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

Percentage Accurate: 78.6% → 88.3%

Time: 13.4s

Alternatives: 16

Speedup: 0.8×

• 37.1% 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: 78.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \end{array} \]

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
 (if (<= z -8.5e-19)
   (fma (* (/ y (* c z)) 9.0) x (fma (* -4.0 (/ a c)) t (/ b (* c z))))
   (if (<= z 1.6e+102)
     (/ (+ (- (* (* 9.0 x) y) (* (* (* 4.0 z) t) a)) b) (* c z))
     (/ (fma (* (/ y z) 9.0) x (* (* a t) -4.0)) 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 <= -8.5e-19) {
		tmp = fma(((y / (c * z)) * 9.0), x, fma((-4.0 * (a / c)), t, (b / (c * z))));
	} else if (z <= 1.6e+102) {
		tmp = ((((9.0 * x) * y) - (((4.0 * z) * t) * a)) + b) / (c * z);
	} else {
		tmp = fma(((y / z) * 9.0), x, ((a * t) * -4.0)) / 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 <= -8.5e-19)
		tmp = fma(Float64(Float64(y / Float64(c * z)) * 9.0), x, fma(Float64(-4.0 * Float64(a / c)), t, Float64(b / Float64(c * z))));
	elseif (z <= 1.6e+102)
		tmp = Float64(Float64(Float64(Float64(Float64(9.0 * x) * y) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z));
	else
		tmp = Float64(fma(Float64(Float64(y / z) * 9.0), x, Float64(Float64(a * t) * -4.0)) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -8.5e-19], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x + N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] * t + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+102], N[(N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0), $MachinePrecision] * x + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000003e-19

   1. Initial program 67.9%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 88.6%

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

   if -8.50000000000000003e-19 < z < 1.6e102

   1. Initial program 93.8%

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

   if 1.6e102 < z

   1. Initial program 37.3%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 84.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{z}{b} \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \end{array} \end{array} \]

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) y)))
   (if (<= t_1 -1e+18)
     (* (* (/ y (* c z)) 9.0) x)
     (if (<= t_1 -5e-49)
       (/ (/ b c) z)
       (if (<= t_1 -5e-233)
         (* (* (/ a c) t) -4.0)
         (if (<= t_1 0.0)
           (/ 1.0 (* (/ z b) c))
           (if (<= t_1 2e+143)
             (* (* (/ t c) a) -4.0)
             (/ (* (* y x) 9.0) (* c z)))))))))

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) * y;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / ((z / b) * c);
	} else if (t_1 <= 2e+143) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = ((y * x) * 9.0) / (c * z);
	}
	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) * y
    if (t_1 <= (-1d+18)) then
        tmp = ((y / (c * z)) * 9.0d0) * x
    else if (t_1 <= (-5d-49)) then
        tmp = (b / c) / z
    else if (t_1 <= (-5d-233)) then
        tmp = ((a / c) * t) * (-4.0d0)
    else if (t_1 <= 0.0d0) then
        tmp = 1.0d0 / ((z / b) * c)
    else if (t_1 <= 2d+143) then
        tmp = ((t / c) * a) * (-4.0d0)
    else
        tmp = ((y * x) * 9.0d0) / (c * z)
    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) * y;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / ((z / b) * c);
	} else if (t_1 <= 2e+143) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = ((y * x) * 9.0) / (c * z);
	}
	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) * y
	tmp = 0
	if t_1 <= -1e+18:
		tmp = ((y / (c * z)) * 9.0) * x
	elif t_1 <= -5e-49:
		tmp = (b / c) / z
	elif t_1 <= -5e-233:
		tmp = ((a / c) * t) * -4.0
	elif t_1 <= 0.0:
		tmp = 1.0 / ((z / b) * c)
	elif t_1 <= 2e+143:
		tmp = ((t / c) * a) * -4.0
	else:
		tmp = ((y * x) * 9.0) / (c * z)
	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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = Float64(Float64(Float64(y / Float64(c * z)) * 9.0) * x);
	elseif (t_1 <= -5e-49)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_1 <= -5e-233)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(1.0 / Float64(Float64(z / b) * c));
	elseif (t_1 <= 2e+143)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	else
		tmp = Float64(Float64(Float64(y * x) * 9.0) / Float64(c * z));
	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) * y;
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = ((y / (c * z)) * 9.0) * x;
	elseif (t_1 <= -5e-49)
		tmp = (b / c) / z;
	elseif (t_1 <= -5e-233)
		tmp = ((a / c) * t) * -4.0;
	elseif (t_1 <= 0.0)
		tmp = 1.0 / ((z / b) * c);
	elseif (t_1 <= 2e+143)
		tmp = ((t / c) * a) * -4.0;
	else
		tmp = ((y * x) * 9.0) / (c * z);
	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[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, -5e-49], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -5e-233], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(1.0 / N[(N[(z / b), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+143], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e18

   1. Initial program 63.1%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 58.1

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

   5. Applied rewrites 58.1%

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

   7. Applied rewrites 56.4%

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

   if -1e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-49

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   7. Applied rewrites 66.7%

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

   if -4.9999999999999999e-49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 76.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 63.4

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

   8. Applied rewrites 63.4%

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

   10. Applied rewrites 66.1%

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

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 61.4

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

   8. Applied rewrites 61.4%

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

   10. Applied rewrites 62.5%

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

   if 0.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e143

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   8. Applied rewrites 55.5%

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

   10. Applied rewrites 55.5%

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

   if 2e143 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 72.9

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

   5. Applied rewrites 72.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 0:\\ \;\;\;\;\frac{1}{\frac{z}{b} \cdot c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \end{array} \end{array} \]

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) y)))
   (if (<= t_1 -1e+18)
     (* (* (/ y (* c z)) 9.0) x)
     (if (<= t_1 -5e-49)
       (/ (/ b c) z)
       (if (<= t_1 -5e-233)
         (* (* (/ a c) t) -4.0)
         (if (<= t_1 0.0)
           (/ (/ b z) c)
           (if (<= t_1 2e+143)
             (* (* (/ t c) a) -4.0)
             (/ (* (* y x) 9.0) (* c z)))))))))

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) * y;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+143) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = ((y * x) * 9.0) / (c * z);
	}
	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) * y
    if (t_1 <= (-1d+18)) then
        tmp = ((y / (c * z)) * 9.0d0) * x
    else if (t_1 <= (-5d-49)) then
        tmp = (b / c) / z
    else if (t_1 <= (-5d-233)) then
        tmp = ((a / c) * t) * (-4.0d0)
    else if (t_1 <= 0.0d0) then
        tmp = (b / z) / c
    else if (t_1 <= 2d+143) then
        tmp = ((t / c) * a) * (-4.0d0)
    else
        tmp = ((y * x) * 9.0d0) / (c * z)
    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) * y;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = ((y / (c * z)) * 9.0) * x;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+143) {
		tmp = ((t / c) * a) * -4.0;
	} else {
		tmp = ((y * x) * 9.0) / (c * z);
	}
	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) * y
	tmp = 0
	if t_1 <= -1e+18:
		tmp = ((y / (c * z)) * 9.0) * x
	elif t_1 <= -5e-49:
		tmp = (b / c) / z
	elif t_1 <= -5e-233:
		tmp = ((a / c) * t) * -4.0
	elif t_1 <= 0.0:
		tmp = (b / z) / c
	elif t_1 <= 2e+143:
		tmp = ((t / c) * a) * -4.0
	else:
		tmp = ((y * x) * 9.0) / (c * z)
	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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = Float64(Float64(Float64(y / Float64(c * z)) * 9.0) * x);
	elseif (t_1 <= -5e-49)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_1 <= -5e-233)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 2e+143)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	else
		tmp = Float64(Float64(Float64(y * x) * 9.0) / Float64(c * z));
	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) * y;
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = ((y / (c * z)) * 9.0) * x;
	elseif (t_1 <= -5e-49)
		tmp = (b / c) / z;
	elseif (t_1 <= -5e-233)
		tmp = ((a / c) * t) * -4.0;
	elseif (t_1 <= 0.0)
		tmp = (b / z) / c;
	elseif (t_1 <= 2e+143)
		tmp = ((t / c) * a) * -4.0;
	else
		tmp = ((y * x) * 9.0) / (c * z);
	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[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, -5e-49], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -5e-233], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+143], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e18

   1. Initial program 63.1%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 58.1

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

   5. Applied rewrites 58.1%

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

   7. Applied rewrites 56.4%

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

   if -1e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-49

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   7. Applied rewrites 66.7%

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

   if -4.9999999999999999e-49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 76.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 63.4

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

   8. Applied rewrites 63.4%

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

   10. Applied rewrites 66.1%

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

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 61.4

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

   8. Applied rewrites 61.4%

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

   if 0.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e143

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   8. Applied rewrites 55.5%

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

   10. Applied rewrites 55.5%

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

   if 2e143 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 72.9

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

   5. Applied rewrites 72.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 0:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot 9}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (* 9.0 x) y)) (t_2 (* (* (/ y (* c z)) 9.0) x)))
   (if (<= t_1 -1e+18)
     t_2
     (if (<= t_1 -5e-49)
       (/ (/ b c) z)
       (if (<= t_1 -5e-233)
         (* (* (/ a c) t) -4.0)
         (if (<= t_1 0.0)
           (/ (/ b z) c)
           (if (<= t_1 1e+143) (* (* (/ t c) a) -4.0) 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 = (9.0 * x) * y;
	double t_2 = ((y / (c * z)) * 9.0) * x;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = t_2;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = (b / z) / c;
	} else if (t_1 <= 1e+143) {
		tmp = ((t / c) * a) * -4.0;
	} 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 = (9.0d0 * x) * y
    t_2 = ((y / (c * z)) * 9.0d0) * x
    if (t_1 <= (-1d+18)) then
        tmp = t_2
    else if (t_1 <= (-5d-49)) then
        tmp = (b / c) / z
    else if (t_1 <= (-5d-233)) then
        tmp = ((a / c) * t) * (-4.0d0)
    else if (t_1 <= 0.0d0) then
        tmp = (b / z) / c
    else if (t_1 <= 1d+143) then
        tmp = ((t / c) * a) * (-4.0d0)
    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 = (9.0 * x) * y;
	double t_2 = ((y / (c * z)) * 9.0) * x;
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = t_2;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = (b / z) / c;
	} else if (t_1 <= 1e+143) {
		tmp = ((t / c) * a) * -4.0;
	} 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 = (9.0 * x) * y
	t_2 = ((y / (c * z)) * 9.0) * x
	tmp = 0
	if t_1 <= -1e+18:
		tmp = t_2
	elif t_1 <= -5e-49:
		tmp = (b / c) / z
	elif t_1 <= -5e-233:
		tmp = ((a / c) * t) * -4.0
	elif t_1 <= 0.0:
		tmp = (b / z) / c
	elif t_1 <= 1e+143:
		tmp = ((t / c) * a) * -4.0
	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(9.0 * x) * y)
	t_2 = Float64(Float64(Float64(y / Float64(c * z)) * 9.0) * x)
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = t_2;
	elseif (t_1 <= -5e-49)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_1 <= -5e-233)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 1e+143)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	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 = (9.0 * x) * y;
	t_2 = ((y / (c * z)) * 9.0) * x;
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = t_2;
	elseif (t_1 <= -5e-49)
		tmp = (b / c) / z;
	elseif (t_1 <= -5e-233)
		tmp = ((a / c) * t) * -4.0;
	elseif (t_1 <= 0.0)
		tmp = (b / z) / c;
	elseif (t_1 <= 1e+143)
		tmp = ((t / c) * a) * -4.0;
	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[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], t$95$2, If[LessEqual[t$95$1, -5e-49], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -5e-233], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+143], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e18 or 1e143 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 61.8

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

   5. Applied rewrites 61.8%

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

   7. Applied rewrites 63.9%

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

   if -1e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-49

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   7. Applied rewrites 66.7%

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

   if -4.9999999999999999e-49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 76.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 63.4

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

   8. Applied rewrites 63.4%

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

   10. Applied rewrites 66.1%

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

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 61.4

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

   8. Applied rewrites 61.4%

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

   if 0.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e143

   1. Initial program 81.8%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.9

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

   8. Applied rewrites 54.9%

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

   10. Applied rewrites 54.9%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 0:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{c \cdot z} \cdot 9\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \frac{x}{c \cdot z} \cdot \left(y \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (* 9.0 x) y)) (t_2 (* (/ x (* c z)) (* y 9.0))))
   (if (<= t_1 -1e+18)
     t_2
     (if (<= t_1 -5e-49)
       (/ (/ b c) z)
       (if (<= t_1 -5e-233)
         (* (* (/ a c) t) -4.0)
         (if (<= t_1 0.0)
           (/ (/ b z) c)
           (if (<= t_1 2e+143) (* (* (/ t c) a) -4.0) 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 = (9.0 * x) * y;
	double t_2 = (x / (c * z)) * (y * 9.0);
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = t_2;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+143) {
		tmp = ((t / c) * a) * -4.0;
	} 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 = (9.0d0 * x) * y
    t_2 = (x / (c * z)) * (y * 9.0d0)
    if (t_1 <= (-1d+18)) then
        tmp = t_2
    else if (t_1 <= (-5d-49)) then
        tmp = (b / c) / z
    else if (t_1 <= (-5d-233)) then
        tmp = ((a / c) * t) * (-4.0d0)
    else if (t_1 <= 0.0d0) then
        tmp = (b / z) / c
    else if (t_1 <= 2d+143) then
        tmp = ((t / c) * a) * (-4.0d0)
    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 = (9.0 * x) * y;
	double t_2 = (x / (c * z)) * (y * 9.0);
	double tmp;
	if (t_1 <= -1e+18) {
		tmp = t_2;
	} else if (t_1 <= -5e-49) {
		tmp = (b / c) / z;
	} else if (t_1 <= -5e-233) {
		tmp = ((a / c) * t) * -4.0;
	} else if (t_1 <= 0.0) {
		tmp = (b / z) / c;
	} else if (t_1 <= 2e+143) {
		tmp = ((t / c) * a) * -4.0;
	} 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 = (9.0 * x) * y
	t_2 = (x / (c * z)) * (y * 9.0)
	tmp = 0
	if t_1 <= -1e+18:
		tmp = t_2
	elif t_1 <= -5e-49:
		tmp = (b / c) / z
	elif t_1 <= -5e-233:
		tmp = ((a / c) * t) * -4.0
	elif t_1 <= 0.0:
		tmp = (b / z) / c
	elif t_1 <= 2e+143:
		tmp = ((t / c) * a) * -4.0
	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(9.0 * x) * y)
	t_2 = Float64(Float64(x / Float64(c * z)) * Float64(y * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+18)
		tmp = t_2;
	elseif (t_1 <= -5e-49)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_1 <= -5e-233)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (t_1 <= 2e+143)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	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 = (9.0 * x) * y;
	t_2 = (x / (c * z)) * (y * 9.0);
	tmp = 0.0;
	if (t_1 <= -1e+18)
		tmp = t_2;
	elseif (t_1 <= -5e-49)
		tmp = (b / c) / z;
	elseif (t_1 <= -5e-233)
		tmp = ((a / c) * t) * -4.0;
	elseif (t_1 <= 0.0)
		tmp = (b / z) / c;
	elseif (t_1 <= 2e+143)
		tmp = ((t / c) * a) * -4.0;
	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[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(c * z), $MachinePrecision]), $MachinePrecision] * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+18], t$95$2, If[LessEqual[t$95$1, -5e-49], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -5e-233], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+143], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e18 or 2e143 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 62.5

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

   5. Applied rewrites 62.5%

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

   7. Applied rewrites 62.5%

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

   9. Applied rewrites 61.2%

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

   if -1e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999999e-49

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   7. Applied rewrites 66.7%

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

   if -4.9999999999999999e-49 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000012e-233

   1. Initial program 76.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 63.4

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

   8. Applied rewrites 63.4%

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

   10. Applied rewrites 66.1%

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

   if -5.00000000000000012e-233 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0

   1. Initial program 86.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 61.4

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

   8. Applied rewrites 61.4%

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

   if 0.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2e143

   1. Initial program 82.1%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 55.5

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

   8. Applied rewrites 55.5%

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

   10. Applied rewrites 55.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{c \cdot z} \cdot \left(y \cdot 9\right)\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-233}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 0:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 2 \cdot 10^{+143}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{c \cdot z} \cdot \left(y \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-53}:\\ \;\;\;\;\frac{t\_2}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t\_2}{c}}{z}\\ \end{array} \end{array} \]

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) y)) (t_2 (fma (* y x) 9.0 b)))
   (if (<= t_1 -5e+305)
     (* (/ x z) (/ (* y 9.0) c))
     (if (<= t_1 -5e-53)
       (/ t_2 (* c z))
       (if (<= t_1 0.0)
         (/ (/ (fma (* (* a t) -4.0) z b) z) c)
         (if (<= t_1 1e+142)
           (fma (* -4.0 (/ a c)) t (/ b (* c z)))
           (/ (/ t_2 c) z)))))))

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) * y;
	double t_2 = fma((y * x), 9.0, b);
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = (x / z) * ((y * 9.0) / c);
	} else if (t_1 <= -5e-53) {
		tmp = t_2 / (c * z);
	} else if (t_1 <= 0.0) {
		tmp = (fma(((a * t) * -4.0), z, b) / z) / c;
	} else if (t_1 <= 1e+142) {
		tmp = fma((-4.0 * (a / c)), t, (b / (c * z)));
	} else {
		tmp = (t_2 / c) / z;
	}
	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(9.0 * x) * y)
	t_2 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (t_1 <= -5e+305)
		tmp = Float64(Float64(x / z) * Float64(Float64(y * 9.0) / c));
	elseif (t_1 <= -5e-53)
		tmp = Float64(t_2 / Float64(c * z));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / z) / c);
	elseif (t_1 <= 1e+142)
		tmp = fma(Float64(-4.0 * Float64(a / c)), t, Float64(b / Float64(c * z)));
	else
		tmp = Float64(Float64(t_2 / c) / z);
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+305], N[(N[(x / z), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-53], N[(t$95$2 / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+142], N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] * t + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000009e305

   1. Initial program 40.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.7%

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

   if -5.00000000000000009e305 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e-53

   1. Initial program 75.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -5e-53 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 0.0

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if 0.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000005e142

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 54.3

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

   8. Applied rewrites 54.3%

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

   9. Taylor expanded in x around inf

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

       1. cancel-sign-sub-inv N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

   11. Applied rewrites 67.5%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 79.2%

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

   if 1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.2%

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

   3. Taylor expanded in a around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 0:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(a \cdot t\right) \cdot -4\\ t_2 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(t\_1, z, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, t\_1\right)}{c}\\ \end{array} \end{array} \]

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 (* (* a t) -4.0)) (t_2 (* (* 9.0 x) y)))
   (if (<= t_2 -5e+305)
     (* (/ x z) (/ (* y 9.0) c))
     (if (<= t_2 -5e-53)
       (/ (fma (* y x) 9.0 b) (* c z))
       (if (<= t_2 5e-31)
         (/ (/ (fma t_1 z b) z) c)
         (/ (fma (* (/ y z) 9.0) x t_1) 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 = (a * t) * -4.0;
	double t_2 = (9.0 * x) * y;
	double tmp;
	if (t_2 <= -5e+305) {
		tmp = (x / z) * ((y * 9.0) / c);
	} else if (t_2 <= -5e-53) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else if (t_2 <= 5e-31) {
		tmp = (fma(t_1, z, b) / z) / c;
	} else {
		tmp = fma(((y / z) * 9.0), x, t_1) / 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(Float64(a * t) * -4.0)
	t_2 = Float64(Float64(9.0 * x) * y)
	tmp = 0.0
	if (t_2 <= -5e+305)
		tmp = Float64(Float64(x / z) * Float64(Float64(y * 9.0) / c));
	elseif (t_2 <= -5e-53)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	elseif (t_2 <= 5e-31)
		tmp = Float64(Float64(fma(t_1, z, b) / z) / c);
	else
		tmp = Float64(fma(Float64(Float64(y / z) * 9.0), x, t_1) / 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[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+305], N[(N[(x / z), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-53], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-31], N[(N[(N[(t$95$1 * z + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0), $MachinePrecision] * x + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000009e305

   1. Initial program 40.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.7%

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

   if -5.00000000000000009e305 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e-53

   1. Initial program 75.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -5e-53 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e-31

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 87.3

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

   5. Applied rewrites 87.3%

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

   if 5e-31 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 81.7%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 83.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 5 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{-19}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{c \cdot z}\\ \end{array} \end{array} \]

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) y)))
   (if (<= t_1 -5e+305)
     (* (/ x z) (/ (* y 9.0) c))
     (if (<= t_1 -5e-53)
       (/ (fma (* y x) 9.0 b) (* c z))
       (if (<= t_1 1e-19)
         (/ (/ (fma (* (* a t) -4.0) z b) z) c)
         (/ (fma -4.0 (* (* t z) a) (* (* y x) 9.0)) (* c z)))))))

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) * y;
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = (x / z) * ((y * 9.0) / c);
	} else if (t_1 <= -5e-53) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else if (t_1 <= 1e-19) {
		tmp = (fma(((a * t) * -4.0), z, b) / z) / c;
	} else {
		tmp = fma(-4.0, ((t * z) * a), ((y * x) * 9.0)) / (c * z);
	}
	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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -5e+305)
		tmp = Float64(Float64(x / z) * Float64(Float64(y * 9.0) / c));
	elseif (t_1 <= -5e-53)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	elseif (t_1 <= 1e-19)
		tmp = Float64(Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / z) / c);
	else
		tmp = Float64(fma(-4.0, Float64(Float64(t * z) * a), Float64(Float64(y * x) * 9.0)) / Float64(c * z));
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+305], N[(N[(x / z), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-53], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-19], N[(N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(-4.0 * N[(N[(t * z), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000009e305

   1. Initial program 40.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.7%

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

   if -5.00000000000000009e305 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e-53

   1. Initial program 75.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 72.5

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

   5. Applied rewrites 72.5%

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

   if -5e-53 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999998e-20

   1. Initial program 80.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 86.6

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

   5. Applied rewrites 86.6%

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

   if 9.9999999999999998e-20 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 82.7%

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

   3. Taylor expanded in b around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 75.6

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

   5. Applied rewrites 75.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{-53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{-19}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, \left(t \cdot z\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;\frac{t\_2}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t\_2}{c}}{z}\\ \end{array} \end{array} \]

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) y)) (t_2 (fma (* y x) 9.0 b)))
   (if (<= t_1 -5e+305)
     (* (/ x z) (/ (* y 9.0) c))
     (if (<= t_1 -5e+71)
       (/ t_2 (* c z))
       (if (<= t_1 1e+142)
         (fma (* -4.0 (/ a c)) t (/ b (* c z)))
         (/ (/ t_2 c) z))))))

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) * y;
	double t_2 = fma((y * x), 9.0, b);
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = (x / z) * ((y * 9.0) / c);
	} else if (t_1 <= -5e+71) {
		tmp = t_2 / (c * z);
	} else if (t_1 <= 1e+142) {
		tmp = fma((-4.0 * (a / c)), t, (b / (c * z)));
	} else {
		tmp = (t_2 / c) / z;
	}
	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(9.0 * x) * y)
	t_2 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (t_1 <= -5e+305)
		tmp = Float64(Float64(x / z) * Float64(Float64(y * 9.0) / c));
	elseif (t_1 <= -5e+71)
		tmp = Float64(t_2 / Float64(c * z));
	elseif (t_1 <= 1e+142)
		tmp = fma(Float64(-4.0 * Float64(a / c)), t, Float64(b / Float64(c * z)));
	else
		tmp = Float64(Float64(t_2 / c) / z);
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+305], N[(N[(x / z), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+71], N[(t$95$2 / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+142], N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] * t + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000009e305

   1. Initial program 40.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.7%

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

   if -5.00000000000000009e305 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999972e71

   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. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if -4.99999999999999972e71 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000005e142

   1. Initial program 81.3%

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

   3. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate-*l/ N/A

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

      16. associate-*l* N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 48.9

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

   8. Applied rewrites 48.9%

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

   9. Taylor expanded in x around inf

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

       1. cancel-sign-sub-inv N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

   11. Applied rewrites 58.5%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 78.5%

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

   if 1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.2%

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

   3. Taylor expanded in a around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+71}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ t_2 := \mathsf{fma}\left(y \cdot x, 9, b\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{t\_2}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{+142}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t\_2}{c}}{z}\\ \end{array} \end{array} \]

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) y)) (t_2 (fma (* y x) 9.0 b)))
   (if (<= t_1 -5e+305)
     (* (/ x z) (/ (* y 9.0) c))
     (if (<= t_1 -2e+18)
       (/ t_2 (* c z))
       (if (<= t_1 1e+142)
         (/ (fma (* (* a t) -4.0) z b) (* c z))
         (/ (/ t_2 c) z))))))

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) * y;
	double t_2 = fma((y * x), 9.0, b);
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = (x / z) * ((y * 9.0) / c);
	} else if (t_1 <= -2e+18) {
		tmp = t_2 / (c * z);
	} else if (t_1 <= 1e+142) {
		tmp = fma(((a * t) * -4.0), z, b) / (c * z);
	} else {
		tmp = (t_2 / c) / z;
	}
	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(9.0 * x) * y)
	t_2 = fma(Float64(y * x), 9.0, b)
	tmp = 0.0
	if (t_1 <= -5e+305)
		tmp = Float64(Float64(x / z) * Float64(Float64(y * 9.0) / c));
	elseif (t_1 <= -2e+18)
		tmp = Float64(t_2 / Float64(c * z));
	elseif (t_1 <= 1e+142)
		tmp = Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / Float64(c * z));
	else
		tmp = Float64(Float64(t_2 / c) / z);
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+305], N[(N[(x / z), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+18], N[(t$95$2 / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+142], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000009e305

   1. Initial program 40.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.7%

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

   if -5.00000000000000009e305 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18

   1. Initial program 74.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000005e142

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if 1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.2%

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

   3. Taylor expanded in a around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+142}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \left(9 \cdot x\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;t\_1 \leq 10^{+142}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{z}\\ \end{array} \end{array} \]

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) y)))
   (if (<= t_1 -5e+305)
     (* (/ x z) (/ (* y 9.0) c))
     (if (<= t_1 -2e+18)
       (/ (fma (* y x) 9.0 b) (* c z))
       (if (<= t_1 1e+142)
         (/ (fma (* (* a t) -4.0) z b) (* c z))
         (/ (* (* (/ y c) 9.0) x) z))))))

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) * y;
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = (x / z) * ((y * 9.0) / c);
	} else if (t_1 <= -2e+18) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else if (t_1 <= 1e+142) {
		tmp = fma(((a * t) * -4.0), z, b) / (c * z);
	} else {
		tmp = (((y / c) * 9.0) * x) / z;
	}
	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(9.0 * x) * y)
	tmp = 0.0
	if (t_1 <= -5e+305)
		tmp = Float64(Float64(x / z) * Float64(Float64(y * 9.0) / c));
	elseif (t_1 <= -2e+18)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	elseif (t_1 <= 1e+142)
		tmp = Float64(fma(Float64(Float64(a * t) * -4.0), z, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(Float64(y / c) * 9.0) * x) / z);
	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[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+305], N[(N[(x / z), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+18], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+142], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] * z + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y / c), $MachinePrecision] * 9.0), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5.00000000000000009e305

   1. Initial program 40.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. times-frac N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.7%

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

   if -5.00000000000000009e305 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e18

   1. Initial program 74.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 74.4

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

   5. Applied rewrites 74.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if -2e18 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000005e142

   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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]

      2. metadata-eval N/A

         \[\leadsto \frac{b + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z \cdot c} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b}}{z \cdot c} \]

      4. associate-*r* N/A

         \[\leadsto \frac{-4 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot z\right)} + b}{z \cdot c} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right) \cdot z} + b}{z \cdot c} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4 \cdot \left(a \cdot t\right), z, b\right)}}{z \cdot c} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{-4 \cdot \left(a \cdot t\right)}, z, b\right)}{z \cdot c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot \color{blue}{\left(t \cdot a\right)}, z, b\right)}{z \cdot c} \]

      9. lower-*.f64 76.2

         \[\leadsto \frac{\mathsf{fma}\left(-4 \cdot \color{blue}{\left(t \cdot a\right)}, z, b\right)}{z \cdot c} \]

   5. Applied rewrites 76.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-4 \cdot \left(t \cdot a\right), z, b\right)}}{z \cdot c} \]

   if 1.00000000000000005e142 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 77.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c} \cdot \frac{x}{z}} \]

      6. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot 9}}{c} \cdot \frac{x}{z} \]

      7. associate-*l/ N/A

         \[\leadsto \color{blue}{\left(\frac{y}{c} \cdot 9\right)} \cdot \frac{x}{z} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{y}{c} \cdot 9\right)} \cdot \frac{x}{z} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(\color{blue}{\frac{y}{c}} \cdot 9\right) \cdot \frac{x}{z} \]

      10. lower-/.f64 66.0

          \[\leadsto \left(\frac{y}{c} \cdot 9\right) \cdot \color{blue}{\frac{x}{z}} \]

   5. Applied rewrites 66.0%

      \[\leadsto \color{blue}{\left(\frac{y}{c} \cdot 9\right) \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.7%

      \[\leadsto \frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{\color{blue}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot x\right) \cdot y \leq -5 \cdot 10^{+305}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot 9}{c}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq -2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{elif}\;\left(9 \cdot x\right) \cdot y \leq 10^{+142}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a \cdot t\right) \cdot -4, z, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\frac{y}{c} \cdot 9\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{\frac{b}{z}}{c}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \end{array} \]

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
 (if (<= z -7.5e+144)
   (fma (* -4.0 (/ a c)) t (/ (/ b z) c))
   (if (<= z 1.6e+102)
     (/ (+ (- (* (* 9.0 x) y) (* (* (* 4.0 z) t) a)) b) (* c z))
     (/ (fma (* (/ y z) 9.0) x (* (* a t) -4.0)) 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 <= -7.5e+144) {
		tmp = fma((-4.0 * (a / c)), t, ((b / z) / c));
	} else if (z <= 1.6e+102) {
		tmp = ((((9.0 * x) * y) - (((4.0 * z) * t) * a)) + b) / (c * z);
	} else {
		tmp = fma(((y / z) * 9.0), x, ((a * t) * -4.0)) / 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 <= -7.5e+144)
		tmp = fma(Float64(-4.0 * Float64(a / c)), t, Float64(Float64(b / z) / c));
	elseif (z <= 1.6e+102)
		tmp = Float64(Float64(Float64(Float64(Float64(9.0 * x) * y) - Float64(Float64(Float64(4.0 * z) * t) * a)) + b) / Float64(c * z));
	else
		tmp = Float64(fma(Float64(Float64(y / z) * 9.0), x, Float64(Float64(a * t) * -4.0)) / c);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.5e+144], N[(N[(-4.0 * N[(a / c), $MachinePrecision]), $MachinePrecision] * t + N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+102], N[(N[(N[(N[(N[(9.0 * x), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(4.0 * z), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * 9.0), $MachinePrecision] * x + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000006e144

   1. Initial program 54.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      5. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c \cdot z} \cdot x} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \cdot x + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(9 \cdot \frac{y}{c \cdot z}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z} \cdot 9}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z} \cdot 9}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\frac{b}{c \cdot z} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \frac{b}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      15. associate-*l/ N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} + \frac{b}{c \cdot z}\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\left(-4 \cdot \frac{a}{c}\right) \cdot t} + \frac{b}{c \cdot z}\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)}\right) \]

   5. Applied rewrites 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto -4 \cdot \frac{a \cdot t}{c} + \color{blue}{\frac{b}{c \cdot z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 82.9%

      \[\leadsto \mathsf{fma}\left(\frac{a}{c} \cdot -4, \color{blue}{t}, \frac{\frac{b}{z}}{c}\right) \]

   if -7.5000000000000006e144 < z < 1.6e102

   1. Initial program 90.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   if 1.6e102 < z

   1. Initial program 37.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}}{c} \]

      4. cancel-sign-sub-inv N/A

         \[\leadsto \frac{\frac{\color{blue}{9 \cdot \left(x \cdot y\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z}}{c} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\frac{9 \cdot \left(x \cdot y\right) + \color{blue}{-4} \cdot \left(a \cdot \left(t \cdot z\right)\right)}{z}}{c} \]

      6. +-commutative N/A

         \[\leadsto \frac{\frac{\color{blue}{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + 9 \cdot \left(x \cdot y\right)}}{z}}{c} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-4, a \cdot \left(t \cdot z\right), 9 \cdot \left(x \cdot y\right)\right)}}{z}}{c} \]

      8. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(t \cdot z\right) \cdot a}, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      11. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \color{blue}{\left(z \cdot t\right)} \cdot a, 9 \cdot \left(x \cdot y\right)\right)}{z}}{c} \]

      12. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(x \cdot y\right) \cdot 9}\right)}{z}}{c} \]

      14. *-commutative N/A

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

      15. lower-*.f64 47.7

          \[\leadsto \frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \color{blue}{\left(y \cdot x\right)} \cdot 9\right)}{z}}{c} \]

   5. Applied rewrites 47.7%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(-4, \left(z \cdot t\right) \cdot a, \left(y \cdot x\right) \cdot 9\right)}{z}}{c}} \]

   6. Taylor expanded in a around 0

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c} \]
   7. Step-by-step derivation

   8. Applied rewrites 84.3%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, \left(t \cdot a\right) \cdot -4\right)}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{\frac{b}{z}}{c}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;\frac{\left(\left(9 \cdot x\right) \cdot y - \left(\left(4 \cdot z\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{y}{z} \cdot 9, x, \left(a \cdot t\right) \cdot -4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+126}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \end{array} \]

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 (<= z -3.9e+126)
   (* (* (/ a c) t) -4.0)
   (if (<= z 6.5e-48) (/ (fma (* y x) 9.0 b) (* c z)) (* (/ (* a t) c) -4.0))))

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 <= -3.9e+126) {
		tmp = ((a / c) * t) * -4.0;
	} else if (z <= 6.5e-48) {
		tmp = fma((y * x), 9.0, b) / (c * z);
	} else {
		tmp = ((a * t) / c) * -4.0;
	}
	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 <= -3.9e+126)
		tmp = Float64(Float64(Float64(a / c) * t) * -4.0);
	elseif (z <= 6.5e-48)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	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_] := If[LessEqual[z, -3.9e+126], N[(N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 6.5e-48], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.89999999999999993e126

   1. Initial program 58.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      5. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c \cdot z} \cdot x} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \cdot x + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(9 \cdot \frac{y}{c \cdot z}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z} \cdot 9}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z} \cdot 9}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\frac{b}{c \cdot z} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \frac{b}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      15. associate-*l/ N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} + \frac{b}{c \cdot z}\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\left(-4 \cdot \frac{a}{c}\right) \cdot t} + \frac{b}{c \cdot z}\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)}\right) \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 66.7

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   8. Applied rewrites 66.7%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   9. Step-by-step derivation

   10. Applied rewrites 66.8%

       \[\leadsto \left(\frac{a}{c} \cdot t\right) \cdot -4 \]

   if -3.89999999999999993e126 < z < 6.5e-48

   1. Initial program 90.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right) + b}}{z \cdot c} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot y\right) \cdot 9} + b}{z \cdot c} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x \cdot y, 9, b\right)}}{z \cdot c} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

      5. lower-*.f64 74.6

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{y \cdot x}, 9, b\right)}{z \cdot c} \]

   5. Applied rewrites 74.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y \cdot x, 9, b\right)}}{z \cdot c} \]

   if 6.5e-48 < z

   1. Initial program 58.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      4. lower-*.f64 65.6

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

   5. Applied rewrites 65.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{t \cdot a}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+126}:\\ \;\;\;\;\left(\frac{a}{c} \cdot t\right) \cdot -4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-63}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \end{array} \]

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 (<= z -1.26e-63)
   (* (* (/ t c) a) -4.0)
   (if (<= z 1.15e-88) (/ b (* c z)) (* (/ (* a t) c) -4.0))))

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 <= -1.26e-63) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= 1.15e-88) {
		tmp = b / (c * z);
	} else {
		tmp = ((a * t) / c) * -4.0;
	}
	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 <= (-1.26d-63)) then
        tmp = ((t / c) * a) * (-4.0d0)
    else if (z <= 1.15d-88) then
        tmp = b / (c * z)
    else
        tmp = ((a * t) / c) * (-4.0d0)
    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 <= -1.26e-63) {
		tmp = ((t / c) * a) * -4.0;
	} else if (z <= 1.15e-88) {
		tmp = b / (c * z);
	} else {
		tmp = ((a * t) / c) * -4.0;
	}
	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 <= -1.26e-63:
		tmp = ((t / c) * a) * -4.0
	elif z <= 1.15e-88:
		tmp = b / (c * z)
	else:
		tmp = ((a * t) / c) * -4.0
	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 <= -1.26e-63)
		tmp = Float64(Float64(Float64(t / c) * a) * -4.0);
	elseif (z <= 1.15e-88)
		tmp = Float64(b / Float64(c * z));
	else
		tmp = Float64(Float64(Float64(a * t) / c) * -4.0);
	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 <= -1.26e-63)
		tmp = ((t / c) * a) * -4.0;
	elseif (z <= 1.15e-88)
		tmp = b / (c * z);
	else
		tmp = ((a * t) / c) * -4.0;
	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[z, -1.26e-63], N[(N[(N[(t / c), $MachinePrecision] * a), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[z, 1.15e-88], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.26e-63

   1. Initial program 69.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      3. *-commutative N/A

         \[\leadsto \frac{9 \cdot \color{blue}{\left(y \cdot x\right)}}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      4. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{c \cdot z} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      5. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{9 \cdot y}{c \cdot z} \cdot x} + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(9 \cdot \frac{y}{c \cdot z}\right)} \cdot x + \left(\frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(9 \cdot \frac{y}{c \cdot z}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z} \cdot 9}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z} \cdot 9}, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9, x, \frac{b}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]

      12. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\frac{b}{c \cdot z} + \left(\mathsf{neg}\left(4\right)\right) \cdot \frac{a \cdot t}{c}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \frac{b}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{-4 \cdot \frac{a \cdot t}{c} + \frac{b}{c \cdot z}}\right) \]

      15. associate-*l/ N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} + \frac{b}{c \cdot z}\right) \]

      16. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\left(-4 \cdot \frac{a}{c}\right) \cdot t} + \frac{b}{c \cdot z}\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \color{blue}{\mathsf{fma}\left(-4 \cdot \frac{a}{c}, t, \frac{b}{c \cdot z}\right)}\right) \]

   5. Applied rewrites 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{c \cdot z} \cdot 9, x, \mathsf{fma}\left(\frac{a}{c} \cdot -4, t, \frac{b}{c \cdot z}\right)\right)} \]

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t}{c}} \cdot -4 \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

      5. lower-*.f64 48.3

         \[\leadsto \frac{\color{blue}{t \cdot a}}{c} \cdot -4 \]

   8. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\frac{t \cdot a}{c} \cdot -4} \]
   9. Step-by-step derivation

   10. Applied rewrites 52.4%

       \[\leadsto \left(a \cdot \frac{t}{c}\right) \cdot -4 \]

   if -1.26e-63 < z < 1.14999999999999993e-88

   1. Initial program 95.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 53.0

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   if 1.14999999999999993e-88 < z

   1. Initial program 61.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      4. lower-*.f64 61.6

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

   5. Applied rewrites 61.6%

      \[\leadsto \color{blue}{-4 \cdot \frac{t \cdot a}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-63}:\\ \;\;\;\;\left(\frac{t}{c} \cdot a\right) \cdot -4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{a \cdot t}{c} \cdot -4\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (/ (* a t) c) -4.0)))
   (if (<= z -2.1e-17) t_1 (if (<= z 1.15e-88) (/ b (* c z)) 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 = ((a * t) / c) * -4.0;
	double tmp;
	if (z <= -2.1e-17) {
		tmp = t_1;
	} else if (z <= 1.15e-88) {
		tmp = b / (c * z);
	} 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 = ((a * t) / c) * (-4.0d0)
    if (z <= (-2.1d-17)) then
        tmp = t_1
    else if (z <= 1.15d-88) then
        tmp = b / (c * z)
    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 = ((a * t) / c) * -4.0;
	double tmp;
	if (z <= -2.1e-17) {
		tmp = t_1;
	} else if (z <= 1.15e-88) {
		tmp = b / (c * z);
	} 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 = ((a * t) / c) * -4.0
	tmp = 0
	if z <= -2.1e-17:
		tmp = t_1
	elif z <= 1.15e-88:
		tmp = b / (c * z)
	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(Float64(Float64(a * t) / c) * -4.0)
	tmp = 0.0
	if (z <= -2.1e-17)
		tmp = t_1;
	elseif (z <= 1.15e-88)
		tmp = Float64(b / Float64(c * z));
	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 = ((a * t) / c) * -4.0;
	tmp = 0.0;
	if (z <= -2.1e-17)
		tmp = t_1;
	elseif (z <= 1.15e-88)
		tmp = b / (c * z);
	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[(N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -2.1e-17], t$95$1, If[LessEqual[z, 1.15e-88], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999992e-17 or 1.14999999999999993e-88 < z

   1. Initial program 64.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

      2. lower-/.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} \]

      3. *-commutative N/A

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      4. lower-*.f64 56.9

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

   5. Applied rewrites 56.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{t \cdot a}{c}} \]

   if -2.09999999999999992e-17 < z < 1.14999999999999993e-88

   1. Initial program 93.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      2. lower-*.f64 50.2

         \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot t}{c} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{c \cdot z} \end{array} \]

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 (* c z)))

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 / (c * z);
}

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 / (c * z)
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 / (c * z);
}

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 / (c * z)

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(c * z))
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 / (c * z);
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[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

   2. lower-*.f64 33.3

      \[\leadsto \frac{b}{\color{blue}{c \cdot z}} \]

5. Applied rewrites 33.3%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024257 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))