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

Percentage Accurate: 80.3% → 87.9%

Time: 13.7s

Alternatives: 12

Speedup: 0.7×

• 37.5% 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: 80.3% 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: 87.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+167}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(a \cdot \frac{t}{c}, -4, \frac{b}{z \cdot c}\right)}{y} - x \cdot \frac{-9}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* x 9.0))))
   (if (<= t_1 -5e+266)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= t_1 2e+167)
       (/ (+ (* t (* -4.0 a)) (/ (- b (* x (* y -9.0))) z)) c)
       (*
        y
        (-
         (/ (fma (* a (/ t c)) -4.0 (/ b (* z c))) y)
         (* x (/ -9.0 (* z c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 * (x * 9.0);
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t_1 <= 2e+167) {
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = y * ((fma((a * (t / c)), -4.0, (b / (z * c))) / y) - (x * (-9.0 / (z * c))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+266)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (t_1 <= 2e+167)
		tmp = Float64(Float64(Float64(t * Float64(-4.0 * a)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	else
		tmp = Float64(y * Float64(Float64(fma(Float64(a * Float64(t / c)), -4.0, Float64(b / Float64(z * c))) / y) - Float64(x * Float64(-9.0 / Float64(z * 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.
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[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+266], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+167], N[(N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(y * N[(N[(N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x * N[(-9.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e266

   1. Initial program 44.2%

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

   3. Simplified 43.8%

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

      1. *-un-lft-identity 43.8%

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

      2. *-commutative 43.8%

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

      3. times-frac 44.5%

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

      4. +-commutative 44.5%

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

   6. Applied egg-rr 44.5%

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

      1. associate-*l/ 44.5%

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

      2. *-un-lft-identity 44.5%

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

   8. Applied egg-rr 44.5%

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

   9. Taylor expanded in x around inf 48.0%

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

       1. *-commutative 48.0%

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

       2. times-frac 88.8%

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

   11. Simplified 88.8%

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

   if -4.9999999999999999e266 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000001e167

   1. Initial program 78.0%

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

   3. Simplified 84.3%

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

      1. *-un-lft-identity 84.3%

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

      2. *-commutative 84.3%

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

      3. times-frac 87.6%

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

      4. +-commutative 87.6%

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

   6. Applied egg-rr 87.6%

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

      1. associate-*l/ 87.7%

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

      2. *-un-lft-identity 87.7%

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

   8. Applied egg-rr 87.7%

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

   9. Taylor expanded in b around 0 91.8%

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

   10. Taylor expanded in z around -inf 92.4%

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

       1. mul-1-neg 92.4%

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

       2. unsub-neg 92.4%

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

       3. associate-*r* 92.4%

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

       4. *-commutative 92.4%

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

       5. mul-1-neg 92.4%

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

       6. unsub-neg 92.4%

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

       7. *-commutative 92.4%

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

       8. associate-*r* 92.4%

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

   12. Simplified 92.4%

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

   if 2.0000000000000001e167 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 67.0%

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

      1. associate-+l- 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 63.0%

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

      4. *-commutative 63.0%

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

      5. associate-+l- 63.0%

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

      6. associate-*l* 63.0%

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

      7. associate-*l* 63.4%

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

      8. *-commutative 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in y around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. *-commutative 74.2%

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

      3. distribute-rgt-neg-in 74.2%

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

   7. Simplified 77.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+167}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(a \cdot \frac{t}{c}, -4, \frac{b}{z \cdot c}\right)}{y} - x \cdot \frac{-9}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ (* t a) c))) (t_2 (/ (/ b c) z)))
   (if (<= b -8.5e+132)
     t_2
     (if (<= b -6.5e+78)
       t_1
       (if (<= b -3.5e+37)
         t_2
         (if (<= b 6e-259)
           t_1
           (if (<= b 2.25e-205)
             (* y (* (/ x z) (/ 9.0 c)))
             (if (<= b 1.1e-105)
               t_1
               (if (<= b 2.1e+80)
                 (* 9.0 (* x (/ y (* z c))))
                 (/ b (* z c)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * ((t * a) / c);
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -8.5e+132) {
		tmp = t_2;
	} else if (b <= -6.5e+78) {
		tmp = t_1;
	} else if (b <= -3.5e+37) {
		tmp = t_2;
	} else if (b <= 6e-259) {
		tmp = t_1;
	} else if (b <= 2.25e-205) {
		tmp = y * ((x / z) * (9.0 / c));
	} else if (b <= 1.1e-105) {
		tmp = t_1;
	} else if (b <= 2.1e+80) {
		tmp = 9.0 * (x * (y / (z * 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.
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) :: tmp
    t_1 = (-4.0d0) * ((t * a) / c)
    t_2 = (b / c) / z
    if (b <= (-8.5d+132)) then
        tmp = t_2
    else if (b <= (-6.5d+78)) then
        tmp = t_1
    else if (b <= (-3.5d+37)) then
        tmp = t_2
    else if (b <= 6d-259) then
        tmp = t_1
    else if (b <= 2.25d-205) then
        tmp = y * ((x / z) * (9.0d0 / c))
    else if (b <= 1.1d-105) then
        tmp = t_1
    else if (b <= 2.1d+80) then
        tmp = 9.0d0 * (x * (y / (z * 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;
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 = -4.0 * ((t * a) / c);
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -8.5e+132) {
		tmp = t_2;
	} else if (b <= -6.5e+78) {
		tmp = t_1;
	} else if (b <= -3.5e+37) {
		tmp = t_2;
	} else if (b <= 6e-259) {
		tmp = t_1;
	} else if (b <= 2.25e-205) {
		tmp = y * ((x / z) * (9.0 / c));
	} else if (b <= 1.1e-105) {
		tmp = t_1;
	} else if (b <= 2.1e+80) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * ((t * a) / c)
	t_2 = (b / c) / z
	tmp = 0
	if b <= -8.5e+132:
		tmp = t_2
	elif b <= -6.5e+78:
		tmp = t_1
	elif b <= -3.5e+37:
		tmp = t_2
	elif b <= 6e-259:
		tmp = t_1
	elif b <= 2.25e-205:
		tmp = y * ((x / z) * (9.0 / c))
	elif b <= 1.1e-105:
		tmp = t_1
	elif b <= 2.1e+80:
		tmp = 9.0 * (x * (y / (z * c)))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(Float64(t * a) / c))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -8.5e+132)
		tmp = t_2;
	elseif (b <= -6.5e+78)
		tmp = t_1;
	elseif (b <= -3.5e+37)
		tmp = t_2;
	elseif (b <= 6e-259)
		tmp = t_1;
	elseif (b <= 2.25e-205)
		tmp = Float64(y * Float64(Float64(x / z) * Float64(9.0 / c)));
	elseif (b <= 1.1e-105)
		tmp = t_1;
	elseif (b <= 2.1e+80)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * 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])){:}
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 = -4.0 * ((t * a) / c);
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (b <= -8.5e+132)
		tmp = t_2;
	elseif (b <= -6.5e+78)
		tmp = t_1;
	elseif (b <= -3.5e+37)
		tmp = t_2;
	elseif (b <= 6e-259)
		tmp = t_1;
	elseif (b <= 2.25e-205)
		tmp = y * ((x / z) * (9.0 / c));
	elseif (b <= 1.1e-105)
		tmp = t_1;
	elseif (b <= 2.1e+80)
		tmp = 9.0 * (x * (y / (z * 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.
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[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -8.5e+132], t$95$2, If[LessEqual[b, -6.5e+78], t$95$1, If[LessEqual[b, -3.5e+37], t$95$2, If[LessEqual[b, 6e-259], t$95$1, If[LessEqual[b, 2.25e-205], N[(y * N[(N[(x / z), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-105], t$95$1, If[LessEqual[b, 2.1e+80], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.49999999999999969e132 or -6.50000000000000036e78 < b < -3.5e37

   1. Initial program 76.5%

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

   3. Simplified 85.0%

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

      1. *-un-lft-identity 85.0%

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

      2. *-commutative 85.0%

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

      3. times-frac 81.1%

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

      4. +-commutative 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. associate-*l/ 81.2%

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

      2. *-un-lft-identity 81.2%

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

   8. Applied egg-rr 81.2%

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

   9. Taylor expanded in b around inf 78.6%

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

       1. associate-/r* 78.8%

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

   11. Simplified 78.8%

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

   if -8.49999999999999969e132 < b < -6.50000000000000036e78 or -3.5e37 < b < 6.0000000000000004e-259 or 2.24999999999999978e-205 < b < 1.10000000000000002e-105

   1. Initial program 72.3%

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

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r* 71.2%

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

      4. *-commutative 71.2%

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

      5. associate-+l- 71.2%

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

      6. associate-*l* 71.2%

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

      7. associate-*l* 74.7%

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

      8. *-commutative 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in z around inf 58.5%

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

      1. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   if 6.0000000000000004e-259 < b < 2.24999999999999978e-205

   1. Initial program 78.1%

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

   3. Simplified 78.5%

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

      1. *-un-lft-identity 78.5%

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

      2. *-commutative 78.5%

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

      3. times-frac 83.8%

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

      4. +-commutative 83.8%

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

   6. Applied egg-rr 83.8%

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

      1. associate-*l/ 84.0%

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

      2. *-un-lft-identity 84.0%

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

   8. Applied egg-rr 84.0%

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

   9. Taylor expanded in x around inf 73.2%

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

       1. associate-*r/ 73.4%

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

       2. associate-*r* 73.4%

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

       3. associate-*l/ 73.3%

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

       4. associate-*r/ 73.4%

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

       5. *-commutative 73.4%

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

       6. associate-*r/ 73.3%

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

       7. *-commutative 73.3%

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

       8. *-commutative 73.3%

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

       9. times-frac 68.3%

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

   11. Simplified 68.3%

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

   if 1.10000000000000002e-105 < b < 2.10000000000000001e80

   1. Initial program 70.5%

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

      1. associate-+l- 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-+l- 75.8%

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

      6. associate-*l* 75.7%

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

      7. associate-*l* 78.4%

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

      8. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in x around inf 43.1%

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

      1. associate-/l* 53.5%

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

      2. *-commutative 53.5%

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

   7. Simplified 53.5%

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

   if 2.10000000000000001e80 < b

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. associate-*r* 75.6%

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

      4. *-commutative 75.6%

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

      5. associate-+l- 75.6%

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

      6. associate-*l* 75.6%

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

      7. associate-*l* 77.8%

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

      8. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in b around inf 59.8%

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

      1. *-commutative 59.8%

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

   7. Simplified 59.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-259}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-105}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+184}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-4 \cdot \left(t \cdot \frac{a}{x}\right) + \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* x 9.0))))
   (if (<= t_1 -5e+266)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= t_1 1e+184)
       (/ (+ (* t (* -4.0 a)) (/ (- b (* x (* y -9.0))) z)) c)
       (/
        (* x (+ (* -4.0 (* t (/ a x))) (+ (* 9.0 (/ y z)) (/ b (* x z)))))
        c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 * (x * 9.0);
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t_1 <= 1e+184) {
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = (x * ((-4.0 * (t * (a / x))) + ((9.0 * (y / z)) + (b / (x * z))))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-5d+266)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (t_1 <= 1d+184) then
        tmp = ((t * ((-4.0d0) * a)) + ((b - (x * (y * (-9.0d0)))) / z)) / c
    else
        tmp = (x * (((-4.0d0) * (t * (a / x))) + ((9.0d0 * (y / z)) + (b / (x * z))))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 * (x * 9.0);
	double tmp;
	if (t_1 <= -5e+266) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (t_1 <= 1e+184) {
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c;
	} else {
		tmp = (x * ((-4.0 * (t * (a / x))) + ((9.0 * (y / z)) + (b / (x * z))))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 * (x * 9.0)
	tmp = 0
	if t_1 <= -5e+266:
		tmp = 9.0 * ((x / z) * (y / c))
	elif t_1 <= 1e+184:
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c
	else:
		tmp = (x * ((-4.0 * (t * (a / x))) + ((9.0 * (y / z)) + (b / (x * z))))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+266)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (t_1 <= 1e+184)
		tmp = Float64(Float64(Float64(t * Float64(-4.0 * a)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	else
		tmp = Float64(Float64(x * Float64(Float64(-4.0 * Float64(t * Float64(a / x))) + Float64(Float64(9.0 * Float64(y / z)) + Float64(b / Float64(x * z))))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -5e+266)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (t_1 <= 1e+184)
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c;
	else
		tmp = (x * ((-4.0 * (t * (a / x))) + ((9.0 * (y / z)) + (b / (x * 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.
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[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+266], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+184], N[(N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x * N[(N[(-4.0 * N[(t * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e266

   1. Initial program 44.2%

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

   3. Simplified 43.8%

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

      1. *-un-lft-identity 43.8%

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

      2. *-commutative 43.8%

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

      3. times-frac 44.5%

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

      4. +-commutative 44.5%

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

   6. Applied egg-rr 44.5%

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

      1. associate-*l/ 44.5%

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

      2. *-un-lft-identity 44.5%

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

   8. Applied egg-rr 44.5%

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

   9. Taylor expanded in x around inf 48.0%

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

       1. *-commutative 48.0%

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

       2. times-frac 88.8%

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

   11. Simplified 88.8%

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

   if -4.9999999999999999e266 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000002e184

   1. Initial program 77.7%

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

   3. Simplified 83.8%

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

      1. *-un-lft-identity 83.8%

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

      2. *-commutative 83.8%

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

      3. times-frac 87.5%

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

      4. +-commutative 87.5%

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

   6. Applied egg-rr 87.5%

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

      1. associate-*l/ 87.6%

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

      2. *-un-lft-identity 87.6%

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

   8. Applied egg-rr 87.6%

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

   9. Taylor expanded in b around 0 91.1%

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

   10. Taylor expanded in z around -inf 92.1%

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

       1. mul-1-neg 92.1%

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

       2. unsub-neg 92.1%

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

       3. associate-*r* 92.1%

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

       4. *-commutative 92.1%

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

       5. mul-1-neg 92.1%

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

       6. unsub-neg 92.1%

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

       7. *-commutative 92.1%

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

       8. associate-*r* 92.1%

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

   12. Simplified 92.1%

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

   if 1.00000000000000002e184 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 66.9%

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

   3. Simplified 66.9%

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

      1. *-un-lft-identity 66.9%

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

      2. *-commutative 66.9%

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

      3. times-frac 69.7%

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

      4. +-commutative 69.7%

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

   6. Applied egg-rr 69.7%

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

      1. associate-*l/ 69.7%

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

      2. *-un-lft-identity 69.7%

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

   8. Applied egg-rr 69.7%

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

   9. Taylor expanded in x around inf 78.0%

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

       1. associate-/l* 82.5%

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

   11. Applied egg-rr 82.5%

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

       1. associate-*r/ 78.0%

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

       2. *-commutative 78.0%

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

       3. associate-/l* 73.4%

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

   13. Simplified 73.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+184}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-4 \cdot \left(t \cdot \frac{a}{x}\right) + \left(9 \cdot \frac{y}{z} + \frac{b}{x \cdot z}\right)\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (/ (+ (* -4.0 (* t a)) (/ b z)) c))
        (t_2 (* 9.0 (* (/ x z) (/ y c)))))
   (if (<= y -9.6e+93)
     t_2
     (if (<= y 1.7e+44)
       t_1
       (if (<= y 6.8e+74)
         (* y (* (/ x z) (/ 9.0 c)))
         (if (<= y 2.25e+192) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = ((-4.0 * (t * a)) + (b / z)) / c;
	double t_2 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (y <= -9.6e+93) {
		tmp = t_2;
	} else if (y <= 1.7e+44) {
		tmp = t_1;
	} else if (y <= 6.8e+74) {
		tmp = y * ((x / z) * (9.0 / c));
	} else if (y <= 2.25e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (((-4.0d0) * (t * a)) + (b / z)) / c
    t_2 = 9.0d0 * ((x / z) * (y / c))
    if (y <= (-9.6d+93)) then
        tmp = t_2
    else if (y <= 1.7d+44) then
        tmp = t_1
    else if (y <= 6.8d+74) then
        tmp = y * ((x / z) * (9.0d0 / c))
    else if (y <= 2.25d+192) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = ((-4.0 * (t * a)) + (b / z)) / c;
	double t_2 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (y <= -9.6e+93) {
		tmp = t_2;
	} else if (y <= 1.7e+44) {
		tmp = t_1;
	} else if (y <= 6.8e+74) {
		tmp = y * ((x / z) * (9.0 / c));
	} else if (y <= 2.25e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = ((-4.0 * (t * a)) + (b / z)) / c
	t_2 = 9.0 * ((x / z) * (y / c))
	tmp = 0
	if y <= -9.6e+93:
		tmp = t_2
	elif y <= 1.7e+44:
		tmp = t_1
	elif y <= 6.8e+74:
		tmp = y * ((x / z) * (9.0 / c))
	elif y <= 2.25e+192:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t * a)) + Float64(b / z)) / c)
	t_2 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (y <= -9.6e+93)
		tmp = t_2;
	elseif (y <= 1.7e+44)
		tmp = t_1;
	elseif (y <= 6.8e+74)
		tmp = Float64(y * Float64(Float64(x / z) * Float64(9.0 / c)));
	elseif (y <= 2.25e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = ((-4.0 * (t * a)) + (b / z)) / c;
	t_2 = 9.0 * ((x / z) * (y / c));
	tmp = 0.0;
	if (y <= -9.6e+93)
		tmp = t_2;
	elseif (y <= 1.7e+44)
		tmp = t_1;
	elseif (y <= 6.8e+74)
		tmp = y * ((x / z) * (9.0 / c));
	elseif (y <= 2.25e+192)
		tmp = t_1;
	else
		tmp = t_2;
	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.
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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+93], t$95$2, If[LessEqual[y, 1.7e+44], t$95$1, If[LessEqual[y, 6.8e+74], N[(y * N[(N[(x / z), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+192], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.60000000000000042e93 or 2.25e192 < y

   1. Initial program 62.9%

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

   3. Simplified 67.4%

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

      1. *-un-lft-identity 67.4%

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

      2. *-commutative 67.4%

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

      3. times-frac 70.6%

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

      4. +-commutative 70.6%

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

   6. Applied egg-rr 70.6%

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

      1. associate-*l/ 70.6%

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

      2. *-un-lft-identity 70.6%

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

   8. Applied egg-rr 70.6%

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

   9. Taylor expanded in x around inf 48.5%

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

       1. *-commutative 48.5%

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

       2. times-frac 63.0%

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

   11. Simplified 63.0%

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

   if -9.60000000000000042e93 < y < 1.7e44 or 6.7999999999999998e74 < y < 2.25e192

   1. Initial program 79.0%

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

   3. Simplified 84.4%

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

      1. *-un-lft-identity 84.4%

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

      2. *-commutative 84.4%

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

      3. times-frac 87.3%

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

      4. +-commutative 87.3%

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

   6. Applied egg-rr 87.3%

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

      1. associate-*l/ 87.4%

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

      2. *-un-lft-identity 87.4%

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

   8. Applied egg-rr 87.4%

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

   9. Taylor expanded in b around 0 89.5%

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

   10. Taylor expanded in x around 0 76.9%

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

   if 1.7e44 < y < 6.7999999999999998e74

   1. Initial program 63.8%

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

   3. Simplified 63.8%

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

      1. *-un-lft-identity 63.8%

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

      2. *-commutative 63.8%

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

      3. times-frac 76.9%

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

      4. +-commutative 76.9%

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

   6. Applied egg-rr 76.9%

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

      1. associate-*l/ 76.7%

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

      2. *-un-lft-identity 76.7%

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

   8. Applied egg-rr 76.7%

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

   9. Taylor expanded in x around inf 51.0%

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

       1. associate-*r/ 51.0%

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

       2. associate-*r* 51.0%

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

       3. associate-*l/ 51.2%

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

       4. associate-*r/ 51.2%

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

       5. *-commutative 51.2%

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

       6. associate-*r/ 51.2%

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

       7. *-commutative 51.2%

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

       8. *-commutative 51.2%

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

       9. times-frac 62.7%

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

   11. Simplified 62.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+93}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+44}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+192}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-125}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 z) (/ y c)))))
   (if (<= y -1.8e-91)
     t_1
     (if (<= y 1.6e-125)
       (* -4.0 (* a (/ t c)))
       (if (<= y 3.4e-38)
         (/ (/ b c) z)
         (if (<= y 1.35e+44) (* -4.0 (/ (* t a) c)) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 / z) * (y / c));
	double tmp;
	if (y <= -1.8e-91) {
		tmp = t_1;
	} else if (y <= 1.6e-125) {
		tmp = -4.0 * (a * (t / c));
	} else if (y <= 3.4e-38) {
		tmp = (b / c) / z;
	} else if (y <= 1.35e+44) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = 9.0d0 * ((x / z) * (y / c))
    if (y <= (-1.8d-91)) then
        tmp = t_1
    else if (y <= 1.6d-125) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (y <= 3.4d-38) then
        tmp = (b / c) / z
    else if (y <= 1.35d+44) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 / z) * (y / c));
	double tmp;
	if (y <= -1.8e-91) {
		tmp = t_1;
	} else if (y <= 1.6e-125) {
		tmp = -4.0 * (a * (t / c));
	} else if (y <= 3.4e-38) {
		tmp = (b / c) / z;
	} else if (y <= 1.35e+44) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 / z) * (y / c))
	tmp = 0
	if y <= -1.8e-91:
		tmp = t_1
	elif y <= 1.6e-125:
		tmp = -4.0 * (a * (t / c))
	elif y <= 3.4e-38:
		tmp = (b / c) / z
	elif y <= 1.35e+44:
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (y <= -1.8e-91)
		tmp = t_1;
	elseif (y <= 1.6e-125)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (y <= 3.4e-38)
		tmp = Float64(Float64(b / c) / z);
	elseif (y <= 1.35e+44)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 / z) * (y / c));
	tmp = 0.0;
	if (y <= -1.8e-91)
		tmp = t_1;
	elseif (y <= 1.6e-125)
		tmp = -4.0 * (a * (t / c));
	elseif (y <= 3.4e-38)
		tmp = (b / c) / z;
	elseif (y <= 1.35e+44)
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = t_1;
	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.
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[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e-91], t$95$1, If[LessEqual[y, 1.6e-125], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-38], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.35e+44], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8e-91 or 1.35e44 < y

   1. Initial program 68.4%

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

   3. Simplified 73.4%

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

      1. *-un-lft-identity 73.4%

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

      2. *-commutative 73.4%

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

      3. times-frac 76.5%

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

      4. +-commutative 76.5%

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

   6. Applied egg-rr 76.5%

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

      1. associate-*l/ 76.5%

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

      2. *-un-lft-identity 76.5%

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

   8. Applied egg-rr 76.5%

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

   9. Taylor expanded in x around inf 44.3%

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

       1. *-commutative 44.3%

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

       2. times-frac 53.4%

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

   11. Simplified 53.4%

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

   if -1.8e-91 < y < 1.5999999999999999e-125

   1. Initial program 81.0%

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

   3. Simplified 86.5%

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

      1. *-un-lft-identity 86.5%

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

      2. *-commutative 86.5%

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

      3. times-frac 88.1%

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

      4. +-commutative 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in z around inf 52.7%

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

      1. associate-/l* 51.4%

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

   9. Simplified 51.4%

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

   if 1.5999999999999999e-125 < y < 3.4000000000000002e-38

   1. Initial program 76.0%

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

   3. Simplified 76.0%

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

      1. *-un-lft-identity 76.0%

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

      2. *-commutative 76.0%

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

      3. times-frac 85.6%

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

      4. +-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

      1. associate-*l/ 85.7%

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

      2. *-un-lft-identity 85.7%

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

   8. Applied egg-rr 85.7%

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

   9. Taylor expanded in b around inf 47.1%

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

       1. associate-/r* 42.5%

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

   11. Simplified 42.5%

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

   if 3.4000000000000002e-38 < y < 1.35e44

   1. Initial program 84.9%

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

      1. associate-+l- 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r* 85.1%

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

      4. *-commutative 85.1%

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

      5. associate-+l- 85.1%

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

      6. associate-*l* 85.1%

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

      7. associate-*l* 92.6%

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

      8. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around inf 48.1%

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

      1. *-commutative 48.1%

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

   7. Simplified 48.1%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-91}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-125}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ (* t a) c))) (t_2 (/ (/ b c) z)))
   (if (<= b -1e+133)
     t_2
     (if (<= b -8.4e+77)
       t_1
       (if (<= b -6.5e+36) t_2 (if (<= b 5.6e+55) t_1 (/ b (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * ((t * a) / c);
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -1e+133) {
		tmp = t_2;
	} else if (b <= -8.4e+77) {
		tmp = t_1;
	} else if (b <= -6.5e+36) {
		tmp = t_2;
	} else if (b <= 5.6e+55) {
		tmp = t_1;
	} 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.
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) :: tmp
    t_1 = (-4.0d0) * ((t * a) / c)
    t_2 = (b / c) / z
    if (b <= (-1d+133)) then
        tmp = t_2
    else if (b <= (-8.4d+77)) then
        tmp = t_1
    else if (b <= (-6.5d+36)) then
        tmp = t_2
    else if (b <= 5.6d+55) then
        tmp = t_1
    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;
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 = -4.0 * ((t * a) / c);
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -1e+133) {
		tmp = t_2;
	} else if (b <= -8.4e+77) {
		tmp = t_1;
	} else if (b <= -6.5e+36) {
		tmp = t_2;
	} else if (b <= 5.6e+55) {
		tmp = t_1;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * ((t * a) / c)
	t_2 = (b / c) / z
	tmp = 0
	if b <= -1e+133:
		tmp = t_2
	elif b <= -8.4e+77:
		tmp = t_1
	elif b <= -6.5e+36:
		tmp = t_2
	elif b <= 5.6e+55:
		tmp = t_1
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(Float64(t * a) / c))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -1e+133)
		tmp = t_2;
	elseif (b <= -8.4e+77)
		tmp = t_1;
	elseif (b <= -6.5e+36)
		tmp = t_2;
	elseif (b <= 5.6e+55)
		tmp = t_1;
	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])){:}
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 = -4.0 * ((t * a) / c);
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (b <= -1e+133)
		tmp = t_2;
	elseif (b <= -8.4e+77)
		tmp = t_1;
	elseif (b <= -6.5e+36)
		tmp = t_2;
	elseif (b <= 5.6e+55)
		tmp = t_1;
	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.
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[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -1e+133], t$95$2, If[LessEqual[b, -8.4e+77], t$95$1, If[LessEqual[b, -6.5e+36], t$95$2, If[LessEqual[b, 5.6e+55], t$95$1, N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1e133 or -8.3999999999999995e77 < b < -6.4999999999999998e36

   1. Initial program 76.5%

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

   3. Simplified 85.0%

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

      1. *-un-lft-identity 85.0%

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

      2. *-commutative 85.0%

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

      3. times-frac 81.1%

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

      4. +-commutative 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. associate-*l/ 81.2%

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

      2. *-un-lft-identity 81.2%

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

   8. Applied egg-rr 81.2%

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

   9. Taylor expanded in b around inf 78.6%

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

       1. associate-/r* 78.8%

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

   11. Simplified 78.8%

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

   if -1e133 < b < -8.3999999999999995e77 or -6.4999999999999998e36 < b < 5.6000000000000002e55

   1. Initial program 71.7%

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

      1. associate-+l- 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

      5. associate-+l- 72.2%

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

      6. associate-*l* 72.2%

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

      7. associate-*l* 75.2%

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

      8. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in z around inf 51.3%

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

      1. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   if 5.6000000000000002e55 < b

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r* 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-+l- 78.1%

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

      6. associate-*l* 78.1%

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

      7. associate-*l* 80.1%

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

      8. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in b around inf 59.9%

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

      1. *-commutative 59.9%

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

   7. Simplified 59.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+55}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= (* y (* x 9.0)) -5e+266)
   (* 9.0 (* (/ x z) (/ y c)))
   (/ (+ (* t (* -4.0 a)) (/ (- b (* x (* y -9.0))) z)) c)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 ((y * (x * 9.0)) <= -5e+266) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 ((y * (x * 9.0d0)) <= (-5d+266)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else
        tmp = ((t * ((-4.0d0) * a)) + ((b - (x * (y * (-9.0d0)))) / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 ((y * (x * 9.0)) <= -5e+266) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else {
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 (y * (x * 9.0)) <= -5e+266:
		tmp = 9.0 * ((x / z) * (y / c))
	else:
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 (Float64(y * Float64(x * 9.0)) <= -5e+266)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	else
		tmp = Float64(Float64(Float64(t * Float64(-4.0 * a)) + Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 ((y * (x * 9.0)) <= -5e+266)
		tmp = 9.0 * ((x / z) * (y / c));
	else
		tmp = ((t * (-4.0 * a)) + ((b - (x * (y * -9.0))) / 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.
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[N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision], -5e+266], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e266

   1. Initial program 44.2%

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

   3. Simplified 43.8%

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

      1. *-un-lft-identity 43.8%

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

      2. *-commutative 43.8%

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

      3. times-frac 44.5%

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

      4. +-commutative 44.5%

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

   6. Applied egg-rr 44.5%

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

      1. associate-*l/ 44.5%

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

      2. *-un-lft-identity 44.5%

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

   8. Applied egg-rr 44.5%

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

   9. Taylor expanded in x around inf 48.0%

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

       1. *-commutative 48.0%

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

       2. times-frac 88.8%

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

   11. Simplified 88.8%

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

   if -4.9999999999999999e266 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.7%

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

   3. Simplified 82.2%

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

      1. *-un-lft-identity 82.2%

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

      2. *-commutative 82.2%

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

      3. times-frac 85.8%

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

      4. +-commutative 85.8%

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

   6. Applied egg-rr 85.8%

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

      1. associate-*l/ 85.9%

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

      2. *-un-lft-identity 85.9%

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

   8. Applied egg-rr 85.9%

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

   9. Taylor expanded in b around 0 88.2%

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

   10. Taylor expanded in z around -inf 89.5%

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

       1. mul-1-neg 89.5%

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

       2. unsub-neg 89.5%

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

       3. associate-*r* 89.5%

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

       4. *-commutative 89.5%

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

       5. mul-1-neg 89.5%

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

       6. unsub-neg 89.5%

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

       7. *-commutative 89.5%

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

       8. associate-*r* 89.5%

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

   12. Simplified 89.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+266}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \leq -0.55:\\ \;\;\;\;\frac{t\_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{t\_1 + \frac{y}{z} \cdot \left(x \cdot 9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (* t a))))
   (if (<= b -0.55)
     (/ (+ t_1 (/ b z)) c)
     (if (<= b 5.2e+105)
       (/ (+ t_1 (* (/ y z) (* x 9.0))) c)
       (/ (+ b (* 9.0 (* x y))) (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (t * a);
	double tmp;
	if (b <= -0.55) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= 5.2e+105) {
		tmp = (t_1 + ((y / z) * (x * 9.0))) / c;
	} else {
		tmp = (b + (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.
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) :: tmp
    t_1 = (-4.0d0) * (t * a)
    if (b <= (-0.55d0)) then
        tmp = (t_1 + (b / z)) / c
    else if (b <= 5.2d+105) then
        tmp = (t_1 + ((y / z) * (x * 9.0d0))) / c
    else
        tmp = (b + (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;
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 = -4.0 * (t * a);
	double tmp;
	if (b <= -0.55) {
		tmp = (t_1 + (b / z)) / c;
	} else if (b <= 5.2e+105) {
		tmp = (t_1 + ((y / z) * (x * 9.0))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (t * a)
	tmp = 0
	if b <= -0.55:
		tmp = (t_1 + (b / z)) / c
	elif b <= 5.2e+105:
		tmp = (t_1 + ((y / z) * (x * 9.0))) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t * a))
	tmp = 0.0
	if (b <= -0.55)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (b <= 5.2e+105)
		tmp = Float64(Float64(t_1 + Float64(Float64(y / z) * Float64(x * 9.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (t * a);
	tmp = 0.0;
	if (b <= -0.55)
		tmp = (t_1 + (b / z)) / c;
	elseif (b <= 5.2e+105)
		tmp = (t_1 + ((y / z) * (x * 9.0))) / c;
	else
		tmp = (b + (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.
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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.55], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 5.2e+105], N[(N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.55000000000000004

   1. Initial program 72.6%

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

   3. Simplified 80.1%

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

      1. *-un-lft-identity 80.1%

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

      2. *-commutative 80.1%

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

      3. times-frac 83.3%

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

      4. +-commutative 83.3%

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

   6. Applied egg-rr 83.3%

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

      1. associate-*l/ 83.4%

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

      2. *-un-lft-identity 83.4%

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

   8. Applied egg-rr 83.4%

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

   9. Taylor expanded in b around 0 81.7%

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

   10. Taylor expanded in x around 0 79.3%

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

   if -0.55000000000000004 < b < 5.2000000000000004e105

   1. Initial program 71.8%

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

   3. Simplified 75.5%

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

      1. *-un-lft-identity 75.5%

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

      2. *-commutative 75.5%

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

      3. times-frac 81.4%

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

      4. +-commutative 81.4%

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

   6. Applied egg-rr 81.4%

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

      1. associate-*l/ 81.4%

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

      2. *-un-lft-identity 81.4%

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

   8. Applied egg-rr 81.4%

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

   9. Taylor expanded in b around 0 85.6%

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

   10. Taylor expanded in x around inf 79.4%

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

       1. associate-*r/ 82.4%

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

       2. associate-*r* 82.4%

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

   12. Simplified 82.4%

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

   if 5.2000000000000004e105 < b

   1. Initial program 81.6%

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

      1. associate-+l- 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

      6. associate-*l* 84.1%

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

      7. associate-*l* 86.7%

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

      8. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x around inf 75.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.55:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{y}{z} \cdot \left(x \cdot 9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-38} \lor \neg \left(z \leq 8 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -8e-38) (not (<= z 8e+114)))
   (/ (+ (* -4.0 (* t a)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -8e-38) || !(z <= 8e+114)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c;
	} else {
		tmp = (b + (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.
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 <= (-8d-38)) .or. (.not. (z <= 8d+114))) then
        tmp = (((-4.0d0) * (t * a)) + (b / z)) / c
    else
        tmp = (b + (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;
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 <= -8e-38) || !(z <= 8e+114)) {
		tmp = ((-4.0 * (t * a)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -8e-38) or not (z <= 8e+114):
		tmp = ((-4.0 * (t * a)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -8e-38) || !(z <= 8e+114))
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -8e-38) || ~((z <= 8e+114)))
		tmp = ((-4.0 * (t * a)) + (b / z)) / c;
	else
		tmp = (b + (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.
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, -8e-38], N[Not[LessEqual[z, 8e+114]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999997e-38 or 8e114 < z

   1. Initial program 54.4%

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

   3. Simplified 65.7%

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

      1. *-un-lft-identity 65.7%

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

      2. *-commutative 65.7%

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

      3. times-frac 76.8%

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

      4. +-commutative 76.8%

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

   6. Applied egg-rr 76.8%

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

      1. associate-*l/ 76.9%

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

      2. *-un-lft-identity 76.9%

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

   8. Applied egg-rr 76.9%

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

   9. Taylor expanded in b around 0 83.9%

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

   10. Taylor expanded in x around 0 77.5%

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

   if -7.9999999999999997e-38 < z < 8e114

   1. Initial program 90.1%

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

      1. associate-+l- 90.1%

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

      2. *-commutative 90.1%

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

      3. associate-*r* 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-+l- 91.5%

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

      6. associate-*l* 91.5%

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

      7. associate-*l* 89.4%

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

      8. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around inf 76.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-38} \lor \neg \left(z \leq 8 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-37} \lor \neg \left(z \leq 1.3 \cdot 10^{+123}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -7.2e-37) (not (<= z 1.3e+123)))
   (* -4.0 (/ (* t a) c))
   (* 9.0 (* x (/ y (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -7.2e-37) || !(z <= 1.3e+123)) {
		tmp = -4.0 * ((t * a) / 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.
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 <= (-7.2d-37)) .or. (.not. (z <= 1.3d+123))) then
        tmp = (-4.0d0) * ((t * a) / 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;
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 <= -7.2e-37) || !(z <= 1.3e+123)) {
		tmp = -4.0 * ((t * a) / 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])
[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 <= -7.2e-37) or not (z <= 1.3e+123):
		tmp = -4.0 * ((t * a) / 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])
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 <= -7.2e-37) || !(z <= 1.3e+123))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -7.2e-37) || ~((z <= 1.3e+123)))
		tmp = -4.0 * ((t * a) / 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.
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, -7.2e-37], N[Not[LessEqual[z, 1.3e+123]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000014e-37 or 1.29999999999999993e123 < z

   1. Initial program 54.9%

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

      1. associate-+l- 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 57.3%

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

      4. *-commutative 57.3%

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

      5. associate-+l- 57.3%

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

      6. associate-*l* 57.3%

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

      7. associate-*l* 64.6%

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

      8. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in z around inf 60.3%

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

      1. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   if -7.20000000000000014e-37 < z < 1.29999999999999993e123

   1. Initial program 89.5%

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

      1. associate-+l- 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*r* 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-+l- 90.8%

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

      6. associate-*l* 90.8%

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

      7. associate-*l* 88.7%

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

      8. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 48.3%

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

      1. associate-/l* 52.4%

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

      2. *-commutative 52.4%

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

   7. Simplified 52.4%

      \[\leadsto \color{blue}{9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-37} \lor \neg \left(z \leq 1.3 \cdot 10^{+123}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -2.85e+35)
   (/ (/ b c) z)
   (if (<= b 4.4e+38) (* -4.0 (* a (/ t c))) (/ b (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 (b <= -2.85e+35) {
		tmp = (b / c) / z;
	} else if (b <= 4.4e+38) {
		tmp = -4.0 * (a * (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.
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 (b <= (-2.85d+35)) then
        tmp = (b / c) / z
    else if (b <= 4.4d+38) then
        tmp = (-4.0d0) * (a * (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;
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 (b <= -2.85e+35) {
		tmp = (b / c) / z;
	} else if (b <= 4.4e+38) {
		tmp = -4.0 * (a * (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])
[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 b <= -2.85e+35:
		tmp = (b / c) / z
	elif b <= 4.4e+38:
		tmp = -4.0 * (a * (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])
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 (b <= -2.85e+35)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 4.4e+38)
		tmp = Float64(-4.0 * Float64(a * Float64(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])){:}
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 (b <= -2.85e+35)
		tmp = (b / c) / z;
	elseif (b <= 4.4e+38)
		tmp = -4.0 * (a * (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.
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[b, -2.85e+35], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 4.4e+38], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.84999999999999997e35

   1. Initial program 71.8%

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

   3. Simplified 78.5%

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

      1. *-un-lft-identity 78.5%

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

      2. *-commutative 78.5%

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

      3. times-frac 81.9%

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

      4. +-commutative 81.9%

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

   6. Applied egg-rr 81.9%

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

      1. associate-*l/ 82.0%

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

      2. *-un-lft-identity 82.0%

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

   8. Applied egg-rr 82.0%

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

   9. Taylor expanded in b around inf 67.0%

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

       1. associate-/r* 67.1%

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

   11. Simplified 67.1%

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

   if -2.84999999999999997e35 < b < 4.40000000000000013e38

   1. Initial program 73.2%

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

   3. Simplified 77.2%

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

      1. *-un-lft-identity 77.2%

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

      2. *-commutative 77.2%

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

      3. times-frac 82.8%

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

      4. +-commutative 82.8%

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

   6. Applied egg-rr 82.8%

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

   7. Taylor expanded in z around inf 51.1%

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

      1. associate-/l* 51.1%

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

   9. Simplified 51.1%

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

   if 4.40000000000000013e38 < b

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

      6. associate-*l* 79.3%

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

      7. associate-*l* 81.2%

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

      8. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in b around inf 56.7%

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

      1. *-commutative 56.7%

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

   7. Simplified 56.7%

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

Alternative 12: 35.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 73.4%

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

   1. associate-+l- 73.4%

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

   2. *-commutative 73.4%

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

   3. associate-*r* 75.2%

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

   4. *-commutative 75.2%

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

   5. associate-+l- 75.2%

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

   6. associate-*l* 75.2%

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

   7. associate-*l* 77.5%

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

   8. *-commutative 77.5%

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

3. Simplified 77.5%

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

5. Taylor expanded in b around inf 35.8%

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

   1. *-commutative 35.8%

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

7. Simplified 35.8%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer target: 81.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024094 
(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)))