} \]

   10. Taylor expanded in a around inf 43.9%

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   11. Step-by-step derivation

       1. associate-*r/ 43.9%

          \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

       2. associate-*r* 43.9%

          \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

       3. associate-*l/ 47.0%

          \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

       4. associate-*r/ 47.0%

          \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \cdot t \]

       5. *-commutative 47.0%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot -4\right)} \cdot t \]

       6. associate-*l* 47.0%

          \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(-4 \cdot t\right)} \]

   12. Simplified 47.0%

       \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(-4 \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+148}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-61}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-7} \lor \neg \left(z \leq 7.5 \cdot 10^{-46}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -4.8e-7) (not (<= z 7.5e-46)))
    (* -4.0 (/ (* a t) c_m))
    (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -4.8e-7) || !(z <= 7.5e-46)) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((z <= (-4.8d-7)) .or. (.not. (z <= 7.5d-46))) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -4.8e-7) || !(z <= 7.5e-46)) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -4.8e-7) or not (z <= 7.5e-46):
		tmp = -4.0 * ((a * t) / c_m)
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -4.8e-7) || !(z <= 7.5e-46))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -4.8e-7) || ~((z <= 7.5e-46)))
		tmp = -4.0 * ((a * t) / c_m);
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -4.8e-7], N[Not[LessEqual[z, 7.5e-46]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999957e-7 or 7.50000000000000027e-46 < z

   1. Initial program 64.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 64.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 64.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 67.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 69.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 52.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   if -4.79999999999999957e-7 < z < 7.50000000000000027e-46

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 95.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 95.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 96.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 93.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-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 b around inf 51.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 51.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-7} \lor \neg \left(z \leq 7.5 \cdot 10^{-46}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+56} \lor \neg \left(t \leq 2.5 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #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 (<= t -9e+56) (not (<= t 2.5e-60)))
    (* a (* t (/ -4.0 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 ((t <= -9e+56) || !(t <= 2.5e-60)) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if ((t <= (-9d+56)) .or. (.not. (t <= 2.5d-60))) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((t <= -9e+56) || !(t <= 2.5e-60)) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (t <= -9e+56) or not (t <= 2.5e-60):
		tmp = a * (t * (-4.0 / c_m))
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((t <= -9e+56) || !(t <= 2.5e-60))
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((t <= -9e+56) || ~((t <= 2.5e-60)))
		tmp = a * (t * (-4.0 / c_m));
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[t, -9e+56], N[Not[LessEqual[t, 2.5e-60]], $MachinePrecision]], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -9.0000000000000006e56 or 2.5000000000000001e-60 < t

   1. Initial program 71.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 76.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 73.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-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 x around inf 67.6%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around inf 47.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 47.6%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. *-commutative 47.6%

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4}}{c} \]

      3. associate-*r/ 47.5%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} \]

      4. associate-*r* 52.8%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]

   if -9.0000000000000006e56 < t < 2.5000000000000001e-60

   1. Initial program 88.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 85.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 89.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+56} \lor \neg \left(t \leq 2.5 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -6.8e+56)
    (* -4.0 (* a (/ t c_m)))
    (if (<= t 2.1e-67) (/ b (* c_m z)) (* a (* t (/ -4.0 c_m)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -6.8e+56) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= 2.1e-67) {
		tmp = b / (c_m * z);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (t <= (-6.8d+56)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= 2.1d-67) then
        tmp = b / (c_m * z)
    else
        tmp = a * (t * ((-4.0d0) / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (t <= -6.8e+56) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= 2.1e-67) {
		tmp = b / (c_m * z);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if t <= -6.8e+56:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= 2.1e-67:
		tmp = b / (c_m * z)
	else:
		tmp = a * (t * (-4.0 / c_m))
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (t <= -6.8e+56)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= 2.1e-67)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (t <= -6.8e+56)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= 2.1e-67)
		tmp = b / (c_m * z);
	else
		tmp = a * (t * (-4.0 / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[t, -6.8e+56], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-67], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -6.80000000000000002e56

   1. Initial program 64.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 64.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 64.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 69.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 57.7%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -6.80000000000000002e56 < t < 2.1000000000000002e-67

   1. Initial program 88.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 85.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 89.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 2.1000000000000002e-67 < t

   1. Initial program 75.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around inf 43.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*r/ 43.9%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

      2. *-commutative 43.9%

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4}}{c} \]

      3. associate-*r/ 43.8%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} \]

      4. associate-*r* 49.5%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]

   8. Simplified 49.5%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= t -1.35e+57)
    (* -4.0 (* a (/ t c_m)))
    (if (<= t 1.3e-62) (/ b (* c_m z)) (* (/ a c_m) (* -4.0 t))))))

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 (t <= -1.35e+57) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= 1.3e-62) {
		tmp = b / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 (t <= (-1.35d+57)) then
        tmp = (-4.0d0) * (a * (t / c_m))
    else if (t <= 1.3d-62) then
        tmp = b / (c_m * z)
    else
        tmp = (a / c_m) * ((-4.0d0) * t)
    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 (t <= -1.35e+57) {
		tmp = -4.0 * (a * (t / c_m));
	} else if (t <= 1.3e-62) {
		tmp = b / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 t <= -1.35e+57:
		tmp = -4.0 * (a * (t / c_m))
	elif t <= 1.3e-62:
		tmp = b / (c_m * z)
	else:
		tmp = (a / c_m) * (-4.0 * t)
	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 (t <= -1.35e+57)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c_m)));
	elseif (t <= 1.3e-62)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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 (t <= -1.35e+57)
		tmp = -4.0 * (a * (t / c_m));
	elseif (t <= 1.3e-62)
		tmp = b / (c_m * z);
	else
		tmp = (a / c_m) * (-4.0 * t);
	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[t, -1.35e+57], N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-62], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.3499999999999999e57

   1. Initial program 64.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 64.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 64.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 71.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 71.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 71.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 71.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 69.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 57.7%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right)} \cdot -4 \]

   7. Simplified 57.7%

      \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

   if -1.3499999999999999e57 < t < 1.3e-62

   1. Initial program 88.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 88.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 88.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 85.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 89.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 89.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 1.3e-62 < t

   1. Initial program 75.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. associate-*l* 79.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      7. associate-*l* 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.8%

      \[\leadsto \color{blue}{x \cdot \left(\left(9 \cdot \frac{y}{c \cdot z} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{a \cdot t}{c \cdot x}\right)} \]

   6. Taylor expanded in z around -inf 74.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      2. *-commutative 74.0%

         \[\leadsto \frac{\color{blue}{\left(a \cdot t\right) \cdot -4}}{c} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      3. associate-*r/ 74.0%

         \[\leadsto \color{blue}{\left(a \cdot t\right) \cdot \frac{-4}{c}} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      4. associate-*r* 80.0%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} + -1 \cdot \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      5. mul-1-neg 80.0%

         \[\leadsto a \cdot \left(t \cdot \frac{-4}{c}\right) + \color{blue}{\left(-\frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z}\right)} \]

      6. unsub-neg 80.0%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right) - \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z}} \]

      7. associate-*r/ 80.0%

         \[\leadsto a \cdot \color{blue}{\frac{t \cdot -4}{c}} - \frac{x \cdot \left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right)}{z} \]

      8. *-commutative 80.0%

         \[\leadsto a \cdot \frac{t \cdot -4}{c} - \frac{\color{blue}{\left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right) \cdot x}}{z} \]

      9. associate-/l* 77.5%

         \[\leadsto a \cdot \frac{t \cdot -4}{c} - \color{blue}{\left(-9 \cdot \frac{y}{c} + -1 \cdot \frac{b}{c \cdot x}\right) \cdot \frac{x}{z}} \]

      10. mul-1-neg 77.5%

          \[\leadsto a \cdot \frac{t \cdot -4}{c} - \left(-9 \cdot \frac{y}{c} + \color{blue}{\left(-\frac{b}{c \cdot x}\right)}\right) \cdot \frac{x}{z} \]

      11. unsub-neg 77.5%

          \[\leadsto a \cdot \frac{t \cdot -4}{c} - \color{blue}{\left(-9 \cdot \frac{y}{c} - \frac{b}{c \cdot x}\right)} \cdot \frac{x}{z} \]

   8. Simplified 77.5%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c} - \left(-9 \cdot \frac{y}{c} - \frac{b}{c \cdot x}\right) \cdot \frac{x}{z}} \]

   9. Taylor expanded in c around 0 86.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) - \frac{x \cdot \left(-9 \cdot y - \frac{b}{x}\right)}{z}}{c}} \]

   10. Taylor expanded in a around inf 43.9%

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   11. Step-by-step derivation

       1. associate-*r/ 43.9%

          \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right)}{c}} \]

       2. associate-*r* 43.9%

          \[\leadsto \frac{\color{blue}{\left(-4 \cdot a\right) \cdot t}}{c} \]

       3. associate-*l/ 47.0%

          \[\leadsto \color{blue}{\frac{-4 \cdot a}{c} \cdot t} \]

       4. associate-*r/ 47.0%

          \[\leadsto \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \cdot t \]

       5. *-commutative 47.0%

          \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot -4\right)} \cdot t \]

       6. associate-*l* 47.0%

          \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(-4 \cdot t\right)} \]

   12. Simplified 47.0%

       \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(-4 \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 78.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 78.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 80.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 80.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 80.2%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. associate-*l* 80.2%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   7. associate-*l* 80.4%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 80.4%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 80.4%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 36.2%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 36.2%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 36.2%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

8. Final simplification 36.2%

   \[\leadsto \frac{b}{c \cdot z} \]
9. Add Preprocessing

Developer target: 80.0% 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 2024078 
(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)))