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

Percentage Accurate: 79.2% → 88.4%

Time: 14.0s

Alternatives: 18

Speedup: 0.7×

• 37.6% 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: 79.2% 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: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* y (* 9.0 x)) (* a (* t (* z 4.0)))) b) (* z c))))
   (if (<= t_1 -4e+78)
     t_1
     (if (<= t_1 0.0)
       (* (/ 1.0 c) (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) z))
       (if (<= t_1 INFINITY)
         (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))
         (* a (/ (* -4.0 t) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	double tmp;
	if (t_1 <= -4e+78) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / c) * ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / z);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0)))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -4e+78)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / z));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+78], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $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)) < -4.00000000000000003e78

   1. Initial program 94.4%

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

   if -4.00000000000000003e78 < (/.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 74.0%

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

      1. +-commutative 74.0%

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

      2. associate-+r- 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-*r* 76.5%

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

      5. *-commutative 76.5%

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

      6. associate-+r- 76.5%

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

      7. +-commutative 76.5%

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

      8. associate-*l* 76.5%

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

      9. associate-*l* 77.0%

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

      10. *-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

   6. Applied egg-rr 93.8%

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

   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 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-+r- 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*r* 93.2%

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

      5. *-commutative 93.2%

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

      6. associate-+r- 93.2%

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

      7. +-commutative 93.2%

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

      8. associate-*l* 92.4%

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

      9. associate-*l* 95.7%

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

      10. *-commutative 95.7%

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

   3. Simplified 95.7%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 0.8%

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

      5. *-commutative 0.8%

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

      6. associate-+r- 0.8%

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

      7. +-commutative 0.8%

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

      8. associate-*l* 0.8%

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

      9. associate-*l* 0.8%

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

      10. *-commutative 0.8%

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

   3. Simplified 0.8%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. associate-/l* 71.8%

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

      2. associate-*r* 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 71.8%

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

      5. associate-*r/ 71.8%

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

      6. *-commutative 71.8%

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

   7. Simplified 71.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq -4 \cdot 10^{+78}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{z}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+128}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \mathsf{fma}\left(-4, a \cdot \frac{t}{y}, \mathsf{fma}\left(9, \frac{x}{z}, \frac{b}{z \cdot y}\right)\right)\right) \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2e+128)
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (if (<= z 1.6e+125)
     (/ (+ (- (* y (* 9.0 x)) (* a (* t (* z 4.0)))) b) (* z c))
     (*
      (* y (fma -4.0 (* a (/ t y)) (fma 9.0 (/ x z) (/ b (* z y)))))
      (/ 1.0 c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2e+128) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 1.6e+125) {
		tmp = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	} else {
		tmp = (y * fma(-4.0, (a * (t / y)), fma(9.0, (x / z), (b / (z * y))))) * (1.0 / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2e+128)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (z <= 1.6e+125)
		tmp = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0)))) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(y * fma(-4.0, Float64(a * Float64(t / y)), fma(9.0, Float64(x / z), Float64(b / Float64(z * y))))) * Float64(1.0 / c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2e+128], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.6e+125], N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(-4.0 * N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / z), $MachinePrecision] + N[(b / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000002e128

   1. Initial program 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-+r- 64.1%

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

      3. *-commutative 64.1%

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

      4. associate-*r* 59.7%

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

      5. *-commutative 59.7%

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

      6. associate-+r- 59.7%

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

      7. +-commutative 59.7%

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

      8. associate-*l* 59.7%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   6. Applied egg-rr 79.8%

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

   7. Taylor expanded in b around 0 71.2%

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

   8. Taylor expanded in a around 0 75.5%

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

   9. Taylor expanded in c around 0 82.2%

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

   if -2.0000000000000002e128 < z < 1.59999999999999992e125

   1. Initial program 95.4%

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

   if 1.59999999999999992e125 < z

   1. Initial program 52.0%

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

      1. +-commutative 52.0%

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

      2. associate-+r- 52.0%

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

      3. *-commutative 52.0%

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

      4. associate-*r* 52.2%

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

      5. *-commutative 52.2%

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

      6. associate-+r- 52.2%

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

      7. +-commutative 52.2%

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

      8. associate-*l* 52.2%

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

      9. associate-*l* 59.5%

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

      10. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   6. Applied egg-rr 58.2%

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

   7. Taylor expanded in y around inf 82.4%

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

      1. fma-define 82.4%

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

      2. associate-/l* 80.0%

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

      3. fma-define 80.0%

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

      4. *-commutative 80.0%

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

   9. Simplified 80.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+128}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+125}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \mathsf{fma}\left(-4, a \cdot \frac{t}{y}, \mathsf{fma}\left(9, \frac{x}{z}, \frac{b}{z \cdot y}\right)\right)\right) \cdot \frac{1}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-319}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* y (* 9.0 x)) (* a (* t (* z 4.0)))) b) (* z c))))
   (if (<= t_1 -5e-319)
     t_1
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* x y) c)) (/ b c))) z)
       (if (<= t_1 INFINITY)
         (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))
         (* a (/ (* -4.0 t) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-319) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-319) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c)
	tmp = 0
	if t_1 <= -5e-319:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z
	elif t_1 <= math.inf:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c)
	else:
		tmp = a * ((-4.0 * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0)))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-319)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e-319)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	elseif (t_1 <= Inf)
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	else
		tmp = a * ((-4.0 * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-319], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $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)) < -4.9999937e-319

   1. Initial program 94.3%

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

   if -4.9999937e-319 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 46.5%

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

      1. +-commutative 46.5%

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

      2. associate-+r- 46.5%

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

      3. *-commutative 46.5%

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

      4. associate-*r* 45.6%

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

      5. *-commutative 45.6%

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

      6. associate-+r- 45.6%

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

      7. +-commutative 45.6%

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

      8. associate-*l* 45.6%

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

      9. associate-*l* 46.5%

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

      10. *-commutative 46.5%

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

   3. Simplified 46.5%

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

   5. Taylor expanded in z around 0 99.4%

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

   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 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-+r- 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*r* 93.2%

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

      5. *-commutative 93.2%

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

      6. associate-+r- 93.2%

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

      7. +-commutative 93.2%

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

      8. associate-*l* 92.4%

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

      9. associate-*l* 95.7%

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

      10. *-commutative 95.7%

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

   3. Simplified 95.7%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 0.8%

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

      5. *-commutative 0.8%

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

      6. associate-+r- 0.8%

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

      7. +-commutative 0.8%

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

      8. associate-*l* 0.8%

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

      9. associate-*l* 0.8%

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

      10. *-commutative 0.8%

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

   3. Simplified 0.8%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. associate-/l* 71.8%

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

      2. associate-*r* 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 71.8%

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

      5. associate-*r/ 71.8%

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

      6. *-commutative 71.8%

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

   7. Simplified 71.8%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq -5 \cdot 10^{-319}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-319}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + 9 \cdot \frac{x \cdot y}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* y (* 9.0 x)) (* a (* t (* z 4.0)))) b) (* z c))))
   (if (<= t_1 -5e-319)
     t_1
     (if (<= t_1 0.0)
       (* t (+ (* -4.0 (/ a c)) (* 9.0 (/ (* x y) (* c (* z t))))))
       (if (<= t_1 INFINITY)
         (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))
         (* a (/ (* -4.0 t) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-319) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t * ((-4.0 * (a / c)) + (9.0 * ((x * y) / (c * (z * t)))));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-319) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t * ((-4.0 * (a / c)) + (9.0 * ((x * y) / (c * (z * t)))));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c)
	tmp = 0
	if t_1 <= -5e-319:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t * ((-4.0 * (a / c)) + (9.0 * ((x * y) / (c * (z * t)))))
	elif t_1 <= math.inf:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c)
	else:
		tmp = a * ((-4.0 * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0)))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-319)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t * Float64(Float64(-4.0 * Float64(a / c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(c * Float64(z * t))))));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e-319)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t * ((-4.0 * (a / c)) + (9.0 * ((x * y) / (c * (z * t)))));
	elseif (t_1 <= Inf)
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	else
		tmp = a * ((-4.0 * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-319], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t * N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $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)) < -4.9999937e-319

   1. Initial program 94.3%

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

   if -4.9999937e-319 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 46.5%

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

      1. +-commutative 46.5%

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

      2. associate-+r- 46.5%

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

      3. *-commutative 46.5%

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

      4. associate-*r* 45.6%

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

      5. *-commutative 45.6%

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

      6. associate-+r- 45.6%

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

      7. +-commutative 45.6%

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

      8. associate-*l* 45.6%

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

      9. associate-*l* 46.5%

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

      10. *-commutative 46.5%

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

   3. Simplified 46.5%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in b around 0 86.3%

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

   8. Taylor expanded in t around inf 79.9%

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

   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 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-+r- 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*r* 93.2%

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

      5. *-commutative 93.2%

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

      6. associate-+r- 93.2%

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

      7. +-commutative 93.2%

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

      8. associate-*l* 92.4%

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

      9. associate-*l* 95.7%

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

      10. *-commutative 95.7%

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

   3. Simplified 95.7%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-+r- 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 0.8%

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

      5. *-commutative 0.8%

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

      6. associate-+r- 0.8%

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

      7. +-commutative 0.8%

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

      8. associate-*l* 0.8%

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

      9. associate-*l* 0.8%

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

      10. *-commutative 0.8%

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

   3. Simplified 0.8%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. associate-/l* 71.8%

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

      2. associate-*r* 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 71.8%

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

      5. associate-*r/ 71.8%

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

      6. *-commutative 71.8%

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

   7. Simplified 71.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq -5 \cdot 10^{-319}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + 9 \cdot \frac{x \cdot y}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := 9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ t_3 := a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+82}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c)))
        (t_2 (* 9.0 (* x (/ (/ y z) c))))
        (t_3 (* a (/ (* -4.0 t) c))))
   (if (<= t -4.5e+158)
     (* t (* a (/ -4.0 c)))
     (if (<= t -2.5e+82)
       (* 9.0 (* x (/ y (* z c))))
       (if (<= t -9.5e+58)
         t_3
         (if (<= t -4.2e+27)
           t_1
           (if (<= t -2.1e-159)
             t_2
             (if (<= t 6.6e-289) t_1 (if (<= t 1.5e-66) t_2 t_3)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double t_2 = 9.0 * (x * ((y / z) / c));
	double t_3 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -4.5e+158) {
		tmp = t * (a * (-4.0 / c));
	} else if (t <= -2.5e+82) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t <= -9.5e+58) {
		tmp = t_3;
	} else if (t <= -4.2e+27) {
		tmp = t_1;
	} else if (t <= -2.1e-159) {
		tmp = t_2;
	} else if (t <= 6.6e-289) {
		tmp = t_1;
	} else if (t <= 1.5e-66) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b / (z * c)
    t_2 = 9.0d0 * (x * ((y / z) / c))
    t_3 = a * (((-4.0d0) * t) / c)
    if (t <= (-4.5d+158)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (t <= (-2.5d+82)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (t <= (-9.5d+58)) then
        tmp = t_3
    else if (t <= (-4.2d+27)) then
        tmp = t_1
    else if (t <= (-2.1d-159)) then
        tmp = t_2
    else if (t <= 6.6d-289) then
        tmp = t_1
    else if (t <= 1.5d-66) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double t_2 = 9.0 * (x * ((y / z) / c));
	double t_3 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -4.5e+158) {
		tmp = t * (a * (-4.0 / c));
	} else if (t <= -2.5e+82) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t <= -9.5e+58) {
		tmp = t_3;
	} else if (t <= -4.2e+27) {
		tmp = t_1;
	} else if (t <= -2.1e-159) {
		tmp = t_2;
	} else if (t <= 6.6e-289) {
		tmp = t_1;
	} else if (t <= 1.5e-66) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	t_2 = 9.0 * (x * ((y / z) / c))
	t_3 = a * ((-4.0 * t) / c)
	tmp = 0
	if t <= -4.5e+158:
		tmp = t * (a * (-4.0 / c))
	elif t <= -2.5e+82:
		tmp = 9.0 * (x * (y / (z * c)))
	elif t <= -9.5e+58:
		tmp = t_3
	elif t <= -4.2e+27:
		tmp = t_1
	elif t <= -2.1e-159:
		tmp = t_2
	elif t <= 6.6e-289:
		tmp = t_1
	elif t <= 1.5e-66:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	t_2 = Float64(9.0 * Float64(x * Float64(Float64(y / z) / c)))
	t_3 = Float64(a * Float64(Float64(-4.0 * t) / c))
	tmp = 0.0
	if (t <= -4.5e+158)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (t <= -2.5e+82)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t <= -9.5e+58)
		tmp = t_3;
	elseif (t <= -4.2e+27)
		tmp = t_1;
	elseif (t <= -2.1e-159)
		tmp = t_2;
	elseif (t <= 6.6e-289)
		tmp = t_1;
	elseif (t <= 1.5e-66)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	t_2 = 9.0 * (x * ((y / z) / c));
	t_3 = a * ((-4.0 * t) / c);
	tmp = 0.0;
	if (t <= -4.5e+158)
		tmp = t * (a * (-4.0 / c));
	elseif (t <= -2.5e+82)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (t <= -9.5e+58)
		tmp = t_3;
	elseif (t <= -4.2e+27)
		tmp = t_1;
	elseif (t <= -2.1e-159)
		tmp = t_2;
	elseif (t <= 6.6e-289)
		tmp = t_1;
	elseif (t <= 1.5e-66)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(N[(y / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+158], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e+82], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e+58], t$95$3, If[LessEqual[t, -4.2e+27], t$95$1, If[LessEqual[t, -2.1e-159], t$95$2, If[LessEqual[t, 6.6e-289], t$95$1, If[LessEqual[t, 1.5e-66], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.50000000000000046e158

   1. Initial program 77.2%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in a around inf 77.2%

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

   6. Taylor expanded in a around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-/l* 79.7%

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

      4. associate-*r* 79.7%

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

      5. *-commutative 79.7%

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

      6. associate-*r/ 79.7%

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

      7. *-commutative 79.7%

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

      8. associate-/l* 79.7%

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

   8. Simplified 79.7%

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

   if -4.50000000000000046e158 < t < -2.50000000000000008e82

   1. Initial program 55.3%

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

      1. +-commutative 55.3%

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

      2. associate-+r- 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*r* 55.3%

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

      5. *-commutative 55.3%

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

      6. associate-+r- 55.3%

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

      7. +-commutative 55.3%

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

      8. associate-*l* 55.3%

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

      9. associate-*l* 55.3%

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

      10. *-commutative 55.3%

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

   3. Simplified 55.3%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. associate-/l* 67.7%

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

      2. *-commutative 67.7%

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

   7. Simplified 67.7%

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

   if -2.50000000000000008e82 < t < -9.5000000000000002e58 or 1.5000000000000001e-66 < t

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-+r- 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*r* 78.2%

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

      5. *-commutative 78.2%

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

      6. associate-+r- 78.2%

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

      7. +-commutative 78.2%

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

      8. associate-*l* 78.2%

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

      9. associate-*l* 77.0%

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

      10. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 52.6%

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

      1. associate-/l* 58.7%

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

      2. associate-*r* 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*r* 58.7%

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

      5. associate-*r/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -9.5000000000000002e58 < t < -4.19999999999999989e27 or -2.0999999999999999e-159 < t < 6.59999999999999994e-289

   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. +-commutative 90.2%

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

      2. associate-+r- 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*r* 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-+r- 85.4%

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

      7. +-commutative 85.4%

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

      8. associate-*l* 85.5%

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

      9. associate-*l* 90.3%

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

      10. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in b around inf 52.9%

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

      1. *-commutative 52.9%

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

   7. Simplified 52.9%

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

   if -4.19999999999999989e27 < t < -2.0999999999999999e-159 or 6.59999999999999994e-289 < t < 1.5000000000000001e-66

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-+r- 92.5%

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

      3. *-commutative 92.5%

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

      4. associate-*r* 88.3%

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

      5. *-commutative 88.3%

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

      6. associate-+r- 88.3%

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

      7. +-commutative 88.3%

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

      8. associate-*l* 87.2%

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

      9. associate-*l* 92.5%

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

      10. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in x around inf 57.7%

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

      1. associate-/l* 57.7%

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

      2. associate-/r* 52.5%

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

   9. Simplified 52.5%

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

   10. Taylor expanded in y around 0 57.7%

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

       1. associate-/l/ 57.7%

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

   12. Simplified 57.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+82}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-159}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-66}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{if}\;t \leq -3 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* x (/ y (* z c)))))
        (t_2 (/ b (* z c)))
        (t_3 (* a (/ (* -4.0 t) c))))
   (if (<= t -3e+158)
     (* t (* a (/ -4.0 c)))
     (if (<= t -2.75e+82)
       t_1
       (if (<= t -2.4e+58)
         t_3
         (if (<= t -2.8e+20)
           t_2
           (if (<= t -1.32e-159)
             t_1
             (if (<= t -7.4e-289) t_2 (if (<= t 1.95e-66) t_1 t_3)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (x * (y / (z * c)));
	double t_2 = b / (z * c);
	double t_3 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -3e+158) {
		tmp = t * (a * (-4.0 / c));
	} else if (t <= -2.75e+82) {
		tmp = t_1;
	} else if (t <= -2.4e+58) {
		tmp = t_3;
	} else if (t <= -2.8e+20) {
		tmp = t_2;
	} else if (t <= -1.32e-159) {
		tmp = t_1;
	} else if (t <= -7.4e-289) {
		tmp = t_2;
	} else if (t <= 1.95e-66) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 9.0d0 * (x * (y / (z * c)))
    t_2 = b / (z * c)
    t_3 = a * (((-4.0d0) * t) / c)
    if (t <= (-3d+158)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (t <= (-2.75d+82)) then
        tmp = t_1
    else if (t <= (-2.4d+58)) then
        tmp = t_3
    else if (t <= (-2.8d+20)) then
        tmp = t_2
    else if (t <= (-1.32d-159)) then
        tmp = t_1
    else if (t <= (-7.4d-289)) then
        tmp = t_2
    else if (t <= 1.95d-66) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (x * (y / (z * c)));
	double t_2 = b / (z * c);
	double t_3 = a * ((-4.0 * t) / c);
	double tmp;
	if (t <= -3e+158) {
		tmp = t * (a * (-4.0 / c));
	} else if (t <= -2.75e+82) {
		tmp = t_1;
	} else if (t <= -2.4e+58) {
		tmp = t_3;
	} else if (t <= -2.8e+20) {
		tmp = t_2;
	} else if (t <= -1.32e-159) {
		tmp = t_1;
	} else if (t <= -7.4e-289) {
		tmp = t_2;
	} else if (t <= 1.95e-66) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * (x * (y / (z * c)))
	t_2 = b / (z * c)
	t_3 = a * ((-4.0 * t) / c)
	tmp = 0
	if t <= -3e+158:
		tmp = t * (a * (-4.0 / c))
	elif t <= -2.75e+82:
		tmp = t_1
	elif t <= -2.4e+58:
		tmp = t_3
	elif t <= -2.8e+20:
		tmp = t_2
	elif t <= -1.32e-159:
		tmp = t_1
	elif t <= -7.4e-289:
		tmp = t_2
	elif t <= 1.95e-66:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))))
	t_2 = Float64(b / Float64(z * c))
	t_3 = Float64(a * Float64(Float64(-4.0 * t) / c))
	tmp = 0.0
	if (t <= -3e+158)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (t <= -2.75e+82)
		tmp = t_1;
	elseif (t <= -2.4e+58)
		tmp = t_3;
	elseif (t <= -2.8e+20)
		tmp = t_2;
	elseif (t <= -1.32e-159)
		tmp = t_1;
	elseif (t <= -7.4e-289)
		tmp = t_2;
	elseif (t <= 1.95e-66)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * (x * (y / (z * c)));
	t_2 = b / (z * c);
	t_3 = a * ((-4.0 * t) / c);
	tmp = 0.0;
	if (t <= -3e+158)
		tmp = t * (a * (-4.0 / c));
	elseif (t <= -2.75e+82)
		tmp = t_1;
	elseif (t <= -2.4e+58)
		tmp = t_3;
	elseif (t <= -2.8e+20)
		tmp = t_2;
	elseif (t <= -1.32e-159)
		tmp = t_1;
	elseif (t <= -7.4e-289)
		tmp = t_2;
	elseif (t <= 1.95e-66)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+158], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e+82], t$95$1, If[LessEqual[t, -2.4e+58], t$95$3, If[LessEqual[t, -2.8e+20], t$95$2, If[LessEqual[t, -1.32e-159], t$95$1, If[LessEqual[t, -7.4e-289], t$95$2, If[LessEqual[t, 1.95e-66], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3e158

   1. Initial program 77.2%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in a around inf 77.2%

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

   6. Taylor expanded in a around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-/l* 79.7%

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

      4. associate-*r* 79.7%

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

      5. *-commutative 79.7%

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

      6. associate-*r/ 79.7%

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

      7. *-commutative 79.7%

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

      8. associate-/l* 79.7%

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

   8. Simplified 79.7%

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

   if -3e158 < t < -2.74999999999999998e82 or -2.8e20 < t < -1.32e-159 or -7.39999999999999977e-289 < t < 1.94999999999999991e-66

   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. +-commutative 88.2%

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

      2. associate-+r- 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*r* 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-+r- 83.8%

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

      7. +-commutative 83.8%

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

      8. associate-*l* 82.9%

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

      9. associate-*l* 88.2%

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

      10. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in x around inf 58.1%

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

      1. associate-/l* 58.1%

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

      2. *-commutative 58.1%

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

   7. Simplified 58.1%

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

   if -2.74999999999999998e82 < t < -2.4e58 or 1.94999999999999991e-66 < t

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-+r- 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-*r* 78.2%

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

      5. *-commutative 78.2%

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

      6. associate-+r- 78.2%

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

      7. +-commutative 78.2%

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

      8. associate-*l* 78.2%

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

      9. associate-*l* 77.0%

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

      10. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 52.6%

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

      1. associate-/l* 58.7%

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

      2. associate-*r* 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-*r* 58.7%

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

      5. associate-*r/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -2.4e58 < t < -2.8e20 or -1.32e-159 < t < -7.39999999999999977e-289

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. associate-+r- 93.7%

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

      3. *-commutative 93.7%

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

      4. associate-*r* 90.7%

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

      5. *-commutative 90.7%

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

      6. associate-+r- 90.7%

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

      7. +-commutative 90.7%

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

      8. associate-*l* 90.7%

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

      9. associate-*l* 93.8%

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

      10. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in b around inf 55.7%

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

      1. *-commutative 55.7%

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

   7. Simplified 55.7%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{+82}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-159}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-289}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{c}\right)}{z}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+75}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-188}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.32e+163)
   (/ (* 9.0 (* y (/ x c))) z)
   (if (<= x -6.2e+132)
     (* -4.0 (/ (* a t) c))
     (if (<= x -1.25e+75)
       (/ (* x (* 9.0 y)) (* z c))
       (if (<= x -2.65e-188)
         (* t (* a (/ -4.0 c)))
         (if (<= x 1.15e-67) (/ b (* z c)) (* 9.0 (* x (/ (/ y z) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.32e+163) {
		tmp = (9.0 * (y * (x / c))) / z;
	} else if (x <= -6.2e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -1.25e+75) {
		tmp = (x * (9.0 * y)) / (z * c);
	} else if (x <= -2.65e-188) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 1.15e-67) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (x <= (-1.32d+163)) then
        tmp = (9.0d0 * (y * (x / c))) / z
    else if (x <= (-6.2d+132)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (x <= (-1.25d+75)) then
        tmp = (x * (9.0d0 * y)) / (z * c)
    else if (x <= (-2.65d-188)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (x <= 1.15d-67) then
        tmp = b / (z * c)
    else
        tmp = 9.0d0 * (x * ((y / z) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.32e+163) {
		tmp = (9.0 * (y * (x / c))) / z;
	} else if (x <= -6.2e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -1.25e+75) {
		tmp = (x * (9.0 * y)) / (z * c);
	} else if (x <= -2.65e-188) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 1.15e-67) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.32e+163:
		tmp = (9.0 * (y * (x / c))) / z
	elif x <= -6.2e+132:
		tmp = -4.0 * ((a * t) / c)
	elif x <= -1.25e+75:
		tmp = (x * (9.0 * y)) / (z * c)
	elif x <= -2.65e-188:
		tmp = t * (a * (-4.0 / c))
	elif x <= 1.15e-67:
		tmp = b / (z * c)
	else:
		tmp = 9.0 * (x * ((y / z) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.32e+163)
		tmp = Float64(Float64(9.0 * Float64(y * Float64(x / c))) / z);
	elseif (x <= -6.2e+132)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (x <= -1.25e+75)
		tmp = Float64(Float64(x * Float64(9.0 * y)) / Float64(z * c));
	elseif (x <= -2.65e-188)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (x <= 1.15e-67)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / z) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.32e+163)
		tmp = (9.0 * (y * (x / c))) / z;
	elseif (x <= -6.2e+132)
		tmp = -4.0 * ((a * t) / c);
	elseif (x <= -1.25e+75)
		tmp = (x * (9.0 * y)) / (z * c);
	elseif (x <= -2.65e-188)
		tmp = t * (a * (-4.0 / c));
	elseif (x <= 1.15e-67)
		tmp = b / (z * c);
	else
		tmp = 9.0 * (x * ((y / z) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.32e+163], N[(N[(9.0 * N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -6.2e+132], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.25e+75], N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.65e-188], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-67], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(N[(y / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.31999999999999995e163

   1. Initial program 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-+r- 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*r* 78.5%

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

      5. *-commutative 78.5%

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

      6. associate-+r- 78.5%

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

      7. +-commutative 78.5%

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

      8. associate-*l* 78.5%

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

      9. associate-*l* 81.6%

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

      10. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 62.0%

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

      3. associate-*l/ 62.0%

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

      4. associate-/l* 55.9%

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

      5. associate-*l* 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 61.9%

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

   10. Simplified 61.9%

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

   if -1.31999999999999995e163 < x < -6.1999999999999995e132

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-+r- 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-+r- 81.5%

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

      7. +-commutative 81.5%

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

      8. associate-*l* 81.5%

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

      9. associate-*l* 91.2%

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

      10. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 50.9%

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

      1. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -6.1999999999999995e132 < x < -1.2500000000000001e75

   1. Initial program 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in a around inf 75.8%

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

   6. Taylor expanded in x around inf 84.4%

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

      1. associate-*r* 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r* 84.4%

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

   8. Simplified 84.4%

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

   if -1.2500000000000001e75 < x < -2.65000000000000007e-188

   1. Initial program 77.9%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in a around inf 74.2%

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

   6. Taylor expanded in a around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. *-commutative 46.7%

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

      3. associate-/l* 51.6%

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

      4. associate-*r* 51.6%

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

      5. *-commutative 51.6%

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

      6. associate-*r/ 51.6%

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

      7. *-commutative 51.6%

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

      8. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -2.65000000000000007e-188 < x < 1.15e-67

   1. Initial program 89.1%

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

      1. +-commutative 89.1%

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

      2. associate-+r- 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*r* 90.3%

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

      5. *-commutative 90.3%

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

      6. associate-+r- 90.3%

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

      7. +-commutative 90.3%

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

      8. associate-*l* 88.9%

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

      9. associate-*l* 90.3%

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

      10. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in b around inf 49.3%

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

      1. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   if 1.15e-67 < x

   1. Initial program 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-+r- 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*r* 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-+r- 78.4%

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

      7. +-commutative 78.4%

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

      8. associate-*l* 78.4%

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

      9. associate-*l* 82.3%

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

      10. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   6. Applied egg-rr 78.9%

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

   7. Taylor expanded in x around inf 54.0%

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

      1. associate-/l* 54.2%

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

      2. associate-/r* 55.7%

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

   9. Simplified 55.7%

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

   10. Taylor expanded in y around 0 54.2%

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

       1. associate-/l/ 55.6%

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

   12. Simplified 55.6%

       \[\leadsto 9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{z}}{c}}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{c}\right)}{z}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+75}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-188}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{c}\right)}{z}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-188}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-77}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.32e+163)
   (/ (* 9.0 (* y (/ x c))) z)
   (if (<= x -6.2e+132)
     (* -4.0 (/ (* a t) c))
     (if (<= x -1.5e+74)
       (* 9.0 (* x (/ y (* z c))))
       (if (<= x -1.95e-188)
         (* t (* a (/ -4.0 c)))
         (if (<= x 1.05e-77) (/ b (* z c)) (* 9.0 (* x (/ (/ y z) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.32e+163) {
		tmp = (9.0 * (y * (x / c))) / z;
	} else if (x <= -6.2e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -1.5e+74) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -1.95e-188) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 1.05e-77) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (x <= (-1.32d+163)) then
        tmp = (9.0d0 * (y * (x / c))) / z
    else if (x <= (-6.2d+132)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (x <= (-1.5d+74)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (x <= (-1.95d-188)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (x <= 1.05d-77) then
        tmp = b / (z * c)
    else
        tmp = 9.0d0 * (x * ((y / z) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.32e+163) {
		tmp = (9.0 * (y * (x / c))) / z;
	} else if (x <= -6.2e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -1.5e+74) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -1.95e-188) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 1.05e-77) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.32e+163:
		tmp = (9.0 * (y * (x / c))) / z
	elif x <= -6.2e+132:
		tmp = -4.0 * ((a * t) / c)
	elif x <= -1.5e+74:
		tmp = 9.0 * (x * (y / (z * c)))
	elif x <= -1.95e-188:
		tmp = t * (a * (-4.0 / c))
	elif x <= 1.05e-77:
		tmp = b / (z * c)
	else:
		tmp = 9.0 * (x * ((y / z) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.32e+163)
		tmp = Float64(Float64(9.0 * Float64(y * Float64(x / c))) / z);
	elseif (x <= -6.2e+132)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (x <= -1.5e+74)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (x <= -1.95e-188)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (x <= 1.05e-77)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / z) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.32e+163)
		tmp = (9.0 * (y * (x / c))) / z;
	elseif (x <= -6.2e+132)
		tmp = -4.0 * ((a * t) / c);
	elseif (x <= -1.5e+74)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (x <= -1.95e-188)
		tmp = t * (a * (-4.0 / c));
	elseif (x <= 1.05e-77)
		tmp = b / (z * c);
	else
		tmp = 9.0 * (x * ((y / z) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.32e+163], N[(N[(9.0 * N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -6.2e+132], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+74], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.95e-188], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-77], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(N[(y / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.31999999999999995e163

   1. Initial program 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-+r- 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*r* 78.5%

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

      5. *-commutative 78.5%

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

      6. associate-+r- 78.5%

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

      7. +-commutative 78.5%

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

      8. associate-*l* 78.5%

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

      9. associate-*l* 81.6%

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

      10. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 62.0%

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

      3. associate-*l/ 62.0%

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

      4. associate-/l* 55.9%

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

      5. associate-*l* 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 61.9%

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

   10. Simplified 61.9%

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

   if -1.31999999999999995e163 < x < -6.1999999999999995e132

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-+r- 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-+r- 81.5%

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

      7. +-commutative 81.5%

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

      8. associate-*l* 81.5%

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

      9. associate-*l* 91.2%

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

      10. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 50.9%

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

      1. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -6.1999999999999995e132 < x < -1.5e74

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-+r- 92.3%

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

      3. *-commutative 92.3%

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

      4. associate-*r* 92.3%

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

      5. *-commutative 92.3%

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

      6. associate-+r- 92.3%

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

      7. +-commutative 92.3%

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

      8. associate-*l* 92.3%

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

      9. associate-*l* 92.3%

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

      10. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 84.5%

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

      1. associate-/l* 84.5%

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

      2. *-commutative 84.5%

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

   7. Simplified 84.5%

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

   if -1.5e74 < x < -1.94999999999999988e-188

   1. Initial program 77.9%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in a around inf 74.2%

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

   6. Taylor expanded in a around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. *-commutative 46.7%

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

      3. associate-/l* 51.6%

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

      4. associate-*r* 51.6%

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

      5. *-commutative 51.6%

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

      6. associate-*r/ 51.6%

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

      7. *-commutative 51.6%

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

      8. associate-/l* 51.5%

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

   8. Simplified 51.5%

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

   if -1.94999999999999988e-188 < x < 1.05000000000000008e-77

   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. +-commutative 90.2%

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

      2. associate-+r- 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*r* 91.5%

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

      5. *-commutative 91.5%

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

      6. associate-+r- 91.5%

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

      7. +-commutative 91.5%

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

      8. associate-*l* 90.0%

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

      9. associate-*l* 91.4%

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

      10. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in b around inf 50.0%

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

      1. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   if 1.05000000000000008e-77 < x

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-+r- 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-*r* 77.6%

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

      5. *-commutative 77.6%

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

      6. associate-+r- 77.6%

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

      7. +-commutative 77.6%

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

      8. associate-*l* 77.7%

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

      9. associate-*l* 81.5%

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

      10. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   6. Applied egg-rr 79.4%

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

   7. Taylor expanded in x around inf 52.7%

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

      1. associate-/l* 53.0%

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

      2. associate-/r* 54.5%

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

   9. Simplified 54.5%

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

   10. Taylor expanded in y around 0 53.0%

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

       1. associate-/l/ 54.3%

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

   12. Simplified 54.3%

       \[\leadsto 9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{z}}{c}}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{c}\right)}{z}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-188}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-77}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+163}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-67}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.35e+163)
   (* 9.0 (/ (* y (/ x c)) z))
   (if (<= x -5.6e+132)
     (* -4.0 (/ (* a t) c))
     (if (<= x -3.5e+74)
       (* 9.0 (* x (/ y (* z c))))
       (if (<= x -1e-185)
         (* t (* a (/ -4.0 c)))
         (if (<= x 2e-67) (/ b (* z c)) (* 9.0 (* x (/ (/ y z) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.35e+163) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (x <= -5.6e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -3.5e+74) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -1e-185) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 2e-67) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (x <= (-1.35d+163)) then
        tmp = 9.0d0 * ((y * (x / c)) / z)
    else if (x <= (-5.6d+132)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (x <= (-3.5d+74)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (x <= (-1d-185)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (x <= 2d-67) then
        tmp = b / (z * c)
    else
        tmp = 9.0d0 * (x * ((y / z) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.35e+163) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (x <= -5.6e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -3.5e+74) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -1e-185) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 2e-67) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.35e+163:
		tmp = 9.0 * ((y * (x / c)) / z)
	elif x <= -5.6e+132:
		tmp = -4.0 * ((a * t) / c)
	elif x <= -3.5e+74:
		tmp = 9.0 * (x * (y / (z * c)))
	elif x <= -1e-185:
		tmp = t * (a * (-4.0 / c))
	elif x <= 2e-67:
		tmp = b / (z * c)
	else:
		tmp = 9.0 * (x * ((y / z) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.35e+163)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / c)) / z));
	elseif (x <= -5.6e+132)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (x <= -3.5e+74)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (x <= -1e-185)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (x <= 2e-67)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / z) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.35e+163)
		tmp = 9.0 * ((y * (x / c)) / z);
	elseif (x <= -5.6e+132)
		tmp = -4.0 * ((a * t) / c);
	elseif (x <= -3.5e+74)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (x <= -1e-185)
		tmp = t * (a * (-4.0 / c));
	elseif (x <= 2e-67)
		tmp = b / (z * c);
	else
		tmp = 9.0 * (x * ((y / z) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.35e+163], N[(9.0 * N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e+132], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e+74], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-185], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-67], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(N[(y / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.35e163

   1. Initial program 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-+r- 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*r* 78.5%

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

      5. *-commutative 78.5%

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

      6. associate-+r- 78.5%

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

      7. +-commutative 78.5%

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

      8. associate-*l* 78.5%

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

      9. associate-*l* 81.6%

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

      10. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   6. Applied egg-rr 76.5%

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

   7. Taylor expanded in x around inf 59.1%

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

      1. associate-/r* 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-/l* 61.8%

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

   9. Simplified 61.8%

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

   if -1.35e163 < x < -5.5999999999999998e132

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-+r- 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-+r- 81.5%

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

      7. +-commutative 81.5%

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

      8. associate-*l* 81.5%

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

      9. associate-*l* 91.2%

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

      10. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 50.9%

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

      1. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -5.5999999999999998e132 < x < -3.50000000000000014e74

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-+r- 92.3%

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

      3. *-commutative 92.3%

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

      4. associate-*r* 92.3%

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

      5. *-commutative 92.3%

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

      6. associate-+r- 92.3%

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

      7. +-commutative 92.3%

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

      8. associate-*l* 92.3%

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

      9. associate-*l* 92.3%

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

      10. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 84.5%

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

      1. associate-/l* 84.5%

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

      2. *-commutative 84.5%

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

   7. Simplified 84.5%

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

   if -3.50000000000000014e74 < x < -9.9999999999999999e-186

   1. Initial program 77.5%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in a around inf 73.8%

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

   6. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. *-commutative 45.8%

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

      3. associate-/l* 50.8%

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

      4. associate-*r* 50.7%

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

      5. *-commutative 50.7%

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

      6. associate-*r/ 50.7%

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

      7. *-commutative 50.7%

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

      8. associate-/l* 50.7%

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

   8. Simplified 50.7%

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

   if -9.9999999999999999e-186 < x < 1.99999999999999989e-67

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-+r- 89.2%

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

      3. *-commutative 89.2%

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

      4. associate-*r* 90.5%

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

      5. *-commutative 90.5%

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

      6. associate-+r- 90.5%

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

      7. +-commutative 90.5%

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

      8. associate-*l* 89.1%

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

      9. associate-*l* 90.4%

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

      10. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in b around inf 48.6%

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

      1. *-commutative 48.6%

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

   7. Simplified 48.6%

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

   if 1.99999999999999989e-67 < x

   1. Initial program 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-+r- 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*r* 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-+r- 78.4%

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

      7. +-commutative 78.4%

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

      8. associate-*l* 78.4%

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

      9. associate-*l* 82.3%

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

      10. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   6. Applied egg-rr 78.9%

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

   7. Taylor expanded in x around inf 54.0%

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

      1. associate-/l* 54.2%

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

      2. associate-/r* 55.7%

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

   9. Simplified 55.7%

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

   10. Taylor expanded in y around 0 54.2%

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

       1. associate-/l/ 55.6%

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

   12. Simplified 55.6%

       \[\leadsto 9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{z}}{c}}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+163}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-67}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+75}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-68}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.32e+163)
   (* 9.0 (* (/ x c) (/ y z)))
   (if (<= x -6.2e+132)
     (* -4.0 (/ (* a t) c))
     (if (<= x -2.15e+75)
       (* 9.0 (* x (/ y (* z c))))
       (if (<= x -3.2e-186)
         (* t (* a (/ -4.0 c)))
         (if (<= x 4.7e-68) (/ b (* z c)) (* 9.0 (* x (/ (/ y z) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.32e+163) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (x <= -6.2e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -2.15e+75) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -3.2e-186) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 4.7e-68) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (x <= (-1.32d+163)) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (x <= (-6.2d+132)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (x <= (-2.15d+75)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (x <= (-3.2d-186)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (x <= 4.7d-68) then
        tmp = b / (z * c)
    else
        tmp = 9.0d0 * (x * ((y / z) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.32e+163) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (x <= -6.2e+132) {
		tmp = -4.0 * ((a * t) / c);
	} else if (x <= -2.15e+75) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -3.2e-186) {
		tmp = t * (a * (-4.0 / c));
	} else if (x <= 4.7e-68) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * (x * ((y / z) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.32e+163:
		tmp = 9.0 * ((x / c) * (y / z))
	elif x <= -6.2e+132:
		tmp = -4.0 * ((a * t) / c)
	elif x <= -2.15e+75:
		tmp = 9.0 * (x * (y / (z * c)))
	elif x <= -3.2e-186:
		tmp = t * (a * (-4.0 / c))
	elif x <= 4.7e-68:
		tmp = b / (z * c)
	else:
		tmp = 9.0 * (x * ((y / z) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.32e+163)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (x <= -6.2e+132)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (x <= -2.15e+75)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (x <= -3.2e-186)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (x <= 4.7e-68)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(x * Float64(Float64(y / z) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.32e+163)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (x <= -6.2e+132)
		tmp = -4.0 * ((a * t) / c);
	elseif (x <= -2.15e+75)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (x <= -3.2e-186)
		tmp = t * (a * (-4.0 / c));
	elseif (x <= 4.7e-68)
		tmp = b / (z * c);
	else
		tmp = 9.0 * (x * ((y / z) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.32e+163], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e+132], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.15e+75], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-186], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e-68], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(N[(y / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.31999999999999995e163

   1. Initial program 81.6%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in a around inf 70.0%

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

   6. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. *-commutative 59.1%

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

      3. times-frac 61.8%

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

   8. Simplified 61.8%

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

   if -1.31999999999999995e163 < x < -6.1999999999999995e132

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-+r- 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-+r- 81.5%

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

      7. +-commutative 81.5%

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

      8. associate-*l* 81.5%

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

      9. associate-*l* 91.2%

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

      10. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf 50.9%

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

      1. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -6.1999999999999995e132 < x < -2.1500000000000001e75

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-+r- 92.3%

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

      3. *-commutative 92.3%

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

      4. associate-*r* 92.3%

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

      5. *-commutative 92.3%

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

      6. associate-+r- 92.3%

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

      7. +-commutative 92.3%

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

      8. associate-*l* 92.3%

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

      9. associate-*l* 92.3%

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

      10. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 84.5%

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

      1. associate-/l* 84.5%

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

      2. *-commutative 84.5%

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

   7. Simplified 84.5%

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

   if -2.1500000000000001e75 < x < -3.2e-186

   1. Initial program 77.5%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in a around inf 73.8%

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

   6. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. *-commutative 45.8%

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

      3. associate-/l* 50.8%

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

      4. associate-*r* 50.7%

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

      5. *-commutative 50.7%

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

      6. associate-*r/ 50.7%

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

      7. *-commutative 50.7%

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

      8. associate-/l* 50.7%

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

   8. Simplified 50.7%

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

   if -3.2e-186 < x < 4.69999999999999988e-68

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-+r- 89.2%

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

      3. *-commutative 89.2%

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

      4. associate-*r* 90.5%

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

      5. *-commutative 90.5%

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

      6. associate-+r- 90.5%

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

      7. +-commutative 90.5%

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

      8. associate-*l* 89.1%

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

      9. associate-*l* 90.4%

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

      10. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in b around inf 48.6%

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

      1. *-commutative 48.6%

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

   7. Simplified 48.6%

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

   if 4.69999999999999988e-68 < x

   1. Initial program 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-+r- 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*r* 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-+r- 78.4%

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

      7. +-commutative 78.4%

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

      8. associate-*l* 78.4%

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

      9. associate-*l* 82.3%

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

      10. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   6. Applied egg-rr 78.9%

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

   7. Taylor expanded in x around inf 54.0%

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

      1. associate-/l* 54.2%

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

      2. associate-/r* 55.7%

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

   9. Simplified 55.7%

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

   10. Taylor expanded in y around 0 54.2%

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

       1. associate-/l/ 55.6%

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

   12. Simplified 55.6%

       \[\leadsto 9 \cdot \left(x \cdot \color{blue}{\frac{\frac{y}{z}}{c}}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+163}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{+75}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-186}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-68}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+127}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x \cdot y}{z \cdot c} + \frac{b}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5.5e+127)
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (if (<= z 2.25e+127)
     (/ (+ (- (* y (* 9.0 x)) (* a (* t (* z 4.0)))) b) (* z c))
     (- (+ (* 9.0 (/ (* x y) (* z c))) (/ b (* z c))) (* 4.0 (/ (* a t) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.5e+127) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 2.25e+127) {
		tmp = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	} else {
		tmp = ((9.0 * ((x * y) / (z * c))) + (b / (z * c))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-5.5d+127)) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else if (z <= 2.25d+127) then
        tmp = (((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0)))) + b) / (z * c)
    else
        tmp = ((9.0d0 * ((x * y) / (z * c))) + (b / (z * c))) - (4.0d0 * ((a * t) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.5e+127) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 2.25e+127) {
		tmp = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	} else {
		tmp = ((9.0 * ((x * y) / (z * c))) + (b / (z * c))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -5.5e+127:
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	elif z <= 2.25e+127:
		tmp = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c)
	else:
		tmp = ((9.0 * ((x * y) / (z * c))) + (b / (z * c))) - (4.0 * ((a * t) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.5e+127)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (z <= 2.25e+127)
		tmp = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0)))) + b) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / Float64(z * c))) + Float64(b / Float64(z * c))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -5.5e+127)
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	elseif (z <= 2.25e+127)
		tmp = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	else
		tmp = ((9.0 * ((x * y) / (z * c))) + (b / (z * c))) - (4.0 * ((a * t) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -5.5e+127], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.25e+127], N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000041e127

   1. Initial program 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-+r- 64.1%

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

      3. *-commutative 64.1%

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

      4. associate-*r* 59.7%

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

      5. *-commutative 59.7%

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

      6. associate-+r- 59.7%

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

      7. +-commutative 59.7%

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

      8. associate-*l* 59.7%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   6. Applied egg-rr 79.8%

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

   7. Taylor expanded in b around 0 71.2%

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

   8. Taylor expanded in a around 0 75.5%

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

   9. Taylor expanded in c around 0 82.2%

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

   if -5.50000000000000041e127 < z < 2.25000000000000017e127

   1. Initial program 95.4%

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

   if 2.25000000000000017e127 < z

   1. Initial program 50.7%

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

      1. +-commutative 50.7%

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

      2. associate-+r- 50.7%

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

      3. *-commutative 50.7%

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

      4. associate-*r* 50.9%

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

      5. *-commutative 50.9%

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

      6. associate-+r- 50.9%

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

      7. +-commutative 50.9%

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

      8. associate-*l* 50.9%

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

      9. associate-*l* 58.4%

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

      10. *-commutative 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 0 81.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+127}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \frac{x \cdot y}{z \cdot c} + \frac{b}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+188}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.7e+127)
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (if (<= z 7.8e+188)
     (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))
     (* t (+ (* -4.0 (/ a c)) (/ b (* c (* z t))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.7e+127) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 7.8e+188) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.7d+127)) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else if (z <= 7.8d+188) then
        tmp = (b + ((x * (9.0d0 * y)) - ((a * t) * (z * 4.0d0)))) / (z * c)
    else
        tmp = t * (((-4.0d0) * (a / c)) + (b / (c * (z * t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.7e+127) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 7.8e+188) {
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	} else {
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.7e+127:
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	elif z <= 7.8e+188:
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c)
	else:
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.7e+127)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (z <= 7.8e+188)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	else
		tmp = Float64(t * Float64(Float64(-4.0 * Float64(a / c)) + Float64(b / Float64(c * Float64(z * t)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.7e+127)
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	elseif (z <= 7.8e+188)
		tmp = (b + ((x * (9.0 * y)) - ((a * t) * (z * 4.0)))) / (z * c);
	else
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.7e+127], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 7.8e+188], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6999999999999998e127

   1. Initial program 64.1%

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

      1. +-commutative 64.1%

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

      2. associate-+r- 64.1%

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

      3. *-commutative 64.1%

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

      4. associate-*r* 59.7%

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

      5. *-commutative 59.7%

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

      6. associate-+r- 59.7%

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

      7. +-commutative 59.7%

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

      8. associate-*l* 59.7%

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

      9. associate-*l* 66.6%

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

      10. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   6. Applied egg-rr 79.8%

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

   7. Taylor expanded in b around 0 71.2%

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

   8. Taylor expanded in a around 0 75.5%

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

   9. Taylor expanded in c around 0 82.2%

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

   if -3.6999999999999998e127 < z < 7.7999999999999999e188

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-+r- 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*r* 93.7%

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

      5. *-commutative 93.7%

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

      6. associate-+r- 93.7%

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

      7. +-commutative 93.7%

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

      8. associate-*l* 93.1%

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

      9. associate-*l* 93.6%

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

      10. *-commutative 93.6%

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

   3. Simplified 93.6%

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

   if 7.7999999999999999e188 < z

   1. Initial program 40.0%

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

      1. +-commutative 40.0%

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

      2. associate-+r- 40.0%

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

      3. *-commutative 40.0%

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

      4. associate-*r* 40.1%

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

      5. *-commutative 40.1%

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

      6. associate-+r- 40.1%

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

      7. +-commutative 40.1%

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

      8. associate-*l* 40.1%

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

      9. associate-*l* 44.3%

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

      10. *-commutative 44.3%

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

   3. Simplified 44.3%

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

   5. Taylor expanded in x around 0 39.8%

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

   6. Taylor expanded in t around inf 78.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+188}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-98} \lor \neg \left(z \leq 1.02 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.5e-98) (not (<= z 1.02e-126)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (/ (+ (* y (* 9.0 x)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.5e-98) || !(z <= 1.02e-126)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.5d-98)) .or. (.not. (z <= 1.02d-126))) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = ((y * (9.0d0 * x)) + b) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.5e-98) || !(z <= 1.02e-126)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.5e-98) or not (z <= 1.02e-126):
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	else:
		tmp = ((y * (9.0 * x)) + b) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.5e-98) || !(z <= 1.02e-126))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(Float64(y * Float64(9.0 * x)) + b) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.5e-98) || ~((z <= 1.02e-126)))
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	else
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.5e-98], N[Not[LessEqual[z, 1.02e-126]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e-98 or 1.02000000000000004e-126 < z

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-+r- 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-*r* 74.7%

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

      5. *-commutative 74.7%

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

      6. associate-+r- 74.7%

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

      7. +-commutative 74.7%

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

      8. associate-*l* 74.7%

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

      9. associate-*l* 78.7%

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

      10. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   6. Applied egg-rr 80.7%

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

   7. Taylor expanded in b around 0 64.6%

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

   8. Taylor expanded in a around 0 69.3%

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

   9. Taylor expanded in c around 0 74.0%

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

   if -1.5e-98 < z < 1.02000000000000004e-126

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+r- 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*r* 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-+r- 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-*l* 98.6%

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

      9. associate-*l* 96.4%

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

      10. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 89.2%

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

      1. associate-*r* 89.2%

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

   7. Simplified 89.2%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-98} \lor \neg \left(z \leq 1.02 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 70.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+158} \lor \neg \left(t \leq 1.55 \cdot 10^{-147}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3e+158) (not (<= t 1.55e-147)))
   (* t (+ (* -4.0 (/ a c)) (/ b (* c (* z t)))))
   (/ (+ (* y (* 9.0 x)) b) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3e+158) || !(t <= 1.55e-147)) {
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))));
	} else {
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-3d+158)) .or. (.not. (t <= 1.55d-147))) then
        tmp = t * (((-4.0d0) * (a / c)) + (b / (c * (z * t))))
    else
        tmp = ((y * (9.0d0 * x)) + b) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3e+158) || !(t <= 1.55e-147)) {
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))));
	} else {
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3e+158) or not (t <= 1.55e-147):
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))))
	else:
		tmp = ((y * (9.0 * x)) + b) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3e+158) || !(t <= 1.55e-147))
		tmp = Float64(t * Float64(Float64(-4.0 * Float64(a / c)) + Float64(b / Float64(c * Float64(z * t)))));
	else
		tmp = Float64(Float64(Float64(y * Float64(9.0 * x)) + b) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3e+158) || ~((t <= 1.55e-147)))
		tmp = t * ((-4.0 * (a / c)) + (b / (c * (z * t))));
	else
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3e+158], N[Not[LessEqual[t, 1.55e-147]], $MachinePrecision]], N[(t * N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e158 or 1.5500000000000001e-147 < t

   1. Initial program 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-+r- 77.6%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 77.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 80.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 80.7%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 80.7%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 80.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 80.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 80.0%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 80.0%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 62.2%

      \[\leadsto \color{blue}{\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]

   6. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(t \cdot z\right)}\right)} \]

   if -3e158 < t < 1.5500000000000001e-147

   1. Initial program 89.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 89.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 89.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 89.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 85.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 85.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 85.5%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 85.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 84.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 89.2%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 89.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.4%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 79.5%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 79.5%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+158} \lor \neg \left(t \leq 1.55 \cdot 10^{-147}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c} + \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -4.3e+158)
   (* t (* a (/ -4.0 c)))
   (if (<= t 5.2e+18)
     (/ (+ (* y (* 9.0 x)) b) (* z c))
     (* a (/ (* -4.0 t) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.3e+158) {
		tmp = t * (a * (-4.0 / c));
	} else if (t <= 5.2e+18) {
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-4.3d+158)) then
        tmp = t * (a * ((-4.0d0) / c))
    else if (t <= 5.2d+18) then
        tmp = ((y * (9.0d0 * x)) + b) / (z * c)
    else
        tmp = a * (((-4.0d0) * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.3e+158) {
		tmp = t * (a * (-4.0 / c));
	} else if (t <= 5.2e+18) {
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	} else {
		tmp = a * ((-4.0 * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -4.3e+158:
		tmp = t * (a * (-4.0 / c))
	elif t <= 5.2e+18:
		tmp = ((y * (9.0 * x)) + b) / (z * c)
	else:
		tmp = a * ((-4.0 * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -4.3e+158)
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	elseif (t <= 5.2e+18)
		tmp = Float64(Float64(Float64(y * Float64(9.0 * x)) + b) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -4.3e+158)
		tmp = t * (a * (-4.0 / c));
	elseif (t <= 5.2e+18)
		tmp = ((y * (9.0 * x)) + b) / (z * c);
	else
		tmp = a * ((-4.0 * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -4.3e+158], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+18], N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3e158

   1. Initial program 77.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 77.2%

      \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot \left(t \cdot z\right) + \left(9 \cdot \frac{x \cdot y}{a} + \frac{b}{a}\right)\right)}}{z \cdot c} \]

   6. Taylor expanded in a around inf 79.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 79.7%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-/l* 79.7%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

      4. associate-*r* 79.7%

         \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]

      5. *-commutative 79.7%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \]

      6. associate-*r/ 79.7%

         \[\leadsto t \cdot \color{blue}{\frac{-4 \cdot a}{c}} \]

      7. *-commutative 79.7%

         \[\leadsto t \cdot \frac{\color{blue}{a \cdot -4}}{c} \]

      8. associate-/l* 79.7%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \frac{-4}{c}\right)} \]

   8. Simplified 79.7%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \frac{-4}{c}\right)} \]

   if -4.3e158 < t < 5.2e18

   1. Initial program 86.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 86.5%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 86.5%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 86.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 83.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 83.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 83.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 83.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 83.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 87.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 87.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.3%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   6. Step-by-step derivation

      1. associate-*r* 75.3%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Simplified 75.3%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   if 5.2e18 < t

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 78.0%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 78.0%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 78.0%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 80.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 80.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 80.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 80.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 78.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 78.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-/l* 65.2%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. associate-*r* 65.2%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot \frac{t}{c}} \]

      3. *-commutative 65.2%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot \frac{t}{c} \]

      4. associate-*r* 65.2%

         \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c}\right)} \]

      5. associate-*r/ 65.2%

         \[\leadsto a \cdot \color{blue}{\frac{-4 \cdot t}{c}} \]

      6. *-commutative 65.2%

         \[\leadsto a \cdot \frac{\color{blue}{t \cdot -4}}{c} \]

   7. Simplified 65.2%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot \left(9 \cdot x\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+58} \lor \neg \left(t \leq 4.8 \cdot 10^{-54}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -9.5e+58) (not (<= t 4.8e-54)))
   (* a (/ (* -4.0 t) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -9.5e+58) || !(t <= 4.8e-54)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-9.5d+58)) .or. (.not. (t <= 4.8d-54))) then
        tmp = a * (((-4.0d0) * t) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -9.5e+58) || !(t <= 4.8e-54)) {
		tmp = a * ((-4.0 * t) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -9.5e+58) or not (t <= 4.8e-54):
		tmp = a * ((-4.0 * t) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -9.5e+58) || !(t <= 4.8e-54))
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -9.5e+58) || ~((t <= 4.8e-54)))
		tmp = a * ((-4.0 * t) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -9.5e+58], N[Not[LessEqual[t, 4.8e-54]], $MachinePrecision]], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000002e58 or 4.80000000000000026e-54 < t

   1. Initial program 74.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 74.4%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 74.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 78.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 78.6%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 78.6%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 78.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 78.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 76.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-/l* 63.2%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. associate-*r* 63.2%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot \frac{t}{c}} \]

      3. *-commutative 63.2%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot \frac{t}{c} \]

      4. associate-*r* 63.2%

         \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c}\right)} \]

      5. associate-*r/ 63.2%

         \[\leadsto a \cdot \color{blue}{\frac{-4 \cdot t}{c}} \]

      6. *-commutative 63.2%

         \[\leadsto a \cdot \frac{\color{blue}{t \cdot -4}}{c} \]

   7. Simplified 63.2%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -9.5000000000000002e58 < t < 4.80000000000000026e-54

   1. Initial program 91.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 91.3%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 91.3%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 91.3%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 87.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 87.1%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 87.1%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 87.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 86.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 91.4%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 91.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 39.1%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 39.1%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+58} \lor \neg \left(t \leq 4.8 \cdot 10^{-54}\right):\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-93}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -4.8e+58)
   (* a (/ (* -4.0 t) c))
   (if (<= t 2e-93) (/ b (* z c)) (* t (* a (/ -4.0 c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.8e+58) {
		tmp = a * ((-4.0 * t) / c);
	} else if (t <= 2e-93) {
		tmp = b / (z * c);
	} else {
		tmp = t * (a * (-4.0 / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-4.8d+58)) then
        tmp = a * (((-4.0d0) * t) / c)
    else if (t <= 2d-93) then
        tmp = b / (z * c)
    else
        tmp = t * (a * ((-4.0d0) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.8e+58) {
		tmp = a * ((-4.0 * t) / c);
	} else if (t <= 2e-93) {
		tmp = b / (z * c);
	} else {
		tmp = t * (a * (-4.0 / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -4.8e+58:
		tmp = a * ((-4.0 * t) / c)
	elif t <= 2e-93:
		tmp = b / (z * c)
	else:
		tmp = t * (a * (-4.0 / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -4.8e+58)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c));
	elseif (t <= 2e-93)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -4.8e+58)
		tmp = a * ((-4.0 * t) / c);
	elseif (t <= 2e-93)
		tmp = b / (z * c);
	else
		tmp = t * (a * (-4.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -4.8e+58], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-93], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8e58

   1. Initial program 69.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 69.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 69.9%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 69.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 77.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 77.5%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 77.5%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 77.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 77.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 75.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 75.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   6. Step-by-step derivation

      1. associate-/l* 70.2%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. associate-*r* 70.2%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot \frac{t}{c}} \]

      3. *-commutative 70.2%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot \frac{t}{c} \]

      4. associate-*r* 70.2%

         \[\leadsto \color{blue}{a \cdot \left(-4 \cdot \frac{t}{c}\right)} \]

      5. associate-*r/ 70.2%

         \[\leadsto a \cdot \color{blue}{\frac{-4 \cdot t}{c}} \]

      6. *-commutative 70.2%

         \[\leadsto a \cdot \frac{\color{blue}{t \cdot -4}}{c} \]

   7. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \frac{t \cdot -4}{c}} \]

   if -4.8e58 < t < 1.9999999999999998e-93

   1. Initial program 92.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 92.9%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 92.9%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 92.9%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 88.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 88.4%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 88.4%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 88.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      8. associate-*l* 87.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

      9. associate-*l* 92.9%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

      10. *-commutative 92.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   7. Simplified 39.7%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 1.9999999999999998e-93 < t

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right) + b}{z \cdot c}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 70.6%

      \[\leadsto \frac{\color{blue}{a \cdot \left(-4 \cdot \left(t \cdot z\right) + \left(9 \cdot \frac{x \cdot y}{a} + \frac{b}{a}\right)\right)}}{z \cdot c} \]

   6. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. *-commutative 52.5%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      3. associate-/l* 54.9%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right)} \cdot -4 \]

      4. associate-*r* 54.9%

         \[\leadsto \color{blue}{t \cdot \left(\frac{a}{c} \cdot -4\right)} \]

      5. *-commutative 54.9%

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot \frac{a}{c}\right)} \]

      6. associate-*r/ 54.9%

         \[\leadsto t \cdot \color{blue}{\frac{-4 \cdot a}{c}} \]

      7. *-commutative 54.9%

         \[\leadsto t \cdot \frac{\color{blue}{a \cdot -4}}{c} \]

      8. associate-/l* 54.9%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \frac{-4}{c}\right)} \]

   8. Simplified 54.9%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \frac{-4}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-93}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. +-commutative 83.5%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

   2. associate-+r- 83.5%

      \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

   3. *-commutative 83.5%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

   4. associate-*r* 83.1%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

   5. *-commutative 83.1%

      \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

   6. associate-+r- 83.1%

      \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

   7. +-commutative 83.1%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   8. associate-*l* 82.7%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}{z \cdot c} \]

   9. associate-*l* 84.7%

      \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(a \cdot t\right)}\right) + b}{z \cdot c} \]

   10. *-commutative 84.7%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \color{blue}{\left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 84.7%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 34.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 34.3%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

7. Simplified 34.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer target: 80.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024086 
(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)))